Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of #66343 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C9 |
No aliases for this group.
| derived, Sylow | C92 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #66343 |
| commutator, hypocenter | C92 | C16 |
| Frattini | C32×C4 | #157 |
| Fitting | C4×C92 | C4 |
| socle, prime radical | C2×C32 | #622 |
| cosocle | C9⋊(C9⋊C8) | C2 |
| LCS | G ▷ C92 | |
| UCS | C1 ◁ C4 | |
55 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^4,3^4|a^2=b,b^2=c,c^2=d,e^3=h,f^3=g,e^a=efg^2,f^a=ef^2g^2,g^a=g^2h,h^a=gh,e^b=e^2h^2,f^b=f^2g^2,g^b=g^2,h^b=h^296 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 77);