Finite Group DatabasebetaFinite Group Databasebeta| order | 36972 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C13 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C9⋊(Dic79⋊C13) |
| unambiguous semidirect product | (C79⋊C13)⋊Dic9 |
| unambiguous semidirect product | Dic711⋊C13 |
| derived, Hall | C9×C79 ⋊ C4×C13 |
| Hall | C9×C79⋊C13 ⋊ C4 |
| Hall | Dic711 ⋊ C13 |
| Hall | C79⋊C13 ⋊ Dic9 |
| Sylow | C79 ⋊ C13×Dic9 |
| Sylow | C9 ⋊ Dic79⋊C13 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2844 |
Polycyclic presentation:
2,3,13,79,2,3|a^2=e,b^3=f^2,b^a=b^2f,d^a=d^78,f^a=f^2,d^c=d^18210 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36972, 17);