Finite Group DatabasebetaFinite Group Databasebeta| order | 37620 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct 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×D19×D55 | C3 |
| LCS | G ▷ C5×C11×C19 | |
| UCS | C1 ◁ C3 | |
120 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 43 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 9405 |
783 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37620, 58);