Finite Group DatabasebetaFinite Group Databasebeta| order | 2646 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3×C7 |
| direct product | C3×D3×#3862 |
| Fitting, socle | C32×C72 ⋊ C2×C3 |
| derived | C3×C72 ⋊ C2×C32 |
| Hall | C32×#3862 ⋊ C2 |
| Sylow | C72 ⋊ C32×D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D3×#3862 |
| commutator, cosocle, hypocenter | C3×C72 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C32×C72 | C2×C3 |
| LCS | G ▷ C3×C72 | |
| UCS | C1 ◁ C3 | |
146 conjugacy classes of subgroups.
| transitive degree | μt(G) = 126 |
171 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×ΓL(1,𝔽8)2, C3×D3×#64425, D32×#3862, … |
| maximal normal subgroup of | C3×D3×ΓL(1,𝔽8)2, C3×D3×#64425, D32×#3862, … |
Past the SmallGroups library coverage — no SmallGroups id.