Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of AGL(1,𝔽5)×C42⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2×C4 |
| direct product | C2×AGL(1,𝔽5)×C42⋊C3 |
| unambiguous semidirect product | D5⋊(C4×C42⋊C3) |
| unambiguous semidirect product | (C2×C42×AGL(1,𝔽5))⋊C3 |
| Fitting | C2×C42×C5 ⋊ C3×C4 |
| derived | C42×C5 ⋊ C2×C3×C4 |
| Hall | C2×C42×AGL(1,𝔽5) ⋊ C3 |
| Sylow | C5 ⋊ C2×C4×C42⋊C3 |
504 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 60 |
80 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 238211);