Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of C3⋊AGL(1,𝔽9) |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#63725 |
| derived, Sylow | C33 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | C3⋊AGL(1,𝔽9) |
| commutator, hypocenter | C33 | C32 |
| Fitting | C33×C4 | C8 |
| socle, prime radical | C2×C33 | C16 |
| cosocle | C3×#3708 | C2 |
| LCS | G ▷ C33 | |
| UCS | C1 ◁ C4 | |
38 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^5,3^3|a^2=b,b^2=c,c^2=d,d^2=e,f^a=f^2g^2,g^a=fg^2,h^a=h^2,f^b=g^2,g^b=f,f^c=f^2,g^c=g^260 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#63725, #13165056, #13165057, … |
| maximal normal subgroup of | D3×#63725, #13165056, #13165057, … |
| maximal quotient of | C3⋊#10590011, C2×C3⋊#63725 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2668);