Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | A4×#4007 |
| unambiguous semidirect product | (C22×#4007)⋊C3 |
| Fitting | C22×C5×D4 ⋊ C3×C4 |
| Hall | C22×#4007 ⋊ C3 |
| Sylow | C5 ⋊ A4×#102 |
524 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
76 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 238263);