Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | C27⋊#95 |
| Sylow | C27 ⋊ #95 |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 864 |
Polycyclic presentation:
2^5,3^3|a^2=c,b^2=d,f^3=g,g^3=h,b^a=be,f^a=f^2g^2h^2,g^a=g^2h^2,h^a=h^2228 conjugacy classes — view the full character table.
| maximal subgroup of | #13133964, #13133966, #13134033, … |
| maximal normal subgroup of | #13133964, #13133966, #13134033, … |
| maximal quotient of | #13134019, #13134020, #13134022, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 38);