Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C3×C9 ⋊ Q32 |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^5,3^3|a^2=e,b^2=cd,c^2=de,d^2=e,f^3=h,b^a=bc,c^a=cd,d^a=de,g^a=g^2,f^b=f^2h^2,h^b=h^287 conjugacy classes — view the full character table.
| maximal subgroup of | #13136984, D9×Dic24, #13136989, … |
| maximal normal subgroup of | #13136984, D9×Dic24, #13136989, … |
| maximal quotient of | #13134993, #13135000, #13135055, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 212);