Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of #13049185 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, Sylow | C32×C9 ⋊ SD16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle | C9×#157 | C22 |
| Frattini | C3 | #89092 |
| Fitting, hypocenter | C32×C9 | SD16 |
| socle | C33 | #215 |
| prime radical | #157⋊D9 | C2 |
| LCS | G ▷ C9×#157 ▷ C9×C3⋊D3 ▷ C32×C9 | |
| UCS | C1 | |
83 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2^4,3^4|b^2=d,c^2=d,g^3=h^2,b^a=bcd,c^a=cd,e^a=e^2f,g^a=g^2h,h^a=h^2,c^b=cd,e^b=f^2,f^b=e,e^c=ef^2,f^c=e^2f^2,e^d=e^2,f^d=f^233 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2903);