Finite Group DatabasebetaFinite Group Databasebeta| order | 2904 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×D33⋊D11 |
| Fitting, socle | C2×C3×C112 ⋊ C22 |
| derived, Hall | C3×C112 ⋊ C23 |
| Sylow | C112 ⋊ C22×D3 |
| Sylow | C3 ⋊ C2×D112 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D33⋊D11 |
| commutator, cosocle, hypocenter | C3×C112 | C23 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C112 | C22 |
| LCS | G ▷ C3×C112 | |
| UCS | C1 ◁ C2 | |
178 conjugacy classes of subgroups.
| transitive degree | μt(G) = 132 |
222 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×D112, #72247168, #72247187, … |
| maximal normal subgroup of | C2×D3×D112, #72247168, #72247187, … |
| maximal quotient of | #72247187 |
Past the SmallGroups library coverage — no SmallGroups id.