Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | C4×C5×Q8 ⋊ Dic3 |
| derived | C5×SL(2,𝔽3) ⋊ C42 |
| Sylow | C5 ⋊ #73063 |
354 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^4,3,5,2^3|a^2=c,b^2=d,g^2=i,h^2=i,b^a=bi,e^a=e^2,f^a=f^2,g^a=gh,h^a=hi,f^c=f^4,g^e=h,h^e=ghi,h^g=hi80 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 238149);