Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×C42×C5 ⋊ C22 |
| Hall | C3×C5 ⋊ #546 |
| Sylow | C5 ⋊ #5554 |
| Sylow | C3 ⋊ #65884 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D3×D5 |
| commutator, socle, cosocle | C22×C3×C5 | C24 |
| Fitting | C3×C42×C5 | C22 |
| hypercenter | C42 | D3×D5 |
| hypocenter | C3×C5 | #546 |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C22 ◁ C42 | |
668 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^6,3,5|c^2=f,d^2=ef,c^a=cf,h^a=h^4,d^b=de,g^b=g^2117 conjugacy classes — view the full character table.
| maximal subgroup of | #14453303, #14453361, #14453369, … |
| maximal normal subgroup of | #14453303, #14453361, #14453369, … |
| maximal quotient of | D20×(C2×D3)⋊C4, #14326086, #14326345, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6931);