Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C9 |
No aliases for this group.
| Fitting | C8×C92 ⋊ C2 |
| Sylow | C92 ⋊ SD16 |
230 conjugacy classes of subgroups.
| transitive degree | μt(G) = 648 |
Polycyclic presentation:
2^4,3^4|b^2=c,c^2=d,e^3=h,f^3=g,b^a=bc,c^a=cd,e^a=e^2h^2,f^a=f^2g^2,g^a=g^2,h^a=h^2327 conjugacy classes — view the full character table.
| maximal subgroup of | SD16×C9⋊D9, #72244240, #72244273, … |
| maximal normal subgroup of | SD16×C9⋊D9, #72244240, #72244273, … |
| maximal quotient of | #72244084, #72244232, C2×#13046731 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 449);