Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C3×#1462 ⋊ C2 |
| Sylow | C3 ⋊ #18162 |
1704 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^8,3|e^2=g,b^a=be,c^a=cf,e^a=eg,i^a=i^2,d^b=dg,e^b=eg,f^b=fh,i^b=i^2,e^c=eh72 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#18162, #72252292, #72252299, … |
| maximal normal subgroup of | D3×#18162, #72252292, #72252299 |
| maximal quotient of | #72252345, #72255489 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 142200);