Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | C9×#127 ⋊ C3 |
| Sylow | #127 ⋊ 3−1+2 |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 108 |
Polycyclic presentation:
2,3^3,2^4|c^3=d,e^2=h,f^2=g,e^a=eh,f^a=fg,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 | D9⋊(#127⋊C3), #13147125, C2×#11721335, … |
| maximal normal subgroup of | D9⋊(#127⋊C3), #13147125, C2×#11721335, … |
| maximal quotient of | #13141192, #13141194, #13141203, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1302);