Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
1084 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 1084 conjugacy classes of subgroups — too many to draw. Only its 59 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:
2^6,3,2^2|a^2=f,e^2=f,b^a=be,c^a=cd,e^a=ef,g^a=g^2,h^a=hi,d^b=df,e^b=ef,e^c=ef,h^g=i,i^g=hi49 conjugacy classes — view the full character table.
| maximal subgroup of | #72227841 |
| maximal quotient of | #72268159, #72271321, #72271682, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1088334);