Finite Group DatabasebetaFinite Group Databasebeta| order | 11890 |
| isoclinism | isoclinic class of D41⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C29 · Schur multiplier (H2) = C1 |
| direct product | C29×D41⋊C5 |
| unambiguous semidirect product | D41⋊(C5×C29) |
| unambiguous semidirect product | (C41⋊C5)⋊(C2×C29) |
| unambiguous semidirect product | (C29×D41)⋊C5 |
| Fitting, socle, Hall | C29×C41 ⋊ C2×C5 |
| derived, Sylow | C41 ⋊ C2×C5×C29 |
| Hall | C29×C41⋊C5 ⋊ C2 |
| Hall | C29×D41 ⋊ C5 |
| Hall | C41⋊C5 ⋊ C2×C29 |
| Hall | D41 ⋊ C5×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | D41⋊C5 |
| commutator, cosocle, hypocenter | C41 | C2×C5×C29 |
| Frattini | C1 | G |
| Fitting, socle | C29×C41 | C2×C5 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C29 | |
16 conjugacy classes of subgroups.
406 conjugacy classes — view the full character table.
| maximal subgroup of | C29×#4223⋊C5, #18011703⋊C5, D29×D41⋊C5, … |
| maximal normal subgroup of | C29×#4223⋊C5, #18011703⋊C5, D29×D41⋊C5, … |
| maximal quotient of | C29×Dic41⋊C5, C2×C29×D41⋊C5, C3×C29×D41⋊C5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11890, 10);