Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C3 ⋊ #11012 |
1422 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|a^2=g,f^2=h,b^a=bd,c^a=ce,d^a=dh,i^a=i^2,c^b=cf,f^b=fh,g^b=gh,f^c=fh90 conjugacy classes — view the full character table.
| maximal subgroup of | #72248003, D3×#11012, #72248220, … |
| maximal normal subgroup of | #72248003, D3×#11012, #72248220, … |
| maximal quotient of | #72271545 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 76297);