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×#344 ⋊ C2 |
| Sylow | C3 ⋊ #11036 |
1310 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^8,3|a^2=g,d^2=h,f^2=h,b^a=bd,c^a=ce,d^a=dh,f^a=fh,i^a=i^2,c^b=cf,d^b=dh,e^b=eh,f^b=fh,i^b=i^2,f^c=fh,i^c=i^290 conjugacy classes — view the full character table.
| maximal subgroup of | #72248194, D3×#11036, #72248218 |
| maximal normal subgroup of | #72248194, D3×#11036, #72248218 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 76456);