Finite Group DatabasebetaFinite Group Databasebeta| order | 10244 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D13×D197 |
| unambiguous semidirect product | (D13×C197)⋊C2 |
| unambiguous semidirect product | (C13×D197)⋊C2 |
| unambiguous semidirect product | D2561⋊C2 |
| Fitting, socle, derived, Hall | C13×C197 ⋊ C22 |
| Sylow | C197 ⋊ C2×D13 |
| Sylow | C13 ⋊ C2×D197 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C13×C197 | C22 |
| LCS | G ▷ C13×C197 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
800 conjugacy classes — view the full character table.
| maximal subgroup of | D13⋊C3×D197, C3×D13×D197, D39×D197, … |
| maximal normal subgroup of | D13⋊C3×D197, C3×D13×D197 |
| maximal quotient of | C3×D13×D197, D39×D197, D13×D591, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10244, 12);