Finite Group DatabasebetaFinite Group Databasebeta| order | 19082 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C47 · Schur multiplier (H2) = C1 |
| direct product | C47×D29⋊C7 |
| unambiguous semidirect product | D29⋊(C7×C47) |
| unambiguous semidirect product | (C29⋊C7)⋊(C2×C47) |
| unambiguous semidirect product | (C47×D29)⋊C7 |
| Fitting, socle, Hall | C29×C47 ⋊ C2×C7 |
| derived, Sylow | C29 ⋊ C2×C7×C47 |
| Hall | C47×C29⋊C7 ⋊ C2 |
| Hall | C47×D29 ⋊ C7 |
| Hall | C29⋊C7 ⋊ C2×C47 |
| Hall | D29 ⋊ C7×C47 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C47 | D29⋊C7 |
| commutator, cosocle, hypocenter | C29 | C2×C7×C47 |
| Frattini | C1 | G |
| Fitting, socle | C29×C47 | C2×C7 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C47 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1363 |
752 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C47×AGL(1,𝔽29), C47⋊AGL(1,𝔽29), D47×D29⋊C7, … |
| maximal normal subgroup of | C47×AGL(1,𝔽29), C47⋊AGL(1,𝔽29), D47×D29⋊C7, … |
| maximal quotient of | C47×Dic29⋊C7, C2×C47×D29⋊C7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19082, 11);