Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of C5⋊S4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
| direct product | C2×A4⋊#168 |
| unambiguous semidirect product | (C2×A4)⋊#168 |
| derived | C5×A4 ⋊ C2×C8 |
| Sylow | C5 ⋊ C2×A4⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | C5⋊S4 |
| commutator, hypocenter | C5×A4 | C2×C8 |
| Frattini | C4 | C2×C5⋊S4 |
| Fitting | C23×C4×C5 | D3 |
| socle | C24×C5 | Dic3 |
| prime radical | C22×C5×A4 | C4 |
| cosocle | C4×C5×A4 | C22 |
| LCS | G ▷ C5×A4 | |
| UCS | C1 ◁ C2×C4 | |
178 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
104 conjugacy classes — view the full character table.
| maximal subgroup of | Dic5×A4⋊C8, #14511753, #14511754, … |
| maximal normal subgroup of | Dic5×A4⋊C8, #14511753, #14511754, … |
| maximal quotient of | C4×A4⋊#168, C4⋊(A4⋊#168), C2×SL(2,𝔽3)⋊#168, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6322);