Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C3×#361 ⋊ C2 |
| Sylow | C3 ⋊ #33471 |
668 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|a^2=f,c^2=fgh,d^2=h,e^2=g,g^2=h,b^a=be,c^a=cg,e^a=eg,g^a=gh,i^a=i^2,e^b=egh,f^b=fh,g^b=gh,i^b=i^2,d^c=dh,e^c=eh,i^c=i^278 conjugacy classes — view the full character table.
| maximal subgroup of | #72222799, #72222819, C3×#10948665, … |
| maximal normal subgroup of | C3×#10948665, #72228227, D3×#33471, … |
| maximal quotient of | #72222799, #72222819, C3×#10948665 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 323046);