Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C27 ⋊ M32 |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 432 |
Polycyclic presentation:
2^5,3^3|a^2=c,c^2=d,d^2=e,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 | #13133957, #13133960, #13133983, … |
| maximal normal subgroup of | #13133957, #13133960, #13133983, … |
| maximal quotient of | #13133955, C4⋊(C27⋊C16), #13134045, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 19);