Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C2×C3×#458 ⋊ C2 |
| Sylow | C3 ⋊ #23903 |
2096 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|b^a=be,c^a=cf,d^a=deh,i^a=i^2,c^b=cg,f^b=fh,i^b=i^2,e^c=eh,f^d=fh72 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#23903, #72248277, #72270620, … |
| maximal normal subgroup of | D3×#23903, #72248277, #72270620, … |
| maximal quotient of | #72247581 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 201179);