Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of D5×C82⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C8 |
| direct product | D5×C82⋊C3 |
| unambiguous semidirect product | C5⋊(C2×C82⋊C3) |
| unambiguous semidirect product | (C82×D5)⋊C3 |
| Fitting, derived | C5×C82 ⋊ C2×C3 |
| Hall | C82×D5 ⋊ C3 |
| Sylow | C5 ⋊ C2×C82⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C5×C82 | C2×C3 |
| Frattini | C42 | D5×A4 |
| socle | C22×C5 | C2×C42⋊C3 |
| LCS | G ▷ C5×C82 | |
| UCS | C1 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
96 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 237239);