Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q8×#737 ⋊ C2 |
| Sylow | #737 ⋊ #41 |
388 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
Polycyclic presentation:
2^3,3,2,3^3|b^2=e,c^2=e,d^3=h,c^a=ce,f^a=f^2,g^a=g^2,c^b=ce,g^f=gh150 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2654);