Finite Group DatabasebetaFinite Group Databasebeta| order | 9008 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C23×D563 |
| unambiguous semidirect product | C563⋊C24 |
| unambiguous semidirect product | (C2×C563)⋊C23 |
| Fitting, socle | C23×C563 ⋊ C2 |
| derived, Sylow | C563 ⋊ C24 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D563 |
| commutator, hypocenter | C563 | C24 |
| Frattini | C1 | G |
| Fitting, socle | C23×C563 | C2 |
| LCS | G ▷ C563 | |
| UCS | C1 ◁ C23 | |
134 conjugacy classes of subgroups.
2264 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22⋊C4×D563, C2×(C2×D563)⋊C4, #31824873, … |
| maximal normal subgroup of | C22⋊C4×D563, C2×(C2×D563)⋊C4, #31824873, … |
| maximal quotient of | C22×C4×D563, C23×Dic563, C2×D4×D563, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9008, 42);