Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| isoclinism | isoclinic class of C3⋊(#6881⋊C2) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊(#6881⋊C2) |
| Fitting, Sylow | C3×#6881 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C3×#733 | C2×C3 |
| Frattini | C3×C9 | C3×C3⋊D3 |
| Fitting | C3×#6881 | C2 |
| socle | C32 | #4178 |
| LCS | G ▷ C3×#733 | |
| UCS | C1 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 81 |
Polycyclic presentation:
2,3^6|c^3=f^2,e^3=g^2,b^a=b^2cef^2g,d^a=d^2,e^a=e^2fg,g^a=g^2,c^b=ce,e^b=ef,f^b=fg,e^c=eg42 conjugacy classes — view the full character table.
| maximal subgroup of | #72222314 |
| maximal normal subgroup of | #72222314 |
| maximal quotient of | #72222268 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1380);