Finite Group DatabasebetaFinite Group Databasebeta| order | 18228 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C31×C49 ⋊ C3×C4 |
| Hall | C31×Dic49 ⋊ C3 |
| Hall | #17986946 ⋊ C4 |
| Hall | Dic49 ⋊ C31⋊C3 |
| Sylow | C49 ⋊ C4×C31⋊C3 |
| Sylow | C31 ⋊ (C49⋊C3)⋊C4 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6076 |
Polycyclic presentation:
2,3,7,31,2,7|a^2=e,c^7=f^6,c^a=c^6f,f^a=f^6,c^b=c^4f^5,d^b=d^5,f^b=f^4548 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18228, 11);