Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×#3150 ⋊ C2 |
| Sylow | C3 ⋊ #13340 |
552 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 101 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=gh,e^2=g,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=egh,f^a=fh,g^a=gh,i^a=i^2,c^b=cf,d^b=dg,e^b=eg,g^b=gh,d^c=dgh,e^c=egh,g^c=gh66 conjugacy classes — view the full character table.
| maximal subgroup of | #72271687, #72271696, #72271704 |
| maximal normal subgroup of | #72271687, #72271696, #72271704 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 88492);