Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C1 |
| direct product | SL(2,𝔽3)×#700 |
| unambiguous semidirect product | (Q8×#700)⋊C3 |
| Hall | Q8×#700 ⋊ C3 |
| Sylow | C5 ⋊ M16×SL(2,𝔽3) |
276 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 62 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
98 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 238215);