Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of #4537 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×#4540 |
| Hall | C3×C5 ⋊ #329 |
| Sylow | C3 ⋊ C5×#329 |
140 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 2 generators on 24 points:
(1,2,3,4,5)(6,7,8)(10,13)(11,15)(17,18)(19,23)(20,22)(21,24);(7,8)(9,10,11,14,12,13,15,16)(18,21,22,23)165 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#67546, C5×#67772, #14279334, … |
| maximal normal subgroup of | C5×#67546, C5×#67772, #14279334, … |
| maximal quotient of | C5×#67639, C5×#67642, C5×#67630, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 434);