Finite Group DatabasebetaFinite Group Databasebeta| order | 20900 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊(C19⋊#1042) |
| unambiguous semidirect product | C19⋊(C11⋊#1042) |
| Fitting, socle, derived, Hall | C52×C11×C19 ⋊ C4 |
| Hall | C52×C19 ⋊ Dic11 |
| Hall | C52×C11 ⋊ Dic19 |
| Hall | C11×C19 ⋊ #1042 |
| Sylow | C52 ⋊ Dic209 |
| Sylow | C19 ⋊ C11⋊#1042 |
| Sylow | C11 ⋊ C19⋊#1042 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C11×C19 | C4 |
| prime radical, cosocle | C5×D5×C11×C19 | C2 |
| LCS | G ▷ C52×C11×C19 | |
| UCS | C1 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4180 |
Polycyclic presentation:
2^2,5^2,11,19|a^2=b,c^a=c^2,d^a=d^4,e^a=e^10,f^a=f^18,c^b=c^42093 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20900, 91);