Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C27 ⋊ Q32 |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 864 |
Polycyclic presentation:
2^5,3^3|a^2=e,b^2=e,c^2=de,d^2=e,f^3=g,g^3=h,b^a=bc,c^a=cd,d^a=de,f^a=f^2g^2h^2,g^a=g^2h^2,h^a=h^2,c^b=cd,d^b=de102 conjugacy classes — view the full character table.
| maximal subgroup of | #13134420, #13134421, Q32×D27, … |
| maximal normal subgroup of | #13134420, #13134421, Q32×D27, … |
| maximal quotient of | #13133985, #13133987, #13134061, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 35);