Finite Group DatabasebetaFinite Group Databasebeta| order | 3712 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×Q32×D29 |
| Fitting | C2×C29×Q32 ⋊ C2 |
| Sylow | C29 ⋊ C22×Q32 |
360 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1856 |
352 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3712, 17621);