Finite Group DatabasebetaFinite Group Databasebeta| order | 37620 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D55⋊(#4294⋊C2) |
| unambiguous semidirect product | (C5⋊(#4294⋊C2))⋊D11 |
| unambiguous semidirect product | (C11⋊(#4294⋊C2))⋊D5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | D55⋊(D19⋊C3) |
| commutator, hypocenter | C5×C11×C19 | C22×C9 |
| Fitting, socle, cosocle | C3×C5×C11×C19 | C22×C3 |
| prime radical | C3×D55⋊D19 | C3 |
| LCS | G ▷ C5×C11×C19 | |
| UCS | C1 ◁ C3 | |
120 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 9405 |
Polycyclic presentation:
2^2,3,5,11,19,3|c^3=g,e^a=e^10,f^a=f^18,d^b=d^4,e^b=e^10,f^c=f^7513 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37620, 61);