Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×C3×#361 ⋊ C2 |
| Sylow | C3 ⋊ #33392 |
1154 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|a^2=f,e^2=g,f^2=h,g^2=h,b^a=be,e^a=eg,g^a=gh,e^b=egh,f^b=fh,g^b=gh,d^c=dh,i^d=i^290 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10948150, #72222835, #72222848, … |
| maximal normal subgroup of | C3×#10948150, #72228227, D3×#33392, … |
| maximal quotient of | C3×#10948150, #72222835, #72222848 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 322531);