Finite Group DatabasebetaFinite Group Databasebeta| order | 17458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C29 · Schur multiplier (H2) = C1 |
| direct product | C29×D301 |
| unambiguous semidirect product | C7⋊(C29×D43) |
| unambiguous semidirect product | C43⋊(D7×C29) |
| Fitting, socle, Hall | C7×C29×C43 ⋊ C2 |
| derived, Hall | C7×C43 ⋊ C2×C29 |
| Hall | C29×C43 ⋊ D7 |
| Hall | C7×C29 ⋊ D43 |
| Sylow | C43 ⋊ D7×C29 |
| Sylow | C7 ⋊ C29×D43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | D301 |
| commutator, cosocle, hypocenter | C7×C43 | C2×C29 |
| Frattini | C1 | G |
| Fitting, socle | C7×C29×C43 | C2 |
| LCS | G ▷ C7×C43 | |
| UCS | C1 ◁ C29 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8729 |
4408 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D7×C29×D43, D29×D301, D203⋊D43, … |
| maximal normal subgroup of | D7×C29×D43, D29×D301, D203⋊D43, … |
| maximal quotient of | C29×Dic301, C2×C29×D301 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17458, 14);