Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Hall | C3×C5 ⋊ #336 |
| Sylow | C5 ⋊ #4550 |
| Sylow | C3 ⋊ #64744 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C22×C4 | D3×D5 |
| commutator | C2×C3×C5 | C4×C8 |
| Fitting, cosocle | C22×C3×C4×C5 | C22 |
| socle, prime radical | C23×C3×C5 | C2×C4 |
| hypocenter | C3×C5 | #336 |
| LCS | G ▷ C2×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C22×C4 | |
236 conjugacy classes of subgroups.
| transitive degree | μt(G) = 960 |
Polycyclic presentation:
2^6,3,5|a^2=c,b^2=d,c^2=f,b^a=be,h^a=h^4,g^b=g^2168 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#4550, #14294284, D3×#64744, … |
| maximal normal subgroup of | D5×#4550, #14294284, D3×#64744, … |
| maximal quotient of | #14276694, #14276708, #14276724, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 162);