Finite Group DatabasebetaFinite Group Databasebeta| order | 1053 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C13 ⋊ C27⋊C3 |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 351 |
Polycyclic presentation:
3^4,13|a^3=c,c^3=d,b^a=bd,e^a=e^3141 conjugacy classes — view the full character table.
| maximal subgroup of | #15691491, #15691492, #15691500, … |
| maximal normal subgroup of | #15691491, #15691492, #15691500, … |
| maximal quotient of | #15691482, C32⋊(C13⋊C27), #15691507, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1053, 27);