Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of #14512455 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C5×#127 ⋊ Dic3 |
| derived | C5×C42⋊C3 ⋊ C2×C4 |
| Sylow | C5 ⋊ #73083 |
336 conjugacy classes of subgroups; only the 27 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 27 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 60 |
Polycyclic presentation:
2^3,3,5,2^4|a^2=c,f^2=h,g^2=i,d^a=d^2,e^a=e^2,f^a=fg,g^a=gi,h^a=hi,f^b=fh,g^b=gi,e^c=e^4,f^d=ghi,g^d=fgh,h^d=i,i^d=hi38 conjugacy classes — view the full character table.
| maximal subgroup of | #72221473, #72243733, #72253377, … |
| maximal normal subgroup of | #72243733, #72253377, AGL(1,𝔽5)×#857⋊C2 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 238153);