Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Hall | C7⋊H(3,𝔽3) ⋊ Q8 |
| Sylow | C7 ⋊ #634⋊C3 |
96 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 504 |
Polycyclic presentation:
2^2,3,2,3^2,7|a^2=d,b^2=d,b^a=bd,g^a=g^6,e^b=e^2,f^b=f^2,e^c=ef,g^c=g^243 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 125);