Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #6249⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #6249⋊C4 |
| Sylow | H(3,𝔽3) ⋊ #106 |
70 conjugacy classes of subgroups.
| transitive degree | μt(G) = 108 |
Polycyclic presentation:
2^5,3^3|a^2=c,b^2=d,c^2=e,b^a=bce,f^a=f^2g^2,g^a=f^2h^2,h^a=h^2,c^b=ce,f^b=fg^2h^2,g^b=g^2,h^b=h^2,f^c=f^2g,g^c=fgh^2,f^e=f^2,g^e=g^2h^2,g^f=gh28 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2194);