Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C3×C5×C22⋊C4 ⋊ C2×C4 |
| Hall | C3×C5 ⋊ C4×#120 |
| Sylow | C5 ⋊ #74379 |
| Sylow | C3 ⋊ AGL(1,𝔽5)×#120 |
2448 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
Polycyclic presentation:
2^7,3,5|a^2=g,d^2=g,b^a=be,c^a=cf,i^a=i^3,h^c=h^2,h^d=h^2,i^d=i^2,i^g=i^4108 conjugacy classes — view the full character table.
| maximal subgroup of | D3×AGL(1,𝔽5)×#120, #72229650, #72260217 |
| maximal normal subgroup of | D3×AGL(1,𝔽5)×#120, #72229650 |
| maximal quotient of | #72229650, #72229778, #72230884, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 47105);