Finite Group DatabasebetaFinite Group Databasebeta| order | 37538 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C137 |
| unambiguous semidirect product | C137⋊D137 |
| Fitting, socle, derived, Sylow | C1372 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C1372 | C2 |
| LCS | G ▷ C1372 | |
| UCS | C1 | |
280 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18769 |
Polycyclic presentation:
2,137^2|b^a=b^136,c^a=c^1369386 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37538, 4);