Finite Group DatabasebetaFinite Group Databasebeta| order | 19074 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊#13181892 |
| Fitting, socle, Hall | C11×C172 ⋊ D3 |
| derived, Hall | C11×C172⋊C3 ⋊ C2 |
| Hall | C172⋊C3 ⋊ D11 |
| Sylow | C172 ⋊ D33 |
| Sylow | C11 ⋊ #13181892 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C11×C172⋊C3 | C2 |
| Fitting, socle | C11×C172 | D3 |
| LCS | G ▷ C11×C172⋊C3 | |
| UCS | C1 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 561 |
Polycyclic presentation:
2,3,11,17^2|b^a=b^2,c^a=c^10,e^a=de^16,d^b=d^2e^12,e^b=d^15e^14570 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#13181892, #13181892⋊D11, ((C17⋊D17)⋊C3)⋊D11, … |
| maximal normal subgroup of | D11×#13181892, #13181892⋊D11, ((C17⋊D17)⋊C3)⋊D11, … |
| maximal quotient of | C11⋊#16812392, C2×C11⋊#13181892 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19074, 12);