Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C5⋊#85654 |
| Hall | #10618941 ⋊ C3 |
| Sylow | C5 ⋊ #85654 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C22 | D5×C22⋊A4 |
| commutator, Fitting, cosocle, hypocenter | C5×Q82 | C2×C3 |
| socle | C22×C5 | C2×C22⋊A4 |
| LCS | G ▷ C5×Q82 | |
| UCS | C1 ◁ C22 | |
504 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 640 |
Polycyclic presentation:
2,3,2^4,5,2^2|a^2=i,c^2=i,d^2=i,e^2=i,f^2=i,g^a=g^4,c^b=d,d^b=cd,e^b=f,f^b=ef,d^c=di,e^c=ei,f^c=fhi,e^d=eh,f^d=fi,f^e=fi76 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 239950);