Finite Group DatabasebetaFinite Group Databasebeta| order | 12231 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting | H(3,𝔽3)×C151 ⋊ C3 |
| Sylow | C151 ⋊ AΣL(1,𝔽27) |
40 conjugacy classes of subgroups.
Polycyclic presentation:
3^4,151|b^a=bc,c^a=cd,e^b=e^32567 conjugacy classes — view the full character table.
| maximal subgroup of | AΣL(1,𝔽27)×C151⋊C3, C3×#27133553, #49144570, … |
| maximal normal subgroup of | AΣL(1,𝔽27)×C151⋊C3, C3×#27133553, #49144570, … |
| maximal quotient of | #49144382, #49144385, #49144386, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12231, 28);