Finite Group DatabasebetaFinite Group Databasebeta| order | 5808 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26×C11 |
| direct product | C22×D3×C11⋊D11 |
| Fitting, socle | C22×C3×C112 ⋊ C22 |
| derived, Hall | C3×C112 ⋊ C24 |
| Sylow | C112 ⋊ C23×D3 |
| Sylow | C3 ⋊ C23×C11⋊D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D3×C11⋊D11 |
| commutator, cosocle, hypocenter | C3×C112 | C24 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C112 | C22 |
| LCS | G ▷ C3×C112 | |
| UCS | C1 ◁ C22 | |
1876 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1452 |
744 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×D3×#11925892, D3×#14515540 |
| maximal normal subgroup of | C22×D3×#11925892, D3×#14515540 |
Past the SmallGroups library coverage — no SmallGroups id.