Finite Group DatabasebetaFinite Group Databasebeta| order | 9008 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | Q8×D563 |
| Fitting | Q8×C563 ⋊ C2 |
| Sylow | C563 ⋊ C2×Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D563 |
| commutator, socle | C2×C563 | C23 |
| Fitting | Q8×C563 | C2 |
| hypercenter | Q8 | D563 |
| hypocenter | C563 | C2×Q8 |
| LCS | G ▷ C2×C563 ▷ C563 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
38 conjugacy classes of subgroups.
1415 conjugacy classes. The character table is too large to display.
| maximal subgroup of | SD16×D563, Q16×D563, #31824934, … |
| maximal normal subgroup of | SD16×D563, Q16×D563, #31824934, … |
| maximal quotient of | C4⋊C4×D563, #31824870, Q8×Dic563, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9008, 37);