Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of C22⋊(C42⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C23×C4 |
| direct product | C2×C5×C22⋊(C42⋊C3) |
| Fitting, Hall | C23×C42×C5 ⋊ C3 |
| derived | C22×C42 ⋊ C2×C3×C5 |
| Sylow | C23×C42 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | C22⋊(C42⋊C3) |
| commutator, cosocle, hypocenter | C22×C42 | C2×C3×C5 |
| Frattini | C22 | C2×C5×C22⋊A4 |
| Fitting | C23×C42×C5 | C3 |
| socle | C25×C5 | A4 |
| LCS | G ▷ C22×C42 | |
| UCS | C1 ◁ C2×C5 | |
1080 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 1080 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| 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, 237078);