Finite Group DatabasebetaFinite Group Databasebeta| order | 36972 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×#27134506 |
| derived, Hall | C13×C79 ⋊ C32×C4 |
| Hall | C3×#15690493 ⋊ C4 |
| Hall | Dic1027 ⋊ C32 |
| Sylow | C79 ⋊ C3×Dic13⋊C3 |
| Sylow | C13 ⋊ C3×(C79⋊C3)⋊C4 |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12324 |
1062 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36972, 109);