Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| isoclinism | isoclinic class of #13094935 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, socle, Hall | C33×C7 ⋊ Q8 |
| Sylow | C33 ⋊ Dic14 |
| Sylow | C7 ⋊ C3⋊PSU(3,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, prime radical, cosocle | C3×C7×C3⋊D3 | C22 |
| Fitting, socle, hypocenter | C33×C7 | Q8 |
| LCS | G ▷ C3×C7×C3⋊D3 ▷ C33×C7 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
Polycyclic presentation:
2^3,3^3,7|a^2=c,b^2=c,b^a=bc,d^a=de^2,e^a=d^2e^2,f^a=f^2,g^a=g^6,d^b=e^2,e^b=d,d^c=d^2,e^c=e^266 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 832);