Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | (C2×D27)⋊C8 |
| Fitting | C2×C8×C27 ⋊ C2 |
| Sylow | C27 ⋊ C22⋊C8 |
100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 432 |
Polycyclic presentation:
2^5,3^3|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 | #13134192, C8×D108, #13134195, … |
| maximal normal subgroup of | #13134192, C8×D108, #13134195, … |
| maximal quotient of | #13133958, #13133959, #13133963, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 27);