Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C3×C5×H(5,𝔽2) ⋊ C4 |
| Hall | C3×C5 ⋊ #1790 |
| Sylow | C5 ⋊ #72142 |
| Sylow | C3 ⋊ #10605017 |
1340 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 1340 conjugacy classes of subgroups — too many to draw. Only its 157 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=f,b^a=bd,c^a=ce,d^a=dg,h^a=h^2,i^a=i^2,e^b=eg,f^b=fg,d^c=dg,i^f=i^4117 conjugacy classes — view the full character table.
| maximal subgroup of | ΓL(1,𝔽16)×B(4,𝔽2), D3×#10605017, AGL(1,𝔽5)×#5244, … |
| maximal normal subgroup of | ΓL(1,𝔽16)×B(4,𝔽2), D3×#10605017, AGL(1,𝔽5)×#5244 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 22836);