Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C9×#126 ⋊ C3 |
| Sylow | #126 ⋊ 3−1+2 |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2,3^3,2^4|c^3=d,e^2=h,f^2=g,e^a=egh,f^a=fh,c^b=cd,e^b=ef,f^b=eg,g^b=h,h^b=gh58 conjugacy classes — view the full character table.
| maximal subgroup of | #13147117, #13147121, C2×#11721332, … |
| maximal normal subgroup of | #13147117, #13147121, C2×#11721332, … |
| maximal quotient of | #13141190, #13141200, #13141205, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1299);