Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×C3×#442 ⋊ C2 |
| Sylow | C3 ⋊ #23573 |
1508 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
Polycyclic presentation:
2^8,3|d^2=e,f^2=h,b^a=be,c^a=cf,f^a=fh,c^b=cg,i^b=i^2,d^c=dh,f^c=fh96 conjugacy classes — view the full character table.
| maximal subgroup of | #72269938, D3×#23573, #72269976, … |
| maximal normal subgroup of | #72269938, D3×#23573, #72269976, … |
| maximal quotient of | #72271532, #72271643, #72271651 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 197789);