Finite Group DatabasebetaFinite Group Databasebeta| order | 15022 |
| isoclinism | isoclinic class of D37 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C29 · Schur multiplier (H2) = C1 |
| direct product | C7×C29×D37 |
| unambiguous semidirect product | C37⋊(C2×C7×C29) |
| Fitting, socle, Hall | C7×C29×C37 ⋊ C2 |
| derived, Sylow | C37 ⋊ C2×C7×C29 |
| Hall | C29×C37 ⋊ C2×C7 |
| Hall | C7×C37 ⋊ C2×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C29 | D37 |
| commutator, cosocle, hypocenter | C37 | C2×C7×C29 |
| Frattini | C1 | G |
| Fitting, socle | C7×C29×C37 | C2 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C7×C29 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7511 |
4060 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×C29×#3866, C7×#16864283, C7×D29×D37, … |
| maximal normal subgroup of | C7×C29×#3866, C7×#16864283, C7×D29×D37, … |
| maximal quotient of | C7×C29×Dic37, C2×C7×C29×D37 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15022, 3);