Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of #65800⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#65800⋊C3 |
| unambiguous semidirect product | D5⋊(#379⋊C3) |
| unambiguous semidirect product | (C2×#65800)⋊C3 |
| Fitting | C25×C5 ⋊ C3×C4 |
| derived | C24×C5 ⋊ C2×C3×C4 |
| Hall | C2×#65800 ⋊ C3 |
| Sylow | C5 ⋊ C2×#379⋊C3 |
1268 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 1268 conjugacy classes of subgroups — too many to draw. Only its 37 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.
| maximal subgroup of | D5×#65800⋊C3, C2×AGL(1,𝔽5)×#120⋊C3, #72243059, … |
| maximal normal subgroup of | C2×AGL(1,𝔽5)×#120⋊C3, #72243059, #72243115, … |
| maximal quotient of | D5×#65800⋊C3, #72243115, #72253796 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 238291);