Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C214 |
| direct product | C23×D3×M16 |
| Fitting | C23×C3×M16 ⋊ C2 |
| Sylow | C3 ⋊ C24×M16 |
13310 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
240 conjugacy classes — view the full character table.
| maximal subgroup of | C23×D3×AGL(1,ℤ/8), C22×D3×#418, C22×D3×#407, … |
| maximal normal subgroup of | C23×D3×AGL(1,ℤ/8), C22×D3×#418, C22×D3×#407, … |
| maximal quotient of | C22×D3×#407 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1083323);