Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C24 |
| direct product | C5×#5535 |
| Fitting | C3×C5×#117 ⋊ C2 |
| Hall | C3×C5 ⋊ #540 |
| Sylow | C3 ⋊ C5×#540 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C5 | C23×D3 |
| commutator, cosocle | C22×C3 | C24×C5 |
| Frattini | C22 | C23×C5×D3 |
| Fitting | C3×C5×#117 | C2 |
| socle | C22×C3×C5 | C24 |
| hypercenter | C5×#117 | D3 |
| hypocenter | C3 | C5×#540 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C22×C5 ◁ C5×#117 | |
480 conjugacy classes of subgroups; only the 190 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 190 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 4 generators on 24 points:
(1,2,3,4,5)(6,7,8)(10,14)(13,16)(17,19,20,23)(18,22,21,24);(9,11,12,15)(10,13,14,16)(19,23)(22,24);(17,18,20,21)(19,22,23,24);(7,8)(9,10)(11,13)(12,14)(15,16)(18,21)(22,24)210 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#82568, C5×#79384, #14435928, … |
| maximal normal subgroup of | C5×#82568, C5×#79384, #14435928, … |
| maximal quotient of | C5×#82231, C5×#73415, C5×#82236, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 10115);