Finite Group DatabasebetaFinite Group Databasebeta| order | 11742 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C19×C103 ⋊ C2×C3 |
| Hall | #19154535 ⋊ C2 |
| Hall | D19×C103 ⋊ C3 |
| Sylow | C103 ⋊ D19⋊C3 |
| Hall | D19 ⋊ C103⋊C3 |
| Sylow | C19 ⋊ C2×C103⋊C3 |
| 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,c^b=c^7,d^b=d^46383 conjugacy classes — view the full character table.
| maximal subgroup of | #26044106⋊C2, C2×#26044110, D19⋊C3×C103⋊C3, … |
| maximal normal subgroup of | #26044106⋊C2, C2×#26044110, D19⋊C3×C103⋊C3, … |
| maximal quotient of | #37553583, C2×#26044110, #47976334, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11742, 20);