Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of D5×A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C22 |
| direct product | C2×A4×#168 |
| unambiguous semidirect product | (C23×#168)⋊C3 |
| derived | C22×C5 ⋊ C2×C3×C8 |
| Hall | C23×#168 ⋊ C3 |
| Sylow | C5 ⋊ C2×C8×A4 |
186 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
128 conjugacy classes — view the full character table.
| maximal subgroup of | #168×SL(2,ℤ/4), #14511766, #14511767, … |
| maximal normal subgroup of | #168×SL(2,ℤ/4), #14511766, #14511767, … |
| maximal quotient of | C4×A4×#168, A4×C4⋊#168, C2×SL(2,𝔽3)×#168, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6376);