Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| isoclinism | isoclinic class of C3⋊D3×AGL(1,𝔽7) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| derived | C32×C7 ⋊ C2×C3×C4 |
| Hall | C32×ΓL(1,𝔽8) ⋊ C2×C4 |
| Sylow | C7 ⋊ C3×C4×C3⋊D3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊D3×AGL(1,𝔽7) |
| commutator, hypocenter | C32×C7 | C2×C3×C4 |
| Fitting, socle, cosocle | C2×C32×C7 | C22×C3 |
| prime radical | C2×C3⋊(C3⋊AGL(1,𝔽7)) | C2 |
| LCS | G ▷ C32×C7 | |
| UCS | C1 ◁ C2 | |
240 conjugacy classes of subgroups.
| transitive degree | μt(G) = 252 |
Polycyclic presentation:
2^2,3,2,3^2,7|a^2=d,b^2=d,g^a=g^6,e^b=e^2,f^b=f^2,g^c=g^284 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 610);