Finite Group DatabasebetaFinite Group Databasebeta| order | 18734 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C17×C29 · Schur multiplier (H2) = C1 |
| direct product | C17×C29×D19 |
| unambiguous semidirect product | C19⋊(C2×C17×C29) |
| Fitting, socle, Hall | C17×C19×C29 ⋊ C2 |
| derived, Sylow | C19 ⋊ C2×C17×C29 |
| Hall | C19×C29 ⋊ C2×C17 |
| Hall | C17×C19 ⋊ C2×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17×C29 | D19 |
| commutator, cosocle, hypocenter | C19 | C2×C17×C29 |
| Frattini | C1 | G |
| Fitting, socle | C17×C19×C29 | C2 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C17×C29 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9367 |
5423 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C17×D19×D29, C29×D17×D19, D19×D493, … |
| maximal normal subgroup of | C17×D19×D29, C29×D17×D19, D19×D493, … |
| maximal quotient of | C17×C29×Dic19, C2×C17×C29×D19 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18734, 3);