Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| isoclinism | isoclinic class of #10624511⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #10624511⋊C2 |
| Fitting, Sylow | #10624511 ⋊ C2 |
| derived | #6869 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | #6869 | C2×C3 |
| Frattini | C32×C9 | C3×D3 |
| Fitting | #10624511 | C2 |
| socle | C3 | #92174 |
| LCS | G ▷ #6869 | |
| UCS | C1 | |
122 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 81 |
Polycyclic presentation:
2,3^6|b^3=e,e^3=g^2,b^a=b^2e^2g,d^a=d^2fg^2,e^a=e^2g,f^a=fg,g^a=g^2,c^b=cd,d^b=df,f^b=fg,d^c=dg,e^c=eg^242 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 628);