Finite Group DatabasebetaFinite Group Databasebeta| order | 19082 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | D47×C29⋊C7 |
| unambiguous semidirect product | C47⋊(C2×C29⋊C7) |
| unambiguous semidirect product | (C29×D47)⋊C7 |
| Fitting, socle, derived, Hall | C29×C47 ⋊ C2×C7 |
| Hall | C47×C29⋊C7 ⋊ C2 |
| Hall | C29×D47 ⋊ C7 |
| Sylow | C47 ⋊ C2×C29⋊C7 |
| Sylow | C29 ⋊ C7×D47 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C29×C47 | C2×C7 |
| LCS | G ▷ C29×C47 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1363 |
275 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D47×D29⋊C7, C2×D47×C29⋊C7 |
| maximal normal subgroup of | D47×D29⋊C7, C2×D47×C29⋊C7 |
| maximal quotient of | Dic47×C29⋊C7, C2×D47×C29⋊C7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19082, 10);