Finite Group DatabasebetaFinite Group Databasebeta| order | 11890 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C29⋊(D41⋊C5) |
| unambiguous semidirect product | (C41⋊C5)⋊D29 |
| unambiguous semidirect product | D1189⋊C5 |
| Fitting, socle, derived, Hall | C29×C41 ⋊ C2×C5 |
| Hall | C29×C41⋊C5 ⋊ C2 |
| Hall | D1189 ⋊ C5 |
| Hall | C41⋊C5 ⋊ D29 |
| Sylow | C41 ⋊ C5×D29 |
| Sylow | C29 ⋊ D41⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C29×C41 | C2×C5 |
| LCS | G ▷ C29×C41 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,29,41|c^a=c^28,d^a=d^40,d^b=d^10196 conjugacy classes — view the full character table.
| maximal subgroup of | #18011700⋊C5, #18011701⋊C5, D29×D41⋊C5, … |
| maximal normal subgroup of | #18011700⋊C5, #18011701⋊C5, D29×D41⋊C5, … |
| maximal quotient of | Dic1189⋊C5, C2×C29⋊(D41⋊C5), C3×C29⋊(D41⋊C5), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11890, 12);