Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C2×C3×B(4,𝔽2) ⋊ C2 |
| Sylow | C3 ⋊ #32899 |
3866 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 3866 conjugacy classes of subgroups — too many to draw. Only its 251 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|d^2=h,b^a=be,c^a=cf,d^a=dg,f^b=fh,e^c=eh,i^d=i^281 conjugacy classes — view the full character table.
| maximal subgroup of | #72271204, D3×#32899, #72271255 |
| maximal normal subgroup of | #72271204, D3×#32899, #72271255 |
| maximal quotient of | #72271277, #72271279, #72271846 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 318342);