Finite Group DatabasebetaFinite Group Databasebeta| order | 3720 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×C3⋊(Dic31⋊C5) |
| derived, Hall | C3×C31 ⋊ C2×C4×C5 |
| Hall | C2×Dic93 ⋊ C5 |
| Hall | C3×ΓL(1,𝔽32) ⋊ C2×C4 |
| Hall | ΓL(1,𝔽32) ⋊ C2×Dic3 |
| Sylow | C31 ⋊ C2×C5×Dic3 |
| Sylow | C3 ⋊ C2×Dic31⋊C5 |
64 conjugacy classes of subgroups.
96 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3⋊(((C31⋊C3)⋊C4)⋊C5), C2×C4×C3⋊(D31⋊C5), C2×D3×Dic31⋊C5, … |
| maximal normal subgroup of | C2×C3⋊(((C31⋊C3)⋊C4)⋊C5), C2×C4×C3⋊(D31⋊C5), C2×D3×Dic31⋊C5, … |
Past the SmallGroups library coverage — no SmallGroups id.