Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C22×AGL(1,ℤ/8) ⋊ D3 |
1476 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 1476 conjugacy classes of subgroups — too many to draw. Only its 119 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^6,3,2^2|e^2=f,b^a=bf,g^a=g^2,h^a=hi,d^b=df,d^c=de,e^c=ef,e^d=ef,h^g=i,i^g=hi55 conjugacy classes — view the full character table.
| maximal subgroup of | #72258607 |
| maximal normal subgroup of | #72258607 |
| maximal quotient of | #72226291, #72226317, #72258886, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1089321);