Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of #686 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42 · Schur multiplier (H2) = C23 |
| direct product | C3×#64749 |
| Hall | C3×C5 ⋊ #340 |
| Sylow | C5 ⋊ C3×#340 |
228 conjugacy classes of subgroups.
| 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)(18,21)(19,24)(22,23);(5,6)(7,8)(9,10,11,12)(17,18,19,22,20,23,24,21)204 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D5×#340, C2×C3×#64749, #14294539, … |
| maximal normal subgroup of | C3×D5×#340, C2×C3×#64749, #14294539, … |
| maximal quotient of | C3×#10598194, C3×#10598195, C3×#10598110, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 301);