Order = 46500000 =
Mult = 1.
Out = 1.

Porting notes

Porting complete, but handling of notes is unsatisfactory.

Standard generators

Standard generators of 53.L3(5) are a, b where a has order 3, b is in class 5B, ab has order 20, ababbbaabbb has order 4 and ababaababb has order 3.

Standard generators of 53.L3(5) are x, y where x has order 2, y has order 3, xy has order 31, xyxy2 has order 25, (xy)5(xy2)4 has order 2 and (xyxyxy2xy2)2xyxy2 has order 3.



Group Presentation Link
53.L3(5) x, y | x2 = y3 = (xy)31 = ((xy)5(xy−1)4)2 = [x, yxy(xy−1)3xyxy(xy−1)3xyxy] = [x, yxy]10 = (xy)6xy−1xy(xyxy−1)3xy−1xy(xy−1)5xyxy−1(xy)5xy−1xy−1 = 1 〉 Details


Representations of 53.L3(5)

Miscellaneous Notes

Group Category Note
53.L3(5) Group theoretic trivia. All elements of order 5 of 53.L3(5) not in the normal 53 map onto class 5A of L3(5).
53.L3(5) Group theoretic trivia. Class 5B is the unique class with centraliser order 2500.