Finite Group DatabasebetaFinite Group Databasebeta| order | 37620 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| direct product | #4294×C11⋊AGL(1,𝔽5) |
| unambiguous semidirect product | C11⋊(AGL(1,𝔽5)×#4294) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C19⋊C3×C11⋊AGL(1,𝔽5) |
| commutator, hypocenter | C5×C11×C19 | C4×C9 |
| Fitting, socle | C3×C5×C11×C19 | C3×C4 |
| prime radical, cosocle | C3×D5×C11×C19 | C2×C3 |
| LCS | G ▷ C5×C11×C19 | |
| UCS | C1 ◁ C3 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9405 |
675 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37620, 56);