Finite Group DatabasebetaFinite Group Databasebeta| order | 10502 |
| automorphism | Aut(G) order 26801104 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D5251 |
| unambiguous semidirect product | C59⋊D89 |
| unambiguous semidirect product | C89⋊D59 |
| Fitting, socle, derived, Hall | C59×C89 ⋊ C2 |
| Sylow | C89 ⋊ D59 |
| Sylow | C59 ⋊ D89 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C59×C89 | C2 |
| LCS | G ▷ C59×C89 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,59,89|b^a=b^58,c^a=c^882627 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D59×D89, C2×D5251, C3×D5251, … |
| maximal normal subgroup of | D59×D89, C2×D5251, C3×D5251 |
| maximal quotient of | Dic5251, C2×D5251, C3×D5251, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10502, 3);