Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| isoclinism | isoclinic class of (C3⋊D3)⋊ΓL(1,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C8 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | (C3⋊(C3⋊C8))⋊ΓL(1,𝔽8) |
| derived | C32×C7 ⋊ C3×C8 |
| Hall | C7⋊H(3,𝔽3) ⋊ C8 |
| Sylow | C7 ⋊ (C3⋊(C3⋊C8))⋊C3 |
68 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 504 |
Polycyclic presentation:
2,3,2^2,3^2,7|a^2=c,c^2=d,e^a=e^2,f^a=f^2,e^b=ef,g^b=g^288 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 52);