Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | #4427 ⋊ Q8 |
| Sylow | C7 ⋊ 3−1+2⋊Q8 |
78 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 504 |
Polycyclic presentation:
2^2,3,2,3,7,3|a^2=d,b^2=d,e^3=g,b^a=bd,f^a=f^6,e^b=e^2g^2,g^b=g^2,e^c=eg,f^c=f^243 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 99);