Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of #65690⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C2×#65690⋊C3 |
| unambiguous semidirect product | D5⋊(#383⋊C3) |
| unambiguous semidirect product | (C2×#65690)⋊C3 |
| Fitting | C2×C42×C5 ⋊ C3×C4 |
| derived | C42×C5 ⋊ C2×C3×C4 |
| Hall | C2×#65690 ⋊ C3 |
| Sylow | C5 ⋊ C2×#383⋊C3 |
288 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 288 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) = 120 |
56 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 238213);