Finite Group DatabasebetaFinite Group Databasebeta| order | 18549 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting | 3−1+2×C229 ⋊ C3 |
| Sylow | C229 ⋊ AΣL(1,𝔽27) |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2061 |
Polycyclic presentation:
3^4,229|b^a=bc,c^a=cd,e^a=e^94,e^b=e^134853 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18549, 30);