Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C25 |
| direct product | C5×#5576 |
| Fitting | C3×C4×C5×Q8 ⋊ C2 |
| Hall | C3×C5 ⋊ #548 |
| Sylow | C3 ⋊ C5×#548 |
580 conjugacy classes of subgroups; only the 226 normal subgroups are shown.
This group has 580 conjugacy classes of subgroups — too many to draw. Only its 226 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) = 480 |
A minimal faithful permutation representation — 4 generators on 20 points:
(1,2,3,4,5)(6,7,8)(9,10,11,12)(13,16,17,15)(14,18,19,20);(13,15,17,16)(14,18,19,20);(13,14,17,19)(15,20,16,18);(7,8)(10,12)225 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#80404, C5×#79794, #14453490, … |
| maximal normal subgroup of | C5×#80404, C5×#79794, #14453490, … |
| maximal quotient of | C5×Q8×(C2×D3)⋊C4, C5×#82457, C5×#82460, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 10156);