Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×Q8×C5⋊S4 |
| Fitting | C23×C5×Q8 ⋊ D3 |
| Sylow | C5 ⋊ C2×Q8×S4 |
1622 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 1622 conjugacy classes of subgroups — too many to draw. Only its 173 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
130 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240297);