Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of C3⋊((C24⋊C5)⋊C2) |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C25 |
| direct product | C22×C3⋊((C24⋊C5)⋊C2) |
| Fitting, socle | C26×C3 ⋊ D5 |
| derived | C3×C24⋊C5 ⋊ C23 |
| Sylow | C3 ⋊ C22×(C24⋊C5)⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | C3⋊((C24⋊C5)⋊C2) |
| commutator, cosocle, hypocenter | C3×C24⋊C5 | C23 |
| Frattini | C1 | G |
| Fitting, socle | C26×C3 | D5 |
| LCS | G ▷ C3×C24⋊C5 | |
| UCS | C1 ◁ C22 | |
2356 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 2356 conjugacy classes of subgroups — too many to draw. Only its 41 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 60 |
72 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240409);