Finite Group DatabasebetaFinite Group Databasebeta| order | 18734 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C17×C19 · Schur multiplier (H2) = C1 |
| direct product | C17×C19×D29 |
| unambiguous semidirect product | C29⋊(C2×C17×C19) |
| Fitting, socle, Hall | C17×C19×C29 ⋊ C2 |
| derived, Sylow | C29 ⋊ C2×C17×C19 |
| Hall | C19×C29 ⋊ C2×C17 |
| Hall | C17×C29 ⋊ C2×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17×C19 | D29 |
| commutator, cosocle, hypocenter | C29 | C2×C17×C19 |
| Frattini | C1 | G |
| Fitting, socle | C17×C19×C29 | C2 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C17×C19 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9367 |
5168 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C17×C19×#1181, C17×C19⋊#1181, C17×D19×D29, … |
| maximal normal subgroup of | C17×C19×#1181, C17×C19⋊#1181, C17×D19×D29, … |
| maximal quotient of | C17×C19×Dic29, C2×C17×C19×D29 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18734, 2);