Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
| direct product | C2×D4×A5 |
| unambiguous semidirect product | C4⋊(C22×A5) |
| unambiguous semidirect product | C22⋊(C22×A5) |
| unambiguous semidirect product | C23⋊(C2×A5) |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×A5 |
| commutator | C2×A5 | C23 |
| Frattini, cosocle | C2 | C23×A5 |
| Fitting, hypercenter | C2×D4 | A5 |
| socle | C22×A5 | C22 |
| hypocenter | A5 | C2×D4 |
| LCS | G ▷ C2×A5 ▷ A5 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
553 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 553 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 40 |
50 conjugacy classes — view the full character table.
| maximal subgroup of | #14514732, #99×A5, #14514735, … |
| maximal normal subgroup of | #14514732, #99×A5, #14514735, … |
| maximal quotient of | C2×C22⋊C4×A5, C2×C4⋊C4×A5, C4×D4×A5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 10886);