Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C27 ⋊ C4⋊Q8 |
136 conjugacy classes of subgroups.
| transitive degree | μt(G) = 864 |
Polycyclic presentation:
2^5,3^3|a^2=d,b^2=e,c^2=d,f^3=g,g^3=h,c^a=cd,f^a=f^2g^2h^2,g^a=g^2h^2,h^a=h^2,c^b=ce144 conjugacy classes — view the full character table.
| maximal subgroup of | #13134261, #13134263, #13134264, … |
| maximal normal subgroup of | #13134261, #13134263, #13134264, … |
| maximal quotient of | #13134153, #13134157, #13134161, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 104);