Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of C9⋊D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C9 |
| unambiguous semidirect product | C9⋊(C9⋊C16) |
| derived, Sylow | C92 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | C9⋊D9 |
| commutator, hypocenter | C92 | C16 |
| Frattini | C32×C8 | C3⋊D3 |
| Fitting, cosocle | C8×C92 | C2 |
| socle, prime radical | C2×C32 | C3⋊(C3⋊C8) |
| LCS | G ▷ C92 | |
| UCS | C1 ◁ C8 | |
115 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1296 |
Polycyclic presentation:
2^4,3^4|a^2=b,b^2=c,c^2=d,e^3=h,f^3=g,e^a=e^2h^2,f^a=f^2g^2,g^a=g^2,h^a=h^2336 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 41);