Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| isoclinism | isoclinic class of #10624709⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | #10624709⋊C2 |
| Fitting, Sylow | #10624709 ⋊ C2 |
| derived | C3×C27 ⋊ C2×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, hypocenter | C3×C27 | C2×C9 |
| Frattini | C3×C9 | C3×C3⋊D3 |
| Fitting | #10624709 | C2 |
| socle | C3 | C3⋊(D9⋊C9) |
| prime radical | C3⋊(D27⋊C3) | C3 |
| cosocle | C3×C27⋊C3 | C2×C3 |
| LCS | G ▷ C3×C27 | |
| UCS | C1 | |
102 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 81 |
Polycyclic presentation:
2,3^6|b^3=f,c^3=e,d^3=g,e^3=g,c^a=c^2e^2g^2,d^a=d^2g^2,e^a=e^2g^2,g^a=g^2,c^b=ce,e^b=eg,f^c=fg^266 conjugacy classes — view the full character table.
| maximal subgroup of | #72221820, #72221841, #72221842, … |
| maximal normal subgroup of | #72221820, #72221841, #72221842, … |
| maximal quotient of | C2×#10624709⋊C2 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1040);