Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D4×SL(2,𝔽5) |
| unambiguous semidirect product | C4⋊(C2×SL(2,𝔽5)) |
| unambiguous semidirect product | C22⋊(C2×SL(2,𝔽5)) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle, cosocle | C22 | C22×A5 |
| commutator | C2×SL(2,𝔽5) | C22 |
| Fitting, hypercenter | C2×D4 | A5 |
| hypocenter | SL(2,𝔽5) | D4 |
| LCS | G ▷ C2×SL(2,𝔽5) ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
180 conjugacy classes of subgroups; only the 25 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 25 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
45 conjugacy classes — view the full character table.
| maximal subgroup of | #14515007, #14515009, #14515020, … |
| maximal normal subgroup of | #14515007, #14515009, #14515020, … |
| maximal quotient of | C22⋊C4×SL(2,𝔽5), C4⋊C4×SL(2,𝔽5), D8×SL(2,𝔽5), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 5746);