Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C22 |
| direct product | SL(2,𝔽3)×C24⋊C5 |
| unambiguous semidirect product | Q8⋊(C3×C24⋊C5) |
| unambiguous semidirect product | (C24×SL(2,𝔽3))⋊C5 |
| Fitting, derived, Sylow | C24×Q8 ⋊ C3×C5 |
| Hall | Q8×C24⋊C5 ⋊ C3 |
| Hall | C24×SL(2,𝔽3) ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | A4×C24⋊C5 |
| commutator, Fitting, cosocle, hypocenter | C24×Q8 | C3×C5 |
| socle | C25 | C5×A4 |
| LCS | G ▷ C24×Q8 | |
| UCS | C1 ◁ C2 | |
381 conjugacy classes of subgroups.
| transitive degree | μt(G) = 40 |
56 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240057);