Finite Group DatabasebetaFinite Group Databasebeta| order | 9008 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C563⋊C16 |
| derived, Sylow | C563 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C8 | D563 |
| commutator, hypocenter | C563 | C16 |
| Fitting | C8×C563 | C2 |
| socle | C2×C563 | C8 |
| LCS | G ▷ C563 | |
| UCS | C1 ◁ C8 | |
10 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,563|a^2=b,b^2=c,c^2=d,e^a=e^5622264 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C16×D563, C2×C563⋊C16, #31824844, … |
| maximal normal subgroup of | C16×D563, C2×C563⋊C16, #31824844, … |
| maximal quotient of | C563⋊C32, C2×C563⋊C16 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9008, 15);