Finite Group DatabasebetaFinite Group Databasebeta| order | 2304 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25×C3 |
| direct product | C4×#10593630 |
| Fitting | C3×C4×#120 ⋊ D3 |
| derived | C3×C22⋊A4 ⋊ C22×C4 |
1910 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 1910 conjugacy classes of subgroups — too many to draw. Only its 89 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:
(2,3)(4,6,7,5)(8,15,11,13)(9,12,14,10);(1,2,3)(4,5,7,6)(8,9)(10,14)(11,15)(12,13);(8,9)(10,15,12,14,11,13)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((2,3)(4,6,7,5)(8,15,11,13)(9,12,14,10), (1,2,3)(4,5,7,6)(8,9)(10,14)(11,15)(12,13), (8,9)(10,15,12,14,11,13));