Finite Group DatabasebetaFinite Group Databasebeta| order | 1161 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C32 |
| unambiguous semidirect product | C32⋊(C43⋊C3) |
| unambiguous semidirect product | C43⋊H(3,𝔽3) |
| unambiguous semidirect product | (C3×C43⋊C3)⋊C3 |
| Fitting | C32×C43 ⋊ C3 |
| Sylow | C43 ⋊ H(3,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C3 | C3×C43⋊C3 |
| commutator, socle, cosocle | C3×C43 | C32 |
| Fitting | C32×C43 | C3 |
| hypercenter | C32 | C43⋊C3 |
| hypocenter | C43 | H(3,𝔽3) |
| LCS | G ▷ C3×C43 ▷ C43 | |
| UCS | C1 ◁ C3 ◁ C32 | |
22 conjugacy classes of subgroups.
| transitive degree | μt(G) = 387 |
Polycyclic presentation:
3^3,43|b^a=bc,d^b=d^36137 conjugacy classes — view the full character table.
| maximal subgroup of | #16812507, #16812508, #16812510, … |
| maximal normal subgroup of | #16812507, #16812508, #16812510, … |
| maximal quotient of | (C3×C43⋊C3)⋊C9, C32⋊(C43⋊C9), #16812506, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1161, 9);