Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C42 |
No aliases for this group.
| Fitting | C3×#1964 ⋊ C2 |
| Sylow | C3 ⋊ #21793 |
1882 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|a^2=g,b^2=e,b^a=be,c^a=cf,d^a=de,f^a=fh,c^b=ce,g^c=gh,i^d=i^284 conjugacy classes — view the full character table.
| maximal subgroup of | #72271026, #72271032, #72271054, … |
| maximal normal subgroup of | #72271026, #72271032, #72271054, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 178821);