Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of #11751554 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C4 |
No aliases for this group.
| derived | C5×C42⋊C3 ⋊ C8 |
| Sylow | C5 ⋊ #67999 |
102 conjugacy classes of subgroups; only the 20 normal subgroups are shown.
This group has 102 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.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^3,3,5,2^4|a^2=b,b^2=c,f^2=h,g^2=i,d^a=d^2,e^a=e^2,f^a=fg,g^a=ghi,h^a=hi,e^b=e^4,f^b=fh,g^b=gi,f^d=gh,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, 237282);