Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C3×C4×#120 ⋊ C2 |
| Sylow | C3 ⋊ #23595 |
1616 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|d^2=e,b^a=be,c^a=cf,g^a=gh,c^b=cg,f^b=fh,i^b=i^2108 conjugacy classes — view the full character table.
| maximal subgroup of | #72271030, #72271042, #72271070, … |
| maximal normal subgroup of | #72271030, #72271042, #72271070, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 198071);