Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #3502 ⋊ D3 |
895 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
Polycyclic presentation:
2^5,3,2^3|c^2=e,d^2=ei,g^2=i,h^2=i,b^a=bi,f^a=f^2,g^a=gh,h^a=hi,d^b=di,d^c=dei,g^f=h,h^f=ghi,h^g=hi59 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1089531);