Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of C22⋊(C22⋊A4) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C29 |
| direct product | C2×C5×C22⋊(C22⋊A4) |
| Fitting, socle, Hall | C27×C5 ⋊ C3 |
| derived | C26 ⋊ C2×C3×C5 |
| Sylow | C27 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | C22⋊(C22⋊A4) |
| commutator, cosocle, hypocenter | C26 | C2×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C27×C5 | C3 |
| LCS | G ▷ C26 | |
| UCS | C1 ◁ C2×C5 | |
19768 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
240 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 237187);