Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
163 conjugacy classes of subgroups; only the 29 normal subgroups are shown.
This group has 163 conjugacy classes of subgroups — too many to draw. Only its 29 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2^3,3^3,2^2|a^2=c,b^2=c,d^3=f,b^a=bc,e^a=e^2,d^b=d^2f^2,f^b=f^2,g^b=h,h^b=g,g^d=h,h^d=gh48 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2228);