Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of #213 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C8 · Schur multiplier (H2) = C22 |
| direct product | C5×D4⋊(C3⋊C8) |
| unambiguous semidirect product | D4⋊(C5×C3⋊C8) |
| Hall | C3×C5 ⋊ D4⋊C8 |
| Sylow | C3 ⋊ C5×D4⋊C8 |
164 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 78 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)(18,21)(19,24)(22,23);(7,8)(9,10,11,13,12,14,15,16)(17,18)(19,21)(20,23)(22,24)240 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D3×D4⋊C8, C2×C5×D4⋊(C3⋊C8), D5×D4⋊(C3⋊C8), … |
| maximal normal subgroup of | C5×D3×D4⋊C8, C2×C5×D4⋊(C3⋊C8), D5×D4⋊(C3⋊C8), … |
| maximal quotient of | C5×#67639, C5×#67638, C5×#67619, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 428);