Finite Group DatabasebetaFinite Group Databasebeta| order | 21756 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×Dic7×C37⋊C3 |
| derived | C7×C37 ⋊ C3×C4×C7 |
| Hall | C7×Dic7×C37 ⋊ C3 |
| Hall | C72×C37⋊C3 ⋊ C4 |
| Hall | C72×C37 ⋊ C3×C4 |
| Sylow | C72 ⋊ C4×C37⋊C3 |
| Sylow | C37 ⋊ C3×C7×Dic7 |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1036 |
1050 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21756, 89);