Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| isoclinism | isoclinic class of C3⋊D63 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊(C7⋊(C9⋊C8)) |
| unambiguous semidirect product | C7⋊(C3⋊(C9⋊C8)) |
| unambiguous semidirect product | C9⋊(C3⋊(C7⋊C8)) |
| derived, Hall | C3×C7×C9 ⋊ C8 |
| Sylow | C3×C9 ⋊ C7⋊C8 |
| Sylow | C7 ⋊ C3⋊(C9⋊C8) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | C3⋊D63 |
| commutator, hypocenter | C3×C7×C9 | C8 |
| Frattini | C3×C4 | C3⋊D21 |
| Fitting, cosocle | C3×C4×C7×C9 | C2 |
| socle, prime radical | C2×C32×C7 | Dic3 |
| LCS | G ▷ C3×C7×C9 | |
| UCS | C1 ◁ C4 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1512 |
Polycyclic presentation:
2^3,3^2,7,3|a^2=b,b^2=c,e^3=g,d^a=d^2,e^a=e^2g^2,f^a=f^6,g^a=g^2384 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 77);