Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C2×Dic5×SL(2,𝔽3) |
| unambiguous semidirect product | (C2×Q8×Dic5)⋊C3 |
| derived | C5×Q8 ⋊ C2×C3×C4 |
| Hall | C2×Q8×Dic5 ⋊ C3 |
| Sylow | C5 ⋊ C2×C4×SL(2,𝔽3) |
216 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | #14511800, #14511801, #14511802, … |
| maximal normal subgroup of | #14511800, #14511801, #14511802, … |
| maximal quotient of | C2×SL(2,𝔽3)×#168, SL(2,𝔽3)×#681, C4×Dic5×SL(2,𝔽3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6386);