Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | Q8×A4⋊AGL(1,𝔽5) |
| Fitting | C22×C5×Q8 ⋊ Dic3 |
| Sylow | C5 ⋊ Q8×SL(2,ℤ/4) |
702 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 702 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) = 120 |
70 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240074);