Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C3×#1874 ⋊ C2 |
| Sylow | C3 ⋊ #24128 |
1400 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
Polycyclic presentation:
2^8,3|d^2=e,g^2=h,b^a=be,c^a=cf,d^a=de,c^b=cg,g^b=gh,i^b=i^2,d^c=dh,g^c=gh,i^d=i^284 conjugacy classes — view the full character table.
| maximal subgroup of | #72269936, #72269938, D3×#24128 |
| maximal normal subgroup of | #72269936, #72269938, D3×#24128 |
| maximal quotient of | #72271426 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 203606);