Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×C5×C22⋊Q8 ⋊ C2 |
| Hall | C3×C5 ⋊ #525 |
| Sylow | C5 ⋊ #5627 |
| Sylow | C3 ⋊ #65961 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D15 |
| commutator, socle, cosocle | C22×C3×C5 | C24 |
| Fitting | C3×C5×C22⋊Q8 | C2 |
| hypercenter | C22⋊Q8 | D15 |
| hypocenter | C3×C5 | #525 |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
660 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^6,3,5|c^2=e,d^2=f,d^a=df,g^a=g^2,h^a=h^4,d^b=def,d^c=df126 conjugacy classes — view the full character table.
| maximal subgroup of | #14282817, #14282854, #14282966, … |
| maximal normal subgroup of | #14282817, #14282854, #14282966, … |
| maximal quotient of | #14319916, #14320530, #14320536, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 10581);