Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | H(3,𝔽3) ⋊ #125 |
100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^5,3^3|a^2=d,b^2=de,c^2=e,b^a=bd,c^a=ce,f^a=f^2g^2h,g^a=f^2g,f^b=fg^2h^2,g^b=f^2g^2,f^d=f^2h,g^d=g^2h^2,g^f=gh46 conjugacy classes — view the full character table.
| maximal subgroup of | #13146711, #13146712, #13146715, … |
| maximal normal subgroup of | #13146711, #13146712, #13146715, … |
| maximal quotient of | #13146716, #13146727, #13146729, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2284);