Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C2×C3×C82 ⋊ C2 |
| Sylow | C3 ⋊ #19603 |
922 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
Polycyclic presentation:
2^8,3|b^2=e,c^2=fh,d^2=g,e^2=g,f^2=h,b^a=be,c^a=cf,e^a=eg,f^a=fh,i^a=i^2204 conjugacy classes — view the full character table.
| maximal subgroup of | #72225817, #72225820, #72225872, … |
| maximal normal subgroup of | #72225817, #72225820, #72225872, … |
| maximal quotient of | #72225820 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 157269);