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Aliases
Subgroups
111589 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 7 generators on 24 points:
(1,2);(3,4);(9,10)(11,16)(12,20)(13,17)(14,19)(15,18)(21,22)(23,24);(1,2)(3,4)(5,6)(7,8)(9,11,13,20,15,21,14,24)(10,16,17,12,18,22,19,23);(5,6);(1,2)(3,4)(5,6)(7,8)(9,12,13,22,15,23,14,16)(10,11,19,24,18,21,17,20);(7,8)
Conjugacy classes & character table
352 conjugacy classes. The character table is too large to display.
Relationships
| maximal subgroup of | #72286489, C24×AGL(1,ℤ/16), C23×#21546, … |
| maximal normal subgroup of | #72286489, C24×AGL(1,ℤ/16), C23×#21546, … |
| maximal quotient of | C24×#1580, C23×#21546, C22×D4×#444, … |
GAP
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((1,2), (3,4), (9,10)(11,16)(12,20)(13,17)(14,19)(15,18)(21,22)(23,24), (1,2)(3,4)(5,6)(7,8)(9,11,13,20,15,21,14,24)(10,16,17,12,18,22,19,23), (5,6), (1,2)(3,4)(5,6)(7,8)(9,12,13,22,15,23,14,16)(10,11,19,24,18,21,17,20), (7,8));
Finite Group Databasebeta