Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×D5⋊GU(2,𝔽3) |
| unambiguous semidirect product | D5⋊(C2×GU(2,𝔽3)) |
| derived | C5×SL(2,𝔽3) ⋊ C22×C4 |
| Sylow | C5 ⋊ C22×GU(2,𝔽3) |
718 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 718 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
92 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#14512506 |
| maximal normal subgroup of | C2×#14512506 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240075);