Finite Group DatabasebetaFinite Group Databasebeta| order | 37050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C13 · Schur multiplier (H2) = C5 |
| direct product | C13×#15668133 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | #15668133 |
| commutator, cosocle, hypocenter | C52×C19 | C2×C3×C13 |
| Frattini | C1 | G |
| Fitting, socle | C52×C13×C19 | C2×C3 |
| LCS | G ▷ C52×C19 | |
| UCS | C1 ◁ C13 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3705 |
1105 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37050, 70);