Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C3×#1773 ⋊ C2 |
| Sylow | C3 ⋊ #20512 |
1014 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^8,3|a^2=f,b^2=g,c^2=g,d^2=f,e^2=h,f^2=h,b^a=be,e^a=eh,i^a=i^2,e^b=eh,d^c=dh,i^c=i^2132 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#20512, #72258725 |
| maximal normal subgroup of | D3×#20512, #72258725 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 168153);