Finite Group DatabasebetaFinite Group Databasebeta| order | 2904 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C112 · Schur multiplier (H2) = C23×C11 |
| direct product | C22×D3×C112 |
| Fitting, socle | C22×C3×C112 ⋊ C2 |
| derived, Sylow | C3 ⋊ C23×C112 |
| Hall | C3×C112 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C112 | D3 |
| commutator, cosocle, hypocenter | C3 | C23×C112 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C112 | C2 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C22×C112 | |
448 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1452 |
1452 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×D3×C11⋊D11, C22×D3×#10597243, D3×C11×C22⋊D11 |
| maximal normal subgroup of | C22×D3×C11⋊D11, C22×D3×#10597243, D3×C11×C22⋊D11 |
Past the SmallGroups library coverage — no SmallGroups id.