Finite Group DatabasebetaFinite Group Databasebeta| order | 9008 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊Dic563 |
| Sylow | C563 ⋊ C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×D563 |
| commutator | C2×C563 | C2×C4 |
| Fitting | C23×C563 | C2 |
| socle | C22×C563 | C22 |
| hypercenter | C23 | D563 |
| hypocenter | C563 | C22⋊C4 |
| LCS | G ▷ C2×C563 ▷ C563 | |
| UCS | C1 ◁ C22 ◁ C23 | |
34 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,563|a^2=d,b^a=bc,e^a=e^5622258 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31824819, #31824820, C22⋊C4×D563, … |
| maximal normal subgroup of | #31824819, #31824820, C22⋊C4×D563, … |
| maximal quotient of | C563⋊#95, C22⋊(C563⋊C8), #31824820, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9008, 18);