Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C2 |
| direct product | C8×D5×SL(2,𝔽3) |
| unambiguous semidirect product | (C8×Q8×D5)⋊C3 |
| Fitting | C5×C8×Q8 ⋊ C2×C3 |
| derived | C5×Q8 ⋊ C2×C3×C8 |
| Hall | C8×Q8×D5 ⋊ C3 |
| Sylow | C5 ⋊ C2×C8×SL(2,𝔽3) |
310 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
224 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 237870);