Finite Group DatabasebetaFinite Group Databasebeta| order | 22932 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #26039363⋊C2 |
| unambiguous semidirect product | #26039367⋊C2 |
| unambiguous semidirect product | #26039369⋊C2 |
| derived, Hall | C13×C49 ⋊ C22×C9 |
| Hall | #19153185 ⋊ C22 |
| Hall | D13×D49 ⋊ C9 |
| Sylow | C49 ⋊ C2×D13⋊C9 |
| Sylow | C13 ⋊ C2×D49⋊C9 |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5733 |
Polycyclic presentation:
2^2,3,7,13,3,7|c^3=f,d^7=g^6,e^a=e^12,d^b=d^6g,g^b=g^6,d^c=d^2g^3,e^c=e^3,g^c=g^2240 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22932, 37);