Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of #10620020 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | #737 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #10620020 |
| commutator, hypocenter | #737 | C16 |
| Frattini, socle | C2×C3 | C3⋊AGL(1,𝔽9) |
| Fitting | C2×#737 | C8 |
| prime radical | C2×H(3,𝔽3) | C3⋊C8 |
| cosocle | #10619833 | C2 |
| LCS | G ▷ #737 | |
| UCS | C1 ◁ C2 | |
38 conjugacy classes of subgroups.
| minimal degree | μ(G) = 97 |
| transitive degree | μt(G) = 432 |
Polycyclic presentation:
2^4,3^4|a^2=b,b^2=c,c^2=d,g^3=h,e^a=e^2f^2,f^a=e^2,g^a=g^2h^2,h^a=h^2,e^b=e^2fh^2,f^b=efh,e^c=e^2h^2,f^c=f^2h^2,f^e=fh54 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 1939);