Finite Group DatabasebetaFinite Group Databasebeta| order | 9008 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | C2×Dic1126 |
| unambiguous semidirect product | (C2×C563)⋊Q8 |
| Sylow | C563 ⋊ C2×Q8 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D563 |
| commutator | C2×C563 | C23 |
| Frattini | C2 | C22×D563 |
| Fitting | C2×C4×C563 | C2 |
| socle | C22×C563 | C22 |
| hypercenter | C2×C4 | D563 |
| hypocenter | C563 | C2×Q8 |
| LCS | G ▷ C2×C563 ▷ C563 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
38 conjugacy classes of subgroups.
2258 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31824823, #31824828, #31824830, … |
| maximal normal subgroup of | #31824823, #31824828, #31824830, … |
| maximal quotient of | C2×Dic563⋊C4, C2×C4⋊Dic563, C4×Dic1126, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9008, 38);