Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C3×C5×#41 ⋊ C22 |
| Hall | C3×C5 ⋊ #585 |
| Sylow | C5 ⋊ #5964 |
| Sylow | C3 ⋊ #66283 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C22×D3×D5 |
| commutator, socle, cosocle | C2×C3×C5 | C25 |
| Frattini | C2 | C23×D3×D5 |
| Fitting | C3×C5×#41 | C22 |
| hypercenter | #41 | D3×D5 |
| hypocenter | C3×C5 | #585 |
| LCS | G ▷ C2×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C4 ◁ #41 | |
1620 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^6,3,5|c^2=f,e^a=ef,h^a=h^4,d^b=df,g^b=g^2,e^d=ef114 conjugacy classes — view the full character table.
| maximal subgroup of | #14412921, #14412922, #14412923, … |
| maximal normal subgroup of | #14412921, #14412922, #14412923, … |
| maximal quotient of | #14479159, #14479160, #14479161, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 11253);