Finite Group DatabasebetaFinite Group Databasebeta| order | 10526 |
| automorphism | Aut(G) order 26146584 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D5263 |
| unambiguous semidirect product | C19⋊D277 |
| unambiguous semidirect product | C277⋊D19 |
| Fitting, socle, derived, Hall | C19×C277 ⋊ C2 |
| Sylow | C277 ⋊ D19 |
| Sylow | C19 ⋊ D277 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C19×C277 | C2 |
| LCS | G ▷ C19×C277 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,19,277|b^a=b^18,c^a=c^2762633 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D19×D277, C2×D5263, C3×D5263, … |
| maximal normal subgroup of | D19×D277, C2×D5263, C3×D5263, … |
| maximal quotient of | Dic5263, C2×D5263, C3×D5263, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10526, 3);