Finite Group DatabasebetaFinite Group Databasebeta| order | 4032 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C215 |
| direct product | C23×D32×D7 |
| Fitting, socle | C23×C32×C7 ⋊ C23 |
| derived, Hall | C32×C7 ⋊ C26 |
| Sylow | C32 ⋊ C25×D7 |
| Sylow | C7 ⋊ C24×D32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D32×D7 |
| commutator, cosocle, hypocenter | C32×C7 | C26 |
| Frattini | C1 | G |
| Fitting, socle | C23×C32×C7 | C23 |
| LCS | G ▷ C32×C7 | |
| UCS | C1 ◁ C23 | |
23348 conjugacy classes of subgroups.
| transitive degree | μt(G) = 336 |
360 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D7×#10595278 |
| maximal normal subgroup of | D7×#10595278 |
| maximal quotient of | D7×#10596675 |
Past the SmallGroups library coverage — no SmallGroups id.