Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of AGL(1,𝔽5)×S4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
| direct product | C4×AGL(1,𝔽5)×S4 |
| Fitting | C22×C4×C5 ⋊ C4×D3 |
| derived | C5×A4 ⋊ C2×C42 |
| Sylow | C5 ⋊ C42×S4 |
994 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 994 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 60 |
100 conjugacy classes — view the full character table.
| maximal subgroup of | D4×AGL(1,𝔽5)×S4, AGL(1,𝔽5)×#1020⋊C4, S4×GL(2,𝔽5) |
| maximal normal subgroup of | D4×AGL(1,𝔽5)×S4 |
| maximal quotient of | AGL(1,𝔽5)×#1020⋊C4 |
| automorphism group of | C22×C5×D5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 239985);