Finite Group DatabasebetaFinite Group Databasebeta| order | 9584 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q8×C599 ⋊ C2 |
| Sylow | C599 ⋊ #41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D599 |
| commutator, socle, cosocle | C2×C599 | C23 |
| Fitting | Q8×C599 | C2 |
| hypercenter | Q8 | D599 |
| hypocenter | C599 | #41 |
| LCS | G ▷ C2×C599 ▷ C599 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,599|c^2=d,b^a=bd,e^a=e^598,e^b=e^598,e^c=e^5981505 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34062736, #34062738, #34062742, … |
| maximal normal subgroup of | #34062736, #34062738, #34062742, … |
| maximal quotient of | #34062673, #34062677, Q8×Dic599, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9584, 41);