Finite Group DatabasebetaFinite Group Databasebeta| order | 18722 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11×C37 · Schur multiplier (H2) = C1 |
| direct product | C37×AGL(1,𝔽23) |
| unambiguous semidirect product | D23⋊(C11×C37) |
| unambiguous semidirect product | (C23⋊C11)⋊(C2×C37) |
| unambiguous semidirect product | (C37×D23)⋊C11 |
| Fitting, socle, Hall | C23×C37 ⋊ C2×C11 |
| derived, Sylow | C23 ⋊ C2×C11×C37 |
| Hall | C37×C23⋊C11 ⋊ C2 |
| Hall | C37×D23 ⋊ C11 |
| Hall | C23⋊C11 ⋊ C2×C37 |
| Hall | D23 ⋊ C11×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C37 | AGL(1,𝔽23) |
| commutator, cosocle, hypocenter | C23 | C2×C11×C37 |
| Frattini | C1 | G |
| Fitting, socle | C23×C37 | C2×C11 |
| LCS | G ▷ C23 | |
| UCS | C1 ◁ C37 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 851 |
851 conjugacy classes. The character table is too large to display.
| 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 | C37×Dic23⋊C11, C2×C37×AGL(1,𝔽23) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18722, 11);