Finite Group DatabasebetaFinite Group Databasebeta| order | 10244 |
| automorphism | Aut(G) order 12046944 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D5122 |
| direct product | C2×D2561 |
| unambiguous semidirect product | (C2×C13)⋊D197 |
| unambiguous semidirect product | (C2×C197)⋊D13 |
| Fitting, socle | C2×C13×C197 ⋊ C2 |
| derived, Hall | C13×C197 ⋊ C22 |
| Sylow | C197 ⋊ C2×D13 |
| Sylow | C13 ⋊ C2×D197 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D2561 |
| commutator, cosocle, hypocenter | C13×C197 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C13×C197 | C2 |
| LCS | G ▷ C13×C197 | |
| UCS | C1 ◁ C2 | |
20 conjugacy classes of subgroups.
2564 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×(C13⋊C3)⋊D197, D3×D2561, C2×C3×D2561, … |
| maximal normal subgroup of | C2×(C13⋊C3)⋊D197, C2×C3×D2561, D10244 |
| maximal quotient of | D3×D2561, C2×C3×D2561, C2×D7683, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10244, 13);