Finite Group DatabasebetaFinite Group Databasebeta| order | 20900 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C52 · Schur multiplier (H2) = C2×C5 |
| Fitting, socle | C2×C5×C11×C19 ⋊ C2×C5 |
| derived, Hall | C11×C19 ⋊ C22×C52 |
| Hall | C5×C19×C11⋊C5 ⋊ C22 |
| Hall | C2×D209 ⋊ C52 |
| Hall | C5×C11⋊C5 ⋊ C2×D19 |
| Sylow | C19 ⋊ C2×C5×AGL(1,𝔽11) |
| Sylow | C11 ⋊ C2×C52×D19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | C19⋊AGL(1,𝔽11) |
| commutator, cosocle, hypocenter | C11×C19 | C22×C52 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C11×C19 | C2×C5 |
| LCS | G ▷ C11×C19 | |
| UCS | C1 ◁ C2×C5 | |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2090 |
740 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20900, 70);