Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of S4×C24⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C23 |
| direct product | S4×C24⋊C5 |
| unambiguous semidirect product | A4⋊(C2×C24⋊C5) |
| unambiguous semidirect product | (C24×S4)⋊C5 |
| Fitting, socle | C26 ⋊ C5×D3 |
| derived | C24×A4 ⋊ C2×C5 |
| Hall | C24×S4 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C24×A4 | C2×C5 |
| Fitting, socle | C26 | C5×D3 |
| LCS | G ▷ C24×A4 | |
| UCS | C1 | |
1065 conjugacy classes of subgroups; only the 12 normal subgroups are shown.
This group has 1065 conjugacy classes of subgroups — too many to draw. Only its 12 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 30 |
40 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240391);