Finite Group DatabasebetaFinite Group Databasebeta| order | 29727 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting | H(3,𝔽3)×C367 ⋊ C3 |
| Sylow | C367 ⋊ AΣL(1,𝔽27) |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3303 |
Polycyclic presentation:
3^4,367|b^a=bc,c^a=cd,e^b=e^2831359 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29727, 28);