Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
No aliases for this group.
| Fitting | C22×C3×H(5,𝔽2) ⋊ C2 |
| Sylow | C3 ⋊ #60372 |
5126 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|f^2=h,b^a=bf,c^a=cg,f^a=fh,i^a=i^2,f^b=fh,e^d=eh129 conjugacy classes — view the full character table.
| maximal subgroup of | #72272146, D3×#60372, #72272182 |
| maximal normal subgroup of | #72272146, D3×#60372, #72272182 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1036101);