Finite Group DatabasebetaFinite Group Databasebeta| order | 37620 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| direct product | #4296×Dic55 |
| unambiguous semidirect product | C11⋊(Dic5×#4296) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D55×#4296 |
| commutator, hypocenter | C5×C11×C19 | C4×C9 |
| Fitting, socle | C2×C5×C11×C19 | C2×C9 |
| prime radical, cosocle | C2×C5×C11×C19⋊C3 | C2×C3 |
| LCS | G ▷ C5×C11×C19 | |
| UCS | C1 ◁ C2 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4180 |
638 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37620, 157);