Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of #4183 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | AΣL(1,𝔽27) ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | #4183 |
| commutator, hypocenter | AΣL(1,𝔽27) | C16 |
| Frattini | C32×C8 | C3⋊D3 |
| Fitting, cosocle | C8×AΣL(1,𝔽27) | C2 |
| socle | C2×C3 | #6180 |
| prime radical | C2×AΣL(1,𝔽27) | C8 |
| LCS | G ▷ AΣL(1,𝔽27) | |
| UCS | C1 ◁ C8 | |
100 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^a=e^2,f^a=f^2,g^a=gh^2,h^a=h^2,f^e=fg,g^f=gh104 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 44);