Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of #4466 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C5 · Schur multiplier (H2) = C2×C4 |
| direct product | C5×#4557 |
| Hall | C3×C5 ⋊ H(3,ℤ/4) |
| Sylow | C3 ⋊ C5×H(3,ℤ/4) |
188 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 94 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) = 240 |
A minimal faithful permutation representation — 2 generators on 24 points:
(1,2,3,4,5)(6,7,8)(9,11,12,20,14,19,13,21)(10,15,16,18,17,23,22,24);(7,8)(9,10)(11,18,19,24)(12,22)(13,16)(14,17)(15,21,23,20)210 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#67778, C5×#67534, #14277992, … |
| maximal normal subgroup of | C5×#67778, C5×#67534, #14277992, … |
| maximal quotient of | C5×#67737, C5×#67660, C5×#67682, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 451);