Finite Group DatabasebetaFinite Group Databasebeta| order | 11520 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C3×AGL(1,𝔽5)×#5935 |
| Fitting | C3×C5×H(5,𝔽2) ⋊ C4×D3 |
| derived | C5×#997 ⋊ C2×C3×C4 |
| Sylow | C5 ⋊ C3×C4×#5935 |
2530 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 2530 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 16 |
| transitive degree | μt(G) = 120 |
A minimal faithful permutation representation — 2 generators on 16 points:
(2,7,5)(3,8,6)(10,11,12,13)(14,15,16);(1,5,7,2,4,8,3,6)(9,10,13,11,12)195 conjugacy classes — view the full character table.
| maximal subgroup of | D3×AGL(1,𝔽5)×#5935 |
| maximal normal subgroup of | D3×AGL(1,𝔽5)×#5935 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((2,7,5)(3,8,6)(10,11,12,13)(14,15,16), (1,5,7,2,4,8,3,6)(9,10,13,11,12));