Finite Group DatabasebetaFinite Group Databasebeta| order | 2880 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C23 |
| direct product | D15×#997 |
| Fitting, derived | C3×C5×H(5,𝔽2) ⋊ C2×C3 |
| Sylow | C5 ⋊ D3×#997 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D15×C22⋊A4 |
| commutator, Fitting, cosocle, hypocenter | C3×C5×H(5,𝔽2) | C2×C3 |
| socle | C2×C3×C5 | C2×C22⋊A4 |
| LCS | G ▷ C3×C5×H(5,𝔽2) | |
| UCS | C1 ◁ C2 | |
794 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 46 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 — 3 generators on 16 points:
(2,5,3)(6,7,8)(10,11)(12,13)(15,16);(2,6)(3,8)(9,10,12,13,11)(14,15,16);(1,7,4,5)(2,3,6,8)99 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D5×#997, D15×#5935, #72231064, … |
| maximal normal subgroup of | D3×D5×#997, D15×#5935, #72231064, … |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((2,5,3)(6,7,8)(10,11)(12,13)(15,16), (2,6)(3,8)(9,10,12,13,11)(14,15,16), (1,7,4,5)(2,3,6,8));