Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of C3⋊((C24⋊C5)⋊C2) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C23 |
| direct product | C4×C3⋊((C24⋊C5)⋊C2) |
| Fitting | C24×C3×C4 ⋊ D5 |
| derived | C3×C24⋊C5 ⋊ C2×C4 |
| Sylow | C3 ⋊ C4×(C24⋊C5)⋊C2 |
716 conjugacy classes of subgroups; only the 23 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 23 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 60 |
72 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240266);