Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of SL(2,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C1 |
| direct product | C16×SL(2,𝔽5) |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C2×C16 | A5 |
| commutator, hypocenter | SL(2,𝔽5) | C16 |
| Frattini, cosocle | C2×C8 | C2×A5 |
| socle | C22 | C8×A5 |
| prime radical | C2×SL(2,𝔽5) | C8 |
| LCS | G ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C2×C16 | |
103 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240614);