Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
| direct product | Q8×SL(2,𝔽5) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle, cosocle | C22 | C22×A5 |
| commutator, prime radical | C2×SL(2,𝔽5) | C22 |
| Fitting, hypercenter | C2×Q8 | A5 |
| hypocenter | SL(2,𝔽5) | Q8 |
| LCS | G ▷ C2×SL(2,𝔽5) ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
134 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
45 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 5747);