Finite Group DatabasebetaFinite Group Databasebeta| order | 18722 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C37⋊AGL(1,𝔽23) |
| unambiguous semidirect product | (C23⋊C11)⋊D37 |
| unambiguous semidirect product | D851⋊C11 |
| Fitting, socle, derived, Hall | C23×C37 ⋊ C2×C11 |
| Hall | C37×C23⋊C11 ⋊ C2 |
| Hall | D851 ⋊ C11 |
| Hall | C23⋊C11 ⋊ D37 |
| Sylow | C37 ⋊ AGL(1,𝔽23) |
| Sylow | C23 ⋊ C11×D37 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C23×C37 | C2×C11 |
| LCS | G ▷ C23×C37 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 851 |
Polycyclic presentation:
2,11,23,37|c^a=c^22,d^a=d^36,c^b=c^2257 conjugacy classes — view the full character table.
| maximal subgroup of | D37×AGL(1,𝔽23), C2×C37⋊AGL(1,𝔽23) |
| maximal normal subgroup of | D37×AGL(1,𝔽23), C2×C37⋊AGL(1,𝔽23) |
| maximal quotient of | (C23⋊C11)⋊Dic37, C2×C37⋊AGL(1,𝔽23) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18722, 12);