Finite Group DatabasebetaFinite Group Databasebeta| order | 21756 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C37×C49 ⋊ C3×C4 |
| Hall | Dic1813 ⋊ C3 |
| Hall | C49×C37⋊C3 ⋊ C4 |
| Hall | C37⋊C3 ⋊ Dic49 |
| Sylow | C49 ⋊ Dic37⋊C3 |
| Sylow | C37 ⋊ C3×Dic49 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7252 |
Polycyclic presentation:
2,3,7,37,2,7|a^2=e,c^7=f^6,c^a=c^6f,d^a=d^36,f^a=f^6,d^b=d^10744 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21756, 4);