Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C2 |
| direct product | C2×SL(2,𝔽3)×#170 |
| unambiguous semidirect product | (C2×Q8×#170)⋊C3 |
| derived | C5×Q8 ⋊ C2×C3×C8 |
| Hall | C2×Q8×#170 ⋊ C3 |
| Sylow | C5 ⋊ C2×C8×SL(2,𝔽3) |
310 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 640 |
140 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 238267);