Finite Group DatabasebetaFinite Group Databasebeta| order | 14350 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊(C7⋊(D41⋊C5)) |
| unambiguous semidirect product | C7⋊(C5⋊(D41⋊C5)) |
| unambiguous semidirect product | (C41⋊C5)⋊D35 |
| unambiguous semidirect product | D1435⋊C5 |
| Fitting, socle, derived | C5×C7×C41 ⋊ C2×C5 |
| Hall | C5×C7×C41⋊C5 ⋊ C2 |
| Hall | C5×C41⋊C5 ⋊ D7 |
| Hall | C7×C41 ⋊ C5×D5 |
| Sylow | C41 ⋊ C5×D35 |
| Sylow | C7 ⋊ C5⋊(D41⋊C5) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C7×C41 | C2×C5 |
| LCS | G ▷ C5×C7×C41 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1435 |
Polycyclic presentation:
2,5^2,7,41|c^a=c^4,d^a=d^6,e^a=e^40,e^b=e^10235 conjugacy classes — view the full character table.
| maximal subgroup of | D35×D41⋊C5, D7×C5⋊(D41⋊C5), D5×C7⋊(D41⋊C5), … |
| maximal normal subgroup of | D35×D41⋊C5, D7×C5⋊(D41⋊C5), D5×C7⋊(D41⋊C5), … |
| maximal quotient of | C7⋊(Dic205⋊C5), C2×C5⋊(C7⋊(D41⋊C5)) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14350, 19);