Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
| direct product | C23×#914 |
| Fitting | C23×C3×SD16 ⋊ C2 |
| Sylow | C3 ⋊ C23×AGL(1,ℤ/8) |
13310 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | C23×D3×AGL(1,ℤ/8), C22×#80146, #72253862, … |
| maximal normal subgroup of | C23×D3×AGL(1,ℤ/8), C22×#80146, #72253862, … |
| maximal quotient of | C22×#80146 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1083361);