Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C3×#1879 ⋊ C2 |
| Sylow | C3 ⋊ #23848 |
2414 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^8,3|e^2=h,b^a=be,c^a=cf,d^a=de,e^a=eh,c^b=cg,e^b=eh,i^b=i^2,i^c=i^2,e^d=eh90 conjugacy classes — view the full character table.
| maximal subgroup of | #72269938, #72269974, D3×#23848, … |
| maximal normal subgroup of | #72269938, #72269974, D3×#23848, … |
| maximal quotient of | #72271472, #72271726 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 200564);