Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C3×#2044 ⋊ C2 |
| Sylow | C3 ⋊ #29637 |
1358 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^8,3|c^2=h,d^2=h,b^a=be,c^a=cf,g^a=gh,c^b=cg,f^b=fh,d^c=de,i^c=i^2,i^d=i^263 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 275293);