Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of #10619732 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C92 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #10619732 |
| commutator, hypocenter | C92 | C16 |
| Frattini, socle, prime radical | C2×C32 | AGL(1,𝔽9) |
| Fitting | C2×C92 | C8 |
| cosocle | #10619526 | C2 |
| LCS | G ▷ C92 | |
| UCS | C1 ◁ C2 | |
30 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=g,f^3=h,e^a=e^2f^2h^2,f^a=e^2h,g^a=g^2h^2,h^a=g^2,e^b=e^2fh,f^b=efh^2,g^b=g^2h,h^b=gh,e^c=e^2g^2,f^c=f^2h^2,g^c=g^2,h^c=h^236 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 654);