Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C25 |
| direct product | C5×#5577 |
| Fitting | C3×C4×C5×Q8 ⋊ C2 |
| Hall | C3×C5 ⋊ #550 |
| Sylow | C3 ⋊ C5×#550 |
624 conjugacy classes of subgroups; only the 230 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 230 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);(13,15,16,19)(14,17,18,20);(13,14,16,18)(15,20,19,17);(7,8)(10,12)(15,19)(17,20)225 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#71032, C5×#68259, #14288916, … |
| maximal normal subgroup of | C5×#71032, C5×#68259, #14288916, … |
| maximal quotient of | C5×#82457, C5×Q8×C4⋊Dic3, C5×#73638, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 10157);