Finite Group DatabasebetaFinite Group Databasebeta| order | 9008 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q8×C563 ⋊ C2 |
| Sylow | C563 ⋊ #41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D563 |
| commutator, socle | C2×C563 | C23 |
| Fitting | Q8×C563 | C2 |
| hypercenter | Q8 | D563 |
| hypocenter | C563 | #41 |
| LCS | G ▷ C2×C563 ▷ C563 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,563|c^2=d,b^a=bd,e^a=e^562,e^b=e^562,e^c=e^5621415 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31824926, #31824928, #31824932, … |
| maximal normal subgroup of | #31824926, #31824928, #31824932, … |
| maximal quotient of | #31824863, #31824867, Q8×Dic563, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9008, 41);