Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
174 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
Polycyclic presentation:
2^3,3^3,2^2|a^2=c,b^2=c,e^3=f,b^a=bc,d^a=d^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 | #13146198, #13146199, #13146203, … |
| maximal normal subgroup of | #13146198, #13146199, #13146203, … |
| maximal quotient of | #13146942, #13146945, #13146947, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2333);