Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Hall | C3×C5 ⋊ #525 |
| Sylow | C5 ⋊ #5828 |
| Sylow | C3 ⋊ #65858 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×D3×D5 |
| commutator, socle, cosocle | C22×C3×C5 | C24 |
| Frattini | C22 | C22×D3×D5 |
| Fitting | C22×C3×C4×C5 | C22 |
| hypercenter | C22×C4 | D3×D5 |
| hypocenter | C3×C5 | #525 |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C2×C4 ◁ C22×C4 | |
660 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 660 conjugacy classes of subgroups — too many to draw. Only its 164 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^6,3,5|b^2=e,c^2=f,b^a=be,d^a=df,h^a=h^4,d^b=df,g^b=g^2120 conjugacy classes — view the full character table.
| maximal subgroup of | #14300550, #14300556, #14301723, … |
| maximal normal subgroup of | #14300550, #14300556, #14301723, … |
| maximal quotient of | #14319944, #14320615, #14321126, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 8785);