Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| isoclinism | isoclinic class of #10624453⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | #10624453⋊C2 |
| Fitting, derived, Sylow | #10624453 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | #10624453 | C2 |
| Frattini | C32×C9 | C3⋊D3 |
| socle | C32 | #4181 |
| LCS | G ▷ #10624453 | |
| UCS | C1 | |
123 conjugacy classes of subgroups.
| transitive degree | μt(G) = 243 |
Polycyclic presentation:
2,3^6|b^3=e,e^3=f,b^a=b^2e^2f^2,c^a=c^2,d^a=df^2g^2,e^a=e^2f^2,f^a=f^2,g^a=g^2,c^b=cd,d^b=df,d^c=dg57 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 532);