Finite Group DatabasebetaFinite Group Databasebeta| order | 10508 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D37×D71 |
| unambiguous semidirect product | (C71×D37)⋊C2 |
| unambiguous semidirect product | (C37×D71)⋊C2 |
| unambiguous semidirect product | D2627⋊C2 |
| Fitting, socle, derived, Hall | C37×C71 ⋊ C22 |
| Sylow | C71 ⋊ C2×D37 |
| Sylow | C37 ⋊ C2×D71 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C37×C71 | C22 |
| LCS | G ▷ C37×C71 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
740 conjugacy classes — view the full character table.
| maximal subgroup of | D71×D37⋊C3, C3×D37×D71, D71×D111, … |
| maximal normal subgroup of | D71×D37⋊C3, C3×D37×D71 |
| maximal quotient of | C3×D37×D71, D71×D111, D37×D213, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10508, 8);