Finite Group DatabasebetaFinite Group Databasebeta| order | 10138 |
| isoclinism | isoclinic class of D37 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C137 · Schur multiplier (H2) = C1 |
| direct product | D37×C137 |
| unambiguous semidirect product | C37⋊(C2×C137) |
| Fitting, socle, Hall | C37×C137 ⋊ C2 |
| derived, Sylow | C37 ⋊ C2×C137 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C137 | D37 |
| commutator, cosocle, hypocenter | C37 | C2×C137 |
| Frattini | C1 | G |
| Fitting, socle | C37×C137 | C2 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C137 | |
8 conjugacy classes of subgroups.
2740 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C137×#3866, #35202500, D37×D137, … |
| maximal normal subgroup of | C137×#3866, #35202500, D37×D137, … |
| maximal quotient of | C137×Dic37, C2×D37×C137, C3×D37×C137, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10138, 1);