Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of #826 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#4562 |
| Hall | C3×C5 ⋊ #357 |
| Sylow | C3 ⋊ C5×#357 |
132 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 62 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)(6,7,8)(14,18)(15,22)(16,23)(19,20)(21,27)(24,28)(25,26);(7,8)(9,10,11,12)(13,14)(15,18)(16,25)(17,21)(19,22)(20,23)(24,27)(26,28)180 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D3×#357, C2×C5×#4562, D5×#4562, … |
| maximal normal subgroup of | C5×D3×#357, C2×C5×#4562, D5×#4562, … |
| maximal quotient of | C5×#67763, C5×#67774, C5×#67790, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 456);