Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of #11751559 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived | C5×C22⋊A4 ⋊ C8 |
| Sylow | C5 ⋊ #67998 |
162 conjugacy classes of subgroups; only the 20 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 20 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:
2^3,3,5,2^4|a^2=b,b^2=c,d^a=d^2,e^a=e^2,f^a=fgi,g^a=gh,h^a=hi,e^b=e^4,f^b=fh,g^b=gi,f^d=g,g^d=fg,h^d=i,i^d=hi38 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 237288);