Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of ((C24⋊C5)⋊C2)⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C22×((C24⋊C5)⋊C2)⋊C3 |
| unambiguous semidirect product | ((C24⋊C5)⋊C2)⋊(C22×C3) |
| unambiguous semidirect product | AGL(1,𝔽16)⋊C23 |
| unambiguous semidirect product | (C2×AGL(1,𝔽16))⋊C22 |
| Fitting, socle | C26 ⋊ C3×D5 |
| derived | C24⋊C5 ⋊ C23×C3 |
| Hall | C22×(C24⋊C5)⋊C2 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | ((C24⋊C5)⋊C2)⋊C3 |
| commutator, cosocle, hypocenter | C24⋊C5 | C23×C3 |
| Frattini | C1 | G |
| Fitting, socle | C26 | C3×D5 |
| LCS | G ▷ C24⋊C5 | |
| UCS | C1 ◁ C22 | |
526 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 60 |
56 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240392);