Finite Group DatabasebetaFinite Group Databasebeta| order | 35868 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C49×C61 ⋊ C3×C4 |
| Hall | Dic2989 ⋊ C3 |
| Hall | #22582218 ⋊ C4 |
| Sylow | C61 ⋊ (C49⋊C3)⋊C4 |
| Sylow | C49 ⋊ Dic61⋊C3 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11956 |
Polycyclic presentation:
2,3,7,61,2,7|a^2=e,c^7=f^6,c^a=c^6f,d^a=d^60,f^a=f^6,c^b=c^2f^3,d^b=d^47,f^b=f^21008 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35868, 23);