Finite Group DatabasebetaFinite Group Databasebeta| order | 20900 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D95⋊AGL(1,𝔽11) |
| unambiguous semidirect product | (C5⋊AGL(1,𝔽11))⋊D19 |
| unambiguous semidirect product | (C19⋊AGL(1,𝔽11))⋊D5 |
| unambiguous semidirect product | (D55⋊D19)⋊C5 |
| Fitting, socle, derived | C5×C11×C19 ⋊ C22×C5 |
| Hall | C5×C19×C11⋊C5 ⋊ C22 |
| Hall | C5×C11⋊C5 ⋊ C2×D19 |
| Hall | C11×C19 ⋊ C2×C5×D5 |
| Sylow | C19 ⋊ D5×AGL(1,𝔽11) |
| Sylow | C11 ⋊ C5×D5×D19 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C11×C19 | C22×C5 |
| LCS | G ▷ C5×C11×C19 | |
| UCS | C1 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1045 |
Polycyclic presentation:
2^2,5^2,11,19|e^a=e^10,f^a=f^18,d^b=d^4,e^b=e^10,e^c=e^4269 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20900, 67);