Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of #686 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42 · Schur multiplier (H2) = C22 |
| direct product | C3×#64778 |
| 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)(13,15,16,24,18,25,17,26)(14,19,20,27,22,28,21,23);(5,6)(7,8)(9,10,11,12)(13,14,17,21,18,22,16,20)(15,23,24,19,25,27,26,28)204 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D5×#341, C2×C3×#64778, #14294637, … |
| maximal normal subgroup of | C3×D5×#341, C2×C3×#64778, #14294637, … |
| maximal quotient of | C3×#10598194, C3×#10598230, C3×#10598158, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 330);