Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of C5⋊#85547 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | C5⋊#85547 |
| Fitting | C22×C42×C5 ⋊ D3 |
| derived | C5×C22⋊(C42⋊C3) ⋊ C2 |
| Sylow | C5 ⋊ #85547 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C5×C22⋊(C42⋊C3) | C2 |
| Frattini | C22 | C5⋊#1020 |
| Fitting | C22×C42×C5 | D3 |
| socle | C24×C5 | S4 |
| LCS | G ▷ C5×C22⋊(C42⋊C3) | |
| UCS | C1 | |
320 conjugacy classes of subgroups; only the 19 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 19 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:
2,3,5,2^6|f^2=h,g^2=i,b^a=b^2,c^a=c^4,d^a=de,f^a=fgi,g^a=gi,h^a=hi,d^b=e,e^b=de,f^b=gh,g^b=fg,h^b=i,i^b=hi72 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 239647);