Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23 |
| direct product | C5×#5126 |
| Fitting | C2×C3×C5×M16 ⋊ C2 |
| Hall | C3×C5 ⋊ #407 |
| Sylow | C3 ⋊ C5×#407 |
380 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 380 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) = 20 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 3 generators on 20 points:
(1,2,3,4,5)(6,7,8)(10,12)(13,14,15,18,16,17,19,20);(14,17)(18,20);(7,8)(9,10)(11,12)240 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#67530, #14277618, C5×#70079, … |
| maximal normal subgroup of | C5×#67530, #14277618, C5×#70079, … |
| maximal quotient of | C5×#69967, C5×#69971, C5×#70826, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4820);