Finite Group Databasebeta

?

← Prev (#72321824) Next (#72321826) →

C₂²×#72279977 #72321825

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

At least 14685 conjugacy classes of subgroups; only the 535963 normal subgroups are shown.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 8 generators on 24 points:

(3,4)(10,11)(13,14)(15,16)(17,18)(19,24)(20,22)(21,23);(9,10,12,11)(17,19,21,22)(18,20,23,24);(6,8)(10,11)(13,14,15,16)(17,18)(19,20)(21,23)(22,24);(10,11)(13,14)(15,16)(19,22)(20,24);(1,2)(3,4);(17,18)(19,20)(21,23)(22,24);(6,8)(17,18)(19,20)(21,23)(22,24);(5,6)(7,8)(9,11,12,10)(17,20)(18,22)(19,23)(21,24)

Conjugacy classes & character table

688 conjugacy classes. The character table is too large to display.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((3,4)(10,11)(13,14)(15,16)(17,18)(19,24)(20,22)(21,23), (9,10,12,11)(17,19,21,22)(18,20,23,24), (6,8)(10,11)(13,14,15,16)(17,18)(19,20)(21,23)(22,24), (10,11)(13,14)(15,16)(19,22)(20,24), (1,2)(3,4), (17,18)(19,20)(21,23)(22,24), (6,8)(17,18)(19,20)(21,23)(22,24), (5,6)(7,8)(9,11,12,10)(17,20)(18,22)(19,23)(21,24));