Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C3×#2957 ⋊ C2 |
| Sylow | C3 ⋊ #60184 |
2604 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|a^2=g,c^2=g,f^2=h,g^2=h,b^a=bf,c^a=ch,f^a=fh,f^b=fh,i^b=i^2,i^c=i^2,e^d=eh,i^e=i^2126 conjugacy classes — view the full character table.
| maximal subgroup of | #72222872, #72222874, #72222878, … |
| maximal normal subgroup of | D3×#60184, #72258527, #72258547, … |
| maximal quotient of | #72222872, #72222874, #72222878 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1033914);