Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | GL(2,𝔽3)⋊#170 |
| derived | C5×SL(2,𝔽3) ⋊ C2×C8 |
| Sylow | C5 ⋊ GL(2,𝔽3)⋊C8 |
224 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^4,3,5,2^3|a^2=c,c^2=d,g^2=i,h^2=i,b^a=bi,f^a=f^2,e^b=e^2,g^b=gh,h^b=hi,f^c=f^4,g^e=h,h^e=ghi,h^g=hi68 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 238083);