Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #12659 |
346 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 143 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=e,b^2=f,c^2=de,f^2=g,g^2=h,b^a=bd,f^a=fh,c^b=cg,d^b=dh,f^c=fh,i^c=i^2108 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#12659, #72258707, #72258722 |
| maximal normal subgroup of | D3×#12659, #72258707, #72258722 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 84901);