Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C3×#3414 ⋊ C2 |
| Sylow | C3 ⋊ #33533 |
1102 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|d^2=h,e^2=gh,g^2=h,b^a=be,c^a=cf,e^a=eg,g^a=gh,e^b=eg,f^b=fh,g^b=gh,d^c=dh,e^c=eh,i^c=i^272 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#33533, #72270647, #72270649, … |
| maximal normal subgroup of | D3×#33533, #72270647, #72270649, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 323481);