Finite Group DatabasebetaFinite Group Databasebeta| order | 37050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52 · Schur multiplier (H2) = C5 |
| direct product | C52×D741 |
| unambiguous semidirect product | C3⋊(C52×D247) |
| unambiguous semidirect product | C13⋊(C52×D57) |
| unambiguous semidirect product | C19⋊(C52×D39) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | D741 |
| commutator, cosocle, hypocenter | C3×C13×C19 | C2×C52 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C13×C19 | C2 |
| LCS | G ▷ C3×C13×C19 | |
| UCS | C1 ◁ C52 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18525 |
9300 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37050, 156);