Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×#1786 ⋊ C2 |
| Sylow | C3 ⋊ #9922 |
1278 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 1278 conjugacy classes of subgroups — too many to draw. Only its 113 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=g,d^2=g,b^a=bd,c^a=ce,d^a=dg,f^a=fh,i^a=i^2,c^b=cf,d^b=dg,d^c=dh,i^c=i^278 conjugacy classes — view the full character table.
| maximal subgroup of | #72255459, #72255463, D3×#9922 |
| maximal normal subgroup of | #72255459, #72255463, D3×#9922 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 69821);