Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| direct product | C2×SL(2,𝔽3)⋊#170 |
| derived | C5×SL(2,𝔽3) ⋊ C2×C8 |
| Sylow | C5 ⋊ C2×SL(2,𝔽3)⋊C8 |
302 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 302 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) = 640 |
92 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 238183);