Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
| direct product | C2×#91902 |
| Sylow | C5 ⋊ C2×C4⋊S4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D5×S4 |
| commutator, cosocle | C2×C5×A4 | C23 |
| Frattini | C2 | C2×D5×S4 |
| Fitting, socle | C24×C5 | C2×D3 |
| hypocenter | C5×A4 | C2×D4 |
| LCS | G ▷ C2×C5×A4 ▷ C5×A4 | |
| UCS | C1 ◁ C22 | |
466 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
68 conjugacy classes — view the full character table.
| maximal subgroup of | #14512429, #14513095, #14513099, … |
| maximal normal subgroup of | #14512429, #14513095, #14513099, … |
| maximal quotient of | C2×#11751573, C2×#11751574, C2×#11751575, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 10986);