Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Fitting | C2×C3×C5×D4 ⋊ C2×C4 |
| Hall | C3×C5 ⋊ C4×#127 |
| Sylow | C5 ⋊ #76293 |
| Sylow | C3 ⋊ AGL(1,𝔽5)×#127 |
1848 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^7,3,5|a^2=g,b^2=e,c^2=f,d^2=g,b^a=be,c^a=cf,h^a=h^2,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)×#127, #72229732, #72229797, … |
| maximal normal subgroup of | D3×AGL(1,𝔽5)×#127, #72229732, #72229797, … |
| maximal quotient of | #72231313, #72231689 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 47986);