Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×C4×C5×D4 ⋊ C2 |
| Hall | C3×C5 ⋊ #525 |
| Sylow | C5 ⋊ #5547 |
| Sylow | C3 ⋊ #65881 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×D15 |
| commutator, socle, cosocle | C22×C3×C5 | C24 |
| Frattini | C22 | C23×D15 |
| Fitting | C3×C4×C5×D4 | C2 |
| hypercenter | C4×D4 | D15 |
| hypocenter | C3×C5 | #525 |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C2×C4 ◁ C4×D4 | |
660 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^6,3,5|c^2=e,d^a=de,g^a=g^2,h^a=h^4,d^b=df168 conjugacy classes — view the full character table.
| maximal subgroup of | #14414901, #14414907, #14414941, … |
| maximal normal subgroup of | #14414901, #14414907, #14414941, … |
| maximal quotient of | #14319913, #14320539, #14320545, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 10501);