Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C3 ⋊ #11389 |
836 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|a^2=g,b^2=f,c^2=f,e^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eh,f^a=fh,i^a=i^2,c^b=cf,d^b=dh,g^b=gh,i^b=i^2,d^c=dh90 conjugacy classes — view the full character table.
| maximal subgroup of | #72271749, #72271774, D3×#11389 |
| maximal normal subgroup of | #72271749, #72271774, D3×#11389 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 78514);