Finite Group DatabasebetaFinite Group Databasebeta| order | 17458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C43⋊C7)⋊D29 |
| Fitting, socle, derived, Hall | C29×C43 ⋊ C2×C7 |
| Hall | C29×C43⋊C7 ⋊ C2 |
| Hall | D1247 ⋊ C7 |
| Hall | C43⋊C7 ⋊ D29 |
| Sylow | C43 ⋊ C7×D29 |
| Sylow | C29 ⋊ D43⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C29×C43 | C2×C7 |
| LCS | G ▷ C29×C43 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1247 |
Polycyclic presentation:
2,7,29,43|c^a=c^28,d^a=d^42,d^b=d^41199 conjugacy classes — view the full character table.
| maximal subgroup of | D29×D43⋊C7, C2×(C43⋊C7)⋊D29 |
| maximal normal subgroup of | D29×D43⋊C7, C2×(C43⋊C7)⋊D29 |
| maximal quotient of | (C43⋊C7)⋊Dic29, C2×(C43⋊C7)⋊D29 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17458, 33);