Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C2×C3×#342 ⋊ C2 |
| Sylow | C3 ⋊ #10745 |
1794 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^8,3|a^2=f,b^2=g,b^a=bd,c^a=ce,d^a=dh,e^b=eh,f^b=fh,d^c=dh,i^c=i^2108 conjugacy classes — view the full character table.
| maximal subgroup of | #72247660, D3×#10745, #72247717 |
| maximal normal subgroup of | #72247660, D3×#10745, #72247717 |
| maximal quotient of | #72247985, #72247987, #72248316, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 74909);