Finite Group DatabasebetaFinite Group Databasebeta| order | 2880 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C23 |
| direct product | C3×C5⋊#5934 |
| Fitting | C3×C5×H(5,𝔽2) ⋊ D3 |
| derived | C5×#997 ⋊ C2×C3 |
| Sylow | C5 ⋊ C3×#5934 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C5⋊#1020 |
| commutator, cosocle, hypocenter | C5×#997 | C2×C3 |
| Frattini | C2 | C3×C5⋊#1020 |
| Fitting | C3×C5×H(5,𝔽2) | D3 |
| socle | C2×C3×C5 | #1020 |
| LCS | G ▷ C5×#997 | |
| UCS | C1 ◁ C2×C3 | |
414 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 30 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:
(1,2,3)(5,6)(7,8)(9,11,13,14)(10,12,15,16);(4,5,7,8,6)(10,11,13)(14,15,16)105 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D5×#5934, D3×C5⋊#5934, #72278170 |
| maximal normal subgroup of | C3×D5×#5934, D3×C5⋊#5934, #72278170 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((1,2,3)(5,6)(7,8)(9,11,13,14)(10,12,15,16), (4,5,7,8,6)(10,11,13)(14,15,16));