Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×C3×#418 ⋊ C2 |
| Sylow | C3 ⋊ #11014 |
1370 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|a^2=g,f^2=h,g^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=fh,i^c=i^290 conjugacy classes — view the full character table.
| maximal subgroup of | #72248370, #72248380, #72248396, … |
| maximal normal subgroup of | #72248370, #72248380, #72248396, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 76312);