Finite Group DatabasebetaFinite Group Databasebeta| order | 20746 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C41⋊AGL(1,𝔽23) |
| unambiguous semidirect product | (C23⋊C11)⋊D41 |
| unambiguous semidirect product | D943⋊C11 |
| Fitting, socle, derived, Hall | C23×C41 ⋊ C2×C11 |
| Hall | C41×C23⋊C11 ⋊ C2 |
| Hall | D943 ⋊ C11 |
| Hall | C23⋊C11 ⋊ D41 |
| Sylow | C41 ⋊ AGL(1,𝔽23) |
| Sylow | C23 ⋊ C11×D41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C23×C41 | C2×C11 |
| LCS | G ▷ C23×C41 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 943 |
Polycyclic presentation:
2,11,23,41|c^a=c^22,d^a=d^40,c^b=c^2283 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20746, 12);