Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Hall | C3×C5 ⋊ C4×#100 |
| Sylow | C5 ⋊ Dic3×#100 |
| Sylow | C3 ⋊ AGL(1,𝔽5)×#100 |
720 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 720 conjugacy classes of subgroups — too many to draw. Only its 140 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
Polycyclic presentation:
2^7,3,5|a^2=e,b^2=f,c^2=e,f^2=g,b^a=bd,f^a=fg,h^a=h^2,i^a=i^3,d^b=dg,h^b=h^2,h^c=h^2,i^c=i^2,i^e=i^487 conjugacy classes — view the full character table.
| maximal subgroup of | #72229797, D3×AGL(1,𝔽5)×#100, #72230866 |
| maximal normal subgroup of | #72229797, D3×AGL(1,𝔽5)×#100, #72230866 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 21153);