Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of #204 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C8 · Schur multiplier (H2) = C2 |
| direct product | C5×#4456 |
| Hall | C3×C5 ⋊ Q8⋊C8 |
| Sylow | C3 ⋊ C5×Q8⋊C8 |
140 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 70 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) = 960 |
A minimal faithful permutation representation — 2 generators on 24 points:
(1,2,3,4,5)(6,7,8)(9,11,12,16,13,10,14,15)(18,22,24,23);(7,8)(9,10,12,15,13,11,14,16)(17,18,20,23,21,24,19,22)300 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D3×Q8⋊C8, C2×C5×#4456, D5×#4456, … |
| maximal normal subgroup of | C5×D3×Q8⋊C8, C2×C5×#4456, D5×#4456, … |
| maximal quotient of | C5×#67478, C5×#67480, C5×#67655, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 350);