Finite Group DatabasebetaFinite Group Databasebeta| order | 10138 |
| isoclinism | isoclinic class of D137 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C37 · Schur multiplier (H2) = C1 |
| direct product | C37×D137 |
| unambiguous semidirect product | C137⋊(C2×C37) |
| Fitting, socle, Hall | C37×C137 ⋊ C2 |
| derived, Sylow | C137 ⋊ C2×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C37 | D137 |
| commutator, cosocle, hypocenter | C137 | C2×C37 |
| Frattini | C1 | G |
| Fitting, socle | C37×C137 | C2 |
| LCS | G ▷ C137 | |
| UCS | C1 ◁ C37 | |
8 conjugacy classes of subgroups.
2590 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C37×#10587739, #35202501, D37×D137, … |
| maximal normal subgroup of | C37×#10587739, #35202501, D37×D137, … |
| maximal quotient of | C37×Dic137, C2×C37×D137, C3×C37×D137, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10138, 2);