Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of D5×A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42 · Schur multiplier (H2) = C2×C4 |
| direct product | C4×A4×Dic5 |
| unambiguous semidirect product | (C22×C4×Dic5)⋊C3 |
| derived | C22×C5 ⋊ C3×C42 |
| Hall | C22×C4×Dic5 ⋊ C3 |
| Sylow | C5 ⋊ C42×A4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | D5×A4 |
| commutator, hypocenter | C22×C5 | C3×C42 |
| Frattini | C22 | C2×D5×A4 |
| Fitting | C23×C4×C5 | C2×C3 |
| socle, cosocle | C24×C5 | C22×C3 |
| prime radical | C22×C5×A4 | C22 |
| LCS | G ▷ C22×C5 | |
| UCS | C1 ◁ C2×C4 | |
266 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 266 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) = 240 |
128 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, A4×#3935, C4×Dic5×SL(2,𝔽3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6378);