Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27×C4 |
No aliases for this group.
| Fitting | C2×C3×#390 ⋊ C2 |
| Sylow | C3 ⋊ #13937 |
4470 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
Polycyclic presentation:
2^8,3|a^2=h,d^2=g,b^a=be,c^a=cf,d^a=de,c^b=cg,i^b=i^2,i^d=i^2132 conjugacy classes — view the full character table.
| maximal subgroup of | #72271044, #72271048, D3×#13937, … |
| maximal normal subgroup of | #72271044, #72271048, D3×#13937, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 92086);