Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of D5×C22⋊A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C25 |
| direct product | C2×D5×C22⋊A4 |
| unambiguous semidirect product | C5⋊(C22×C22⋊A4) |
| unambiguous semidirect product | (C2×C5)⋊(C2×C22⋊A4) |
| Fitting, socle | C25×C5 ⋊ C2×C3 |
| derived | C24×C5 ⋊ C22×C3 |
| Hall | C25×D5 ⋊ C3 |
| Sylow | C5 ⋊ C22×C22⋊A4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D5×C22⋊A4 |
| commutator, cosocle, hypocenter | C24×C5 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C25×C5 | C2×C3 |
| LCS | G ▷ C24×C5 | |
| UCS | C1 ◁ C2 | |
2000 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 2000 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 60 |
64 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#379⋊C3, #10605592⋊C3, #10614343⋊C3, … |
| maximal normal subgroup of | D5×#379⋊C3, #10605592⋊C3, #10614343⋊C3, … |
| maximal quotient of | Dic10×C22⋊A4, C4×D5×C22⋊A4, D20×C22⋊A4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 11383);