Finite Group DatabasebetaFinite Group Databasebeta| order | 2050 |
| isoclinism | isoclinic class of C41⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52 · Schur multiplier (H2) = C5 |
| direct product | C2×C5×C41⋊C5 |
| unambiguous semidirect product | (C2×C41)⋊C52 |
| unambiguous semidirect product | (C2×C5×C41)⋊C5 |
| Fitting, socle | C2×C5×C41 ⋊ C5 |
| derived, Sylow | C41 ⋊ C2×C52 |
| Hall | C2×C41 ⋊ C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | C41⋊C5 |
| commutator, cosocle, hypocenter | C41 | C2×C52 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C41 | C5 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C2×C5 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 410 |
130 conjugacy classes — view the full character table.
| maximal subgroup of | C5×Dic41⋊C5, Dic205⋊C5, Dic5×C41⋊C5, … |
| maximal normal subgroup of | C5×Dic41⋊C5, Dic205⋊C5, Dic5×C41⋊C5, … |
| maximal quotient of | C4×C5×C41⋊C5, C22×C5×C41⋊C5, C5×D7×C41⋊C5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2050, 11);