Finite Group DatabasebetaFinite Group Databasebeta| order | 11742 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C19⋊C3)⋊D103 |
| Fitting, socle, derived, Hall | C19×C103 ⋊ C2×C3 |
| Hall | C19⋊C3×C103 ⋊ C2 |
| Hall | D1957 ⋊ C3 |
| Sylow | C103 ⋊ D19⋊C3 |
| Hall | C19⋊C3 ⋊ D103 |
| Sylow | C19 ⋊ C3×D103 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C19×C103 | C2×C3 |
| LCS | G ▷ C19×C103 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,19,103|c^a=c^18,d^a=d^102,c^b=c^7468 conjugacy classes — view the full character table.
| maximal subgroup of | D19⋊C3×D103, C2×(C19⋊C3)⋊D103, #47976341, … |
| maximal normal subgroup of | D19⋊C3×D103, C2×(C19⋊C3)⋊D103, #47976341, … |
| maximal quotient of | (C19⋊C3)⋊Dic103, C2×(C19⋊C3)⋊D103, #4294⋊D103, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11742, 22);