It is a very nice and very very hard question because it depends on many social parameters mainly unrelated to mathematics.
I am founder of a logic group in our university. It is two years old now and we are extensively under development in both scientific and administrative aspects. We are somehow famous now and some other universities are following a same pattern. Let me to explain more about some parameters which I guess could be useful for you.
1. I have a dream.
First note that you are building a new society in an old society so you should have something new to say. Thus you need an exact plan including all of your goals in short and long time and all possible ways which can help your group to reach them. Determining all of the scientific and non-scientific purposes, designing the structure of your organization and also defining possible opportunities which the group can provide for its members are the main duties of your "president" at the first step. These parameters are so important and you should pay enough attention to design them. Write them all exactly in a "constitution" and ask people to read it before joining your group. This document will be your first tool for defining a new abstract identity like a math group "independent" from its members. The best example is a football club. In fact any football club is just a production of its members including players, coaches, managers, fans, etc. but it has an "independent" identity from its members too. At first a football club is just a name and it is the founders who are its real identity but after a while when all of its founders are retired, the club itself is still operational and can give a new identity to its members and managers.
2. A beautiful name, a beautiful mind!
In order to emphasize on the identity of your math group choose an adequate name, design a pretty logo and find an impressive motto. These simple parameters are very important because they are the first "representatives" of your group everywhere. You should choose them carefully and use these everywhere in your website, documents, colloquiums, mails, posters, etc. Use the advisement of professionals to choose the best. Being too informal in these cases is not recommended because maybe you will participate in official communications with the other mathematical groups in/out of your university and it is better to be formal in these communications. In comparison with managing a country your constitution is your "law", your logo is your "national flag" and your motto is your "national anthem".
3. Build internal and external networks.
By an external network I mean communicating with the other similar scientific/math groups. This helps your group to remain up to date. It also helps the others to be familiar with your activities and this encourages your members to be more active.
By an internal network I mean something like a forum/website just for your members and a very regular announcement system with a particular organizer (a public communication manager) which announces the last news of the group to all members. This helps the members to remain connected with the group even if they are graduated and far from the university for years.
4. Regular Events.
The scientific activities of the group should be very regular. Define different levels of activities in each year and separate the audiences for each part. There are two main levels of activities.
Minor Events: As like as weekly seminars/colloquiums and study/research programs.
Organize such events per week/month/semester. In this case the audiences are "local" including your members, department faculties, university students, etc.
Major Events: As like as organizing national/international conferences.
Organize such events per year/two years.In this case, the audiences are "global" including people from other universities all around of the country/world.
The "regularity" is too important. People should count on your activities as a habit. Also these regular colloquiums will help your members to take the identity of the group more serious. This point of view remains alive even if a part of your members be graduated.
5. Teachers as Members.
Invite your teachers/supervisors to be a member of your group. They can help you scientifically and supervise activities with a better view. Also you can offer a president position to one of them (in your case maybe one of the female faculty members of your department) which helps the group to keep its organization safe from graduating its student members because the faculty members are in the university for a longer time.
6. Remain Neutral to be Popular!
Regarding to your comment on a math group for women, I think your idea for helping women to become researchers in mathematics is very interesting and surely reasonable but I am not sure that organizing a math group just for women is useful in this direction. I think there are better ways for reaching this goal. In principal I believe that if we define a x-group (here x=math) this community should be neutral in any other aspect y different from x in order to be as popular as possible amongst people. I mean a math group should not be politically right or left, religiously up or down, racially white or black, sexually masculine or feminine, etc. Every body who likes math can be a member of a math group and limiting the membership to women seems inappropriate. Of course having a neutral math group in any non-mathematical aspect doesn't mean that each one of your members should be neutral in each non-mathematical aspect. It just says that you should be careful about the population balance of the group because people don't like to be one of the minorities in each community. Thus for example if you have a member with a right political point of view you should search for another member with a left political point of view to keep the political balance of the group safe.
7. Be Active, Be Exciting!
Your scientific activities are the best representatives of your math group but as I said you should have something exciting and new for your audiences. Think about any possible way for encouraging people in general and women in particular.
I wish you a successful math group! Good Luck!