Finite Group DatabasebetaFinite Group Databasebeta| order | 1161 |
| isoclinism | isoclinic class of C43⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C43⋊C27 |
| derived, Sylow | C43 ⋊ C27 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C9 | C43⋊C3 |
| commutator, hypocenter | C43 | C27 |
| Fitting, cosocle | C9×C43 | C3 |
| socle, prime radical | C3×C43 | C9 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C9 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 70 |
| transitive degree | μt(G) = 1161 |
Polycyclic presentation:
3^3,43|a^3=b,b^3=c,d^a=d^36153 conjugacy classes — view the full character table.
| maximal subgroup of | C27×C43⋊C3, C3×C43⋊C27, #16812503, … |
| maximal normal subgroup of | C27×C43⋊C3, C3×C43⋊C27, #16812503, … |
| maximal quotient of | C43⋊C81, C3×C43⋊C27 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1161, 6);