Finite Group DatabasebetaFinite Group Databasebeta| order | 5546 |
| isoclinism | isoclinic class of D59 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C47 · Schur multiplier (H2) = C1 |
| direct product | C47×D59 |
| unambiguous semidirect product | C59⋊(C2×C47) |
| Fitting, socle, Hall | C47×C59 ⋊ C2 |
| derived, Sylow | C59 ⋊ C2×C47 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C47 | D59 |
| commutator, hypocenter | C59 | C2×C47 |
| Frattini | C1 | G |
| Fitting, socle | C47×C59 | C2 |
| LCS | G ▷ C59 | |
| UCS | C1 ◁ C47 | |
8 conjugacy classes of subgroups.
1457 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D47×D59, C2×C47×D59, C3×C47×D59, … |
| maximal normal subgroup of | D47×D59, C2×C47×D59, C3×C47×D59, … |
| maximal quotient of | C47×Dic59, C2×C47×D59, C3×C47×D59, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5546, 2);