Finite Group DatabasebetaFinite Group Databasebeta| order | 20900 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C52×C11 · Schur multiplier (H2) = C5 |
| direct product | C52×C11×Dic19 |
| unambiguous semidirect product | C19⋊(C4×C52×C11) |
| derived, Sylow | C19 ⋊ C4×C52×C11 |
| Hall | C52×C11×C19 ⋊ C4 |
| Hall | C52×C19 ⋊ C4×C11 |
| Hall | C11×C19 ⋊ C4×C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C52×C11 | D19 |
| commutator, hypocenter | C19 | C4×C52×C11 |
| Frattini | C2 | C52×C11×D19 |
| Fitting, socle, prime radical | C2×C52×C11×C19 | C2 |
| cosocle | C2×C19 | C2×C52×C11 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C2×C52×C11 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 20900 |
6050 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20900, 56);