Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (C22⋊C27)⋊Q8 |
102 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
Polycyclic presentation:
2^3,3^3,2^2|a^2=c,b^2=c,d^3=e,e^3=f,b^a=bc,d^a=d^2e^2f^2,e^a=e^2f^2,f^a=f^2,g^a=h,h^a=g,g^d=h,h^d=gh78 conjugacy classes — view the full character table.
| maximal subgroup of | #13136136, #13136139, #13136152, … |
| maximal normal subgroup of | #13136136, #13136139, #13136152, … |
| maximal quotient of | #13136124, #13136127, #13136129, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 611);