Finite Group DatabasebetaFinite Group Databasebeta| order | 4608 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×#72258610 |
| derived | A4×C22⋊A4 ⋊ C2×C4 |
2466 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 2466 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 72 |
A minimal faithful permutation representation — 3 generators on 22 points:
(3,6,5,4)(7,13,14,9,10,16,21,12)(8,22,19,18,15,20,17,11);(1,2)(4,5,6);(4,5,6)(8,9,14)(10,18,11)(12,20,16)(13,17,21)(15,19,22)64 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72258621 |
| maximal normal subgroup of | C2×#72258621 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((3,6,5,4)(7,13,14,9,10,16,21,12)(8,22,19,18,15,20,17,11), (1,2)(4,5,6), (4,5,6)(8,9,14)(10,18,11)(12,20,16)(13,17,21)(15,19,22));