Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26×C4 |
No aliases for this group.
| Fitting | C2×C3×B(4,𝔽2) ⋊ C2 |
| Sylow | C3 ⋊ #25771 |
2090 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|b^2=e,c^2=f,d^2=e,b^a=be,c^a=cf,d^a=de,g^a=gh,c^b=cg,f^b=fh,i^b=i^2,g^c=gh,i^d=i^275 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#25771, #72270940, #72270945, … |
| maximal normal subgroup of | D3×#25771, #72270940, #72270945, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 224846);