Finite Group DatabasebetaFinite Group Databasebeta| order | 2304 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
| direct product | C4×#10593244 |
| Fitting | C24×C3×C4 ⋊ C2×D3 |
| derived | C3×C22⋊A4 ⋊ C22×C4 |
1759 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 1759 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 72 |
A minimal faithful permutation representation — 3 generators on 15 points:
(1,2,3)(4,6,7,5)(9,15,13,12)(10,14);(2,3)(4,5,7,6)(8,9)(10,13,14,12,11,15);(4,5,7,6)96 conjugacy classes — view the full character table.
| maximal subgroup of | C4×D3×#1020⋊C2 |
| maximal normal subgroup of | C4×D3×#1020⋊C2 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((1,2,3)(4,6,7,5)(9,15,13,12)(10,14), (2,3)(4,5,7,6)(8,9)(10,13,14,12,11,15), (4,5,7,6));