Finite Group DatabasebetaFinite Group Databasebeta| order | 19082 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C47 · Schur multiplier (H2) = C1 |
| direct product | C47×D203 |
| unambiguous semidirect product | C7⋊(C47×D29) |
| unambiguous semidirect product | C29⋊(D7×C47) |
| Fitting, socle, Hall | C7×C29×C47 ⋊ C2 |
| derived, Hall | C7×C29 ⋊ C2×C47 |
| Hall | C29×C47 ⋊ D7 |
| Hall | C7×C47 ⋊ D29 |
| Sylow | C29 ⋊ D7×C47 |
| Sylow | C7 ⋊ C47×D29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C47 | D203 |
| commutator, cosocle, hypocenter | C7×C29 | C2×C47 |
| Frattini | C1 | G |
| Fitting, socle | C7×C29×C47 | C2 |
| LCS | G ▷ C7×C29 | |
| UCS | C1 ◁ C47 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9541 |
4841 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D47×D203, D7×C47×D29, D203⋊D47, … |
| maximal normal subgroup of | D47×D203, D7×C47×D29, D203⋊D47, … |
| maximal quotient of | C47×Dic203, C2×C47×D203 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19082, 8);