Finite Group DatabasebetaFinite Group Databasebeta| order | 2304 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C22 |
| direct product | A4×#5398 |
725 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 725 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 144 |
A minimal faithful permutation representation — 2 generators on 24 points:
(2,4,3)(5,6,8)(9,11,18,22,13,20,12,19)(10,14,21,24,16,23,15,17);(1,4)(2,3)(6,7)(9,10,13,16)(11,17,20,24)(12,21,18,15)(14,22,23,19)88 conjugacy classes — view the full character table.
| maximal subgroup of | A4×#85440 |
| maximal normal subgroup of | A4×#85440 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((2,4,3)(5,6,8)(9,11,18,22,13,20,12,19)(10,14,21,24,16,23,15,17), (1,4)(2,3)(6,7)(9,10,13,16)(11,17,20,24)(12,21,18,15)(14,22,23,19));