Finite Group DatabasebetaFinite Group Databasebeta| order | 2664 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C2×C3⋊(#3866⋊C3) |
| Fitting, socle | C2×C3×C37 ⋊ C3×C4 |
| derived | C3×C37 ⋊ C2×C3×C4 |
| Hall | C3×C37⋊C3 ⋊ C2×C4 |
| Sylow | C37 ⋊ C2×C3×Dic3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C3⋊(#3866⋊C3) |
| commutator, hypocenter | C3×C37 | C2×C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C37 | C3×C4 |
| prime radical | C2×C3×D37⋊C3 | C2 |
| cosocle | C3×D37 | C22×C3 |
| LCS | G ▷ C3×C37 | |
| UCS | C1 ◁ C2 | |
74 conjugacy classes of subgroups.
| transitive degree | μt(G) = 222 |
54 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#3866⋊C3, C2×#72228574 |
| maximal normal subgroup of | C2×D3×#3866⋊C3, C2×#72228574 |
Past the SmallGroups library coverage — no SmallGroups id.