Finite Group DatabasebetaFinite Group Databasebeta| order | 10502 |
| isoclinism | isoclinic class of D59 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C89 · Schur multiplier (H2) = C1 |
| direct product | C89×D59 |
| unambiguous semidirect product | C59⋊(C2×C89) |
| Fitting, socle, Hall | C59×C89 ⋊ C2 |
| derived, Sylow | C59 ⋊ C2×C89 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C89 | D59 |
| commutator, cosocle, hypocenter | C59 | C2×C89 |
| Frattini | C1 | G |
| Fitting, socle | C59×C89 | C2 |
| LCS | G ▷ C59 | |
| UCS | C1 ◁ C89 | |
8 conjugacy classes of subgroups.
2759 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D59×D89, C2×C89×D59, C3×C89×D59, … |
| maximal normal subgroup of | D59×D89, C2×C89×D59, C3×C89×D59 |
| maximal quotient of | C89×Dic59, C2×C89×D59, C3×C89×D59, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10502, 1);