Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of C5⋊(#120⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C25 |
| direct product | C22×C5⋊(#120⋊C3) |
| Fitting | C26×C5 ⋊ C2×C3 |
| derived | C24×C5 ⋊ C23×C3 |
| Hall | C22×#4099 ⋊ C3 |
| Sylow | C5 ⋊ C22×#120⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | C5⋊(#120⋊C3) |
| commutator, cosocle, hypocenter | C24×C5 | C23×C3 |
| Frattini | C22 | C22×D5×A4 |
| Fitting | C26×C5 | C2×C3 |
| socle | C24×C5 | C2×A4 |
| LCS | G ▷ C24×C5 | |
| UCS | C1 ◁ C22 | |
1708 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 1708 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
104 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 239940);