Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of #677 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42 · Schur multiplier (H2) = C23 |
| direct product | C3×#64771 |
| Hall | C3×C5 ⋊ #340 |
| Sylow | C5 ⋊ C3×#340 |
228 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 134 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) = 960 |
A minimal faithful permutation representation — 2 generators on 24 points:
(1,2,3)(4,5,7,8,6)(13,14,15,16)(17,18,19,21,20,22,23,24);(5,6)(7,8)(9,10,11,12)(18,21)(19,23)(22,24)276 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#10598265, C3×#10598017, #14278178, … |
| maximal normal subgroup of | C3×#10598265, C3×#10598017, #14278178, … |
| maximal quotient of | C3×#10598145, C3×#10598146, C3×#10598229, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 323);