Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C22 |
No aliases for this group.
271 conjugacy classes of subgroups; only the 23 normal subgroups are shown.
This group has 271 conjugacy classes of subgroups — too many to draw. Only its 23 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
Polycyclic presentation:
2^3,3^3,2^2|b^2=c,b^a=bc,e^a=e^2,f^a=f^2,d^b=d^2,f^b=f^2,g^b=h,h^b=g,e^d=ef,g^d=h,h^d=gh34 conjugacy classes — view the full character table.
| maximal subgroup of | #13164170, #13164175, #13164176, … |
| maximal normal subgroup of | #13164170, #13164175, #13164176, … |
| maximal quotient of | #13146287, #13146290, #13146291, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2238);