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Aliases
Subgroups
96405 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 7 generators on 24 points:
(1,2);(3,4);(5,6);(7,8);(9,10,12,15,19,14,22,23,13,17,21,24,11,16,18,20);(9,10)(11,14)(12,20)(13,17)(15,18)(16,19)(21,23)(22,24);(1,2)(3,4)(5,6)(7,8)(9,11,13,19)(10,14,17,16)(12,18,21,22)(15,23,24,20)
Conjugacy classes & character table
256 conjugacy classes — view the full character table.
Relationships
| maximal subgroup of | C24×AGL(1,ℤ/16), C23×#13037, C23×#33517, … |
| maximal normal subgroup of | C24×AGL(1,ℤ/16), C23×#13037, C23×#33517, … |
| maximal quotient of | C24×#2177, C22×#7624074, C23×#33517, … |
GAP
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((1,2), (3,4), (5,6), (7,8), (9,10,12,15,19,14,22,23,13,17,21,24,11,16,18,20), (9,10)(11,14)(12,20)(13,17)(15,18)(16,19)(21,23)(22,24), (1,2)(3,4)(5,6)(7,8)(9,11,13,19)(10,14,17,16)(12,18,21,22)(15,23,24,20));
Finite Group Databasebeta