Finite Group DatabasebetaFinite Group Databasebeta| order | 2050 |
| isoclinism | isoclinic class of C5⋊(D41⋊C5) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊(D41⋊C5) |
| unambiguous semidirect product | (C41⋊C5)⋊D5 |
| unambiguous semidirect product | D205⋊C5 |
| Fitting, socle, derived | C5×C41 ⋊ C2×C5 |
| Hall | C5×C41⋊C5 ⋊ C2 |
| Sylow | C41 ⋊ C5×D5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C41 | C2×C5 |
| LCS | G ▷ C5×C41 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 205 |
Polycyclic presentation:
2,5^2,41|c^a=c^4,d^a=d^40,d^b=d^1040 conjugacy classes — view the full character table.
| maximal subgroup of | #11717961⋊C5, #11717962⋊C5, D5×D41⋊C5, … |
| maximal normal subgroup of | #11717961⋊C5, #11717962⋊C5, D5×D41⋊C5, … |
| maximal quotient of | Dic205⋊C5, C2×C5⋊(D41⋊C5), C7×C5⋊(D41⋊C5), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2050, 9);