Finite Group DatabasebetaFinite Group Databasebeta| order | 2664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C2×D3×D37⋊C3 |
| Fitting, socle | C2×C3×C37 ⋊ C22×C3 |
| derived | C3×C37 ⋊ C23×C3 |
| Hall | C3×C37⋊C3 ⋊ C23 |
| Sylow | C37 ⋊ C22×C3×D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D3×D37⋊C3 |
| commutator, cosocle, hypocenter | C3×C37 | C23×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C37 | C22×C3 |
| LCS | G ▷ C3×C37 | |
| UCS | C1 ◁ C2 | |
138 conjugacy classes of subgroups.
| transitive degree | μt(G) = 222 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#3866⋊C3, C2×D3×#66526⋊C2 |
| maximal normal subgroup of | C2×D3×#3866⋊C3, C2×D3×#66526⋊C2 |
Past the SmallGroups library coverage — no SmallGroups id.