Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of #677 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42 · Schur multiplier (H2) = C22 |
| direct product | C3×#64772 |
| Hall | C3×C5 ⋊ #341 |
| Sylow | C5 ⋊ C3×#341 |
180 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 2 generators on 28 points:
(1,2,3)(4,5,7,8,6)(9,10,11,12)(13,15,16,23,18,25,17,24)(14,19,26,28,21,27,20,22);(5,6)(7,8)(13,14,16,20,18,21,17,26)(15,22,23,27,25,28,24,19)276 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#10598266, C3×#10598018, #14278224, … |
| maximal normal subgroup of | C3×#10598266, C3×#10598018, #14278224, … |
| maximal quotient of | C3×#10598145, C3×#10598147, C3×#10598238, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 324);