Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×C3×#413 ⋊ C2 |
| Sylow | C3 ⋊ #23521 |
1454 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|c^2=e,e^2=h,b^a=be,c^a=cf,d^a=dh,e^a=eh,c^b=cg,e^b=eh,i^b=i^2,f^c=fh,g^c=gh90 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#23521, #72253368, #72253376, … |
| maximal normal subgroup of | D3×#23521, #72253368, #72253376, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 197378);