Finite Group DatabasebetaFinite Group Databasebeta| order | 20900 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C25 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C19⋊(Dic11⋊C25) |
| unambiguous semidirect product | (C11⋊C25)⋊Dic19 |
| unambiguous semidirect product | Dic209⋊C25 |
| derived, Hall | C11×C19 ⋊ C4×C25 |
| Hall | C19×C11⋊C25 ⋊ C4 |
| Hall | Dic209 ⋊ C25 |
| Hall | C11⋊C25 ⋊ Dic19 |
| Sylow | C19 ⋊ Dic11⋊C25 |
| Sylow | C11 ⋊ C25×Dic19 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C5 | C19⋊AGL(1,𝔽11) |
| commutator, hypocenter | C11×C19 | C4×C25 |
| Fitting, socle, prime radical, cosocle | C2×C5×C11×C19 | C2×C5 |
| LCS | G ▷ C11×C19 | |
| UCS | C1 ◁ C2×C5 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 20900 |
Polycyclic presentation:
2,5,11,19,2,5|a^2=e,b^5=f,c^a=c^10,d^a=d^18,c^b=c^4740 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20900, 12);