Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C22 |
| direct product | A4×C4⋊#170 |
| unambiguous semidirect product | C4⋊(A4×#170) |
| unambiguous semidirect product | (C22×C4⋊#170)⋊C3 |
| Hall | C22×C4⋊#170 ⋊ C3 |
| Sylow | C5 ⋊ A4×C4⋊C8 |
340 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 480 |
112 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 238258);