Finite Group DatabasebetaFinite Group Databasebeta| order | 9008 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×C4×D563 |
| Fitting | C2×C4×C563 ⋊ C2 |
| derived, Sylow | C563 ⋊ C22×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | D563 |
| commutator, hypocenter | C563 | C22×C4 |
| Frattini | C2 | C22×D563 |
| Fitting | C2×C4×C563 | C2 |
| socle | C22×C563 | C22 |
| LCS | G ▷ C563 | |
| UCS | C1 ◁ C2×C4 | |
54 conjugacy classes of subgroups.
2264 conjugacy classes. The character table is too large to display.
| maximal subgroup of | (C2×D563)⋊C8, C42×D563, C22⋊C4×D563, … |
| maximal normal subgroup of | (C2×D563)⋊C8, C42×D563, C22⋊C4×D563, … |
| maximal quotient of | C42×D563, C2×C4×Dic563, C22⋊C4×D563, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9008, 32);