Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C3×#1378 ⋊ C2 |
| Sylow | C3 ⋊ #13374 |
360 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 93 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|a^2=d,b^2=d,e^2=g,g^2=h,b^a=bd,c^a=ce,e^a=eg,f^a=fh,g^a=gh,i^a=i^2,c^b=cf,f^b=fh,d^c=dh,e^c=egh,g^c=gh,i^c=i^278 conjugacy classes — view the full character table.
| maximal subgroup of | #72271482, #72271500, #72271503, … |
| maximal normal subgroup of | #72271482, #72271500, #72271503, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 88692);