Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | S4×C4⋊AGL(1,𝔽5) |
| Fitting | C22×C4×C5 ⋊ C4×D3 |
| Sylow | C5 ⋊ C4⋊C4×S4 |
838 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 838 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 60 |
70 conjugacy classes — view the full character table.
| maximal subgroup of | D4×AGL(1,𝔽5)×S4, #72243722 |
| maximal normal subgroup of | D4×AGL(1,𝔽5)×S4 |
| maximal quotient of | #72243722 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 239987);