Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C3 ⋊ #22694 |
812 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|a^2=g,c^2=f,e^2=h,f^2=h,g^2=h,b^a=be,c^a=cf,e^a=eh,f^a=fh,i^a=i^2,d^b=de,e^b=eh,e^d=eh114 conjugacy classes — view the full character table.
| maximal subgroup of | #72228271, #72228273, #72228276 |
| maximal normal subgroup of | #72228271, #72228273, #72228276 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 188090);