Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| isoclinism | isoclinic class of #13091281 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, Sylow | #10624833 ⋊ C2 |
| derived | C3×C81 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C3×C81 | C2×C3 |
| Frattini | C27 | C3×C3⋊D3 |
| Fitting | #10624833 | C2 |
| socle | C3 | C3×C3⋊D27 |
| LCS | G ▷ C3×C81 | |
| UCS | C1 | |
85 conjugacy classes of subgroups.
| minimal degree | μ(G) = 243 |
| transitive degree | μt(G) = 243 |
Polycyclic presentation:
2,3^6|b^3=e,e^3=f,f^3=g,b^a=b^2e^2f^2g^2,c^a=cg,d^a=d^2,e^a=e^2f^2g^2,f^a=f^2g^2,g^a=g^2,d^c=dg153 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1355);