Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C1 |
| direct product | SL(2,𝔽3)×Dic10 |
| unambiguous semidirect product | C5⋊(Q8×SL(2,𝔽3)) |
| unambiguous semidirect product | (Q8×Dic10)⋊C3 |
| Hall | Q8×Dic10 ⋊ C3 |
| Sylow | C5 ⋊ Q8×SL(2,𝔽3) |
154 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
91 conjugacy classes — view the full character table.
| maximal subgroup of | #14511688, #14511689, #14511690, … |
| maximal normal subgroup of | #14511688, #14511689, #14511690, … |
| maximal quotient of | SL(2,𝔽3)×#683, SL(2,𝔽3)×C4⋊Dic5, C2×SL(2,𝔽3)×Dic10 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6350);