Finite Group DatabasebetaFinite Group Databasebeta| order | 1053 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting | C13×H(3,𝔽3) ⋊ C3 |
| Sylow | C13 ⋊ AΣL(1,𝔽27) |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 117 |
Polycyclic presentation:
3^4,13|b^a=bc,c^a=cd,e^b=e^361 conjugacy classes — view the full character table.
| maximal subgroup of | C13⋊C3×AΣL(1,𝔽27), C3×#11760434, #15691648, … |
| maximal normal subgroup of | C13⋊C3×AΣL(1,𝔽27), C3×#11760434, #15691648, … |
| maximal quotient of | #15691460, #15691463, #15691464, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1053, 28);