Finite Group DatabasebetaFinite Group Databasebeta| order | 9008 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| direct product | C2×C563⋊C8 |
| unambiguous semidirect product | (C2×C563)⋊C8 |
| derived, Sylow | C563 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | D563 |
| commutator, hypocenter | C563 | C2×C8 |
| Frattini | C4 | C2×D563 |
| Fitting | C2×C4×C563 | C2 |
| socle | C22×C563 | C4 |
| LCS | G ▷ C563 | |
| UCS | C1 ◁ C2×C4 | |
22 conjugacy classes of subgroups.
2264 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×Dic563, C4×C563⋊C8, #31824815, … |
| maximal normal subgroup of | C8×Dic563, C4×C563⋊C8, #31824815, … |
| maximal quotient of | C4×C563⋊C8, C22⋊(C563⋊C8), C4⋊(C563⋊C8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9008, 22);