Finite Group DatabasebetaFinite Group Databasebeta| order | 1053 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C13×C27 ⋊ C3 |
| Sylow | C13 ⋊ C27⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C9 | C3×C13⋊C3 |
| commutator, socle | C3×C13 | C3×C9 |
| Fitting | C13×C27 | C3 |
| prime radical | C3×C13⋊C3 | C9 |
| cosocle | C9×C13 | C32 |
| hypercenter | C27 | C13⋊C3 |
| hypocenter | C13 | C27⋊C3 |
| LCS | G ▷ C3×C13 ▷ C13 | |
| UCS | C1 ◁ C9 ◁ C27 | |
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^b=e^9141 conjugacy classes — view the full character table.
| maximal subgroup of | C13⋊C3×C27⋊C3, C3×#11760432, #15691630, … |
| maximal normal subgroup of | C13⋊C3×C27⋊C3, C3×#11760432, #15691630, … |
| maximal quotient of | #15691481, (C3×C13⋊C3)⋊C27, (C13⋊C9)⋊C27, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1053, 26);