Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
182 conjugacy classes of subgroups; only the 18 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 18 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^4,3,2^4|a^2=d,b^2=cd,c^2=d,f^2=h,g^2=i,b^a=bc,c^a=cd,e^a=e^2,f^a=fgi,g^a=gi,h^a=hi,f^b=fh,g^b=gi,f^e=gh,g^e=fg,h^e=i,i^e=hi32 conjugacy classes — view the full character table.
| maximal subgroup of | #72213294, #72213885 |
| maximal normal subgroup of | #72213885 |
| maximal quotient of | #72213281 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1085661);