Finite Group DatabasebetaFinite Group Databasebeta| order | 36224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C211 |
| direct product | C23×(C2×D283)⋊C4 |
| Fitting | C24×C4×C283 ⋊ C2 |
| Sylow | C283 ⋊ C23×C22⋊C4 |
4632 conjugacy classes of subgroups; only the 1413 normal subgroups are shown.
This group has 4632 conjugacy classes of subgroups — too many to draw. Only its 1413 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 18112 |
9104 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36224, 17667);