Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Fitting | C3×C42×C5 ⋊ C2×C4 |
| Hall | C3×C5 ⋊ C4×#127 |
| Sylow | C5 ⋊ #74319 |
| Sylow | C3 ⋊ AGL(1,𝔽5)×#127 |
1848 conjugacy classes of subgroups; only the 290 normal subgroups are shown.
This group has 1848 conjugacy classes of subgroups — too many to draw. Only its 290 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| 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,i^a=i^2,h^d=h^2,i^d=i^3,i^g=i^4114 conjugacy classes — view the full character table.
| maximal subgroup of | D3×AGL(1,𝔽5)×#127, #72229778, #72231292, … |
| maximal normal subgroup of | D3×AGL(1,𝔽5)×#127, #72229778 |
| maximal quotient of | #72231292, #72231684 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 47987);