Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | Dic27⋊C8 |
| Sylow | C27 ⋊ C4⋊C8 |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 864 |
Polycyclic presentation:
2^5,3^3|a^2=d,b^2=c,c^2=e,f^3=g,g^3=h,b^a=bd,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 | C8×Dic54, #13134184, #13134192, … |
| maximal normal subgroup of | C8×Dic54, #13134184, #13134192, … |
| maximal quotient of | #13133975, #13133976, Dic27⋊C16, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 22);