Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#5402 |
| Fitting | C22×C5×C8 ⋊ D3 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C5 | C4⋊S4 |
| commutator, cosocle | C4×A4 | C22×C5 |
| Frattini | C4 | C2×C5×S4 |
| Fitting | C22×C5×C8 | D3 |
| socle | C23×C5 | D12 |
| hypercenter | C5×C8 | S4 |
| hypocenter | A4 | C5×D8 |
| LCS | G ▷ C4×A4 ▷ C2×A4 ▷ A4 | |
| UCS | C1 ◁ C2×C5 ◁ C4×C5 ◁ C5×C8 | |
158 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 30 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 120 |
A minimal faithful permutation representation — 2 generators on 17 points:
(1,2,3,4,5)(6,7,9)(10,11,15,17,13,16,12,14);(7,8)(11,14)(12,15)(16,17)110 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#73035, C5×#73036, C5×#73133, … |
| maximal normal subgroup of | C5×#73035, C5×#73036, C5×#73133, … |
| maximal quotient of | C5×#73013, C5×#73022, C5×#73024, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6268);