Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27×C4 |
No aliases for this group.
| Sylow | C3 ⋊ #20608 |
3798 conjugacy classes of subgroups; only the 555 normal subgroups are shown.
This group has 3798 conjugacy classes of subgroups — too many to draw. Only its 555 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^8,3|a^2=g,d^2=h,b^a=be,c^a=cf,e^a=eh,i^a=i^2,f^b=fh,g^b=gh,e^c=eh132 conjugacy classes — view the full character table.
| maximal subgroup of | #72271637, D3×#20608, #72271718 |
| maximal normal subgroup of | #72271637, D3×#20608, #72271718 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 168832);