Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C42 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×C3×M16×AGL(1,𝔽5) |
| Fitting | C2×C3×C5×M16 ⋊ C4 |
| Hall | C3×C5 ⋊ C2×C4×M16 |
| Sylow | C5 ⋊ C2×C3×C4×M16 |
1312 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
300 conjugacy classes. The character table is too large to display.
| maximal subgroup of | M16×AGL(1,𝔽5)×AGL(1,𝔽7), C2×C3×AGL(1,𝔽5)×AGL(1,ℤ/8) |
| maximal normal subgroup of | C2×C3×AGL(1,𝔽5)×AGL(1,ℤ/8) |
| maximal quotient of | M16×AGL(1,𝔽5)×AGL(1,𝔽7) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 136936);