Finite Group DatabasebetaFinite Group Databasebeta| order | 20900 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×C11⋊C5×D95 |
| unambiguous semidirect product | (C2×C5)⋊(D19×C11⋊C5) |
| unambiguous semidirect product | (C2×C19)⋊(D5×C11⋊C5) |
| unambiguous semidirect product | (C2×C11×D95)⋊C5 |
| Fitting, socle | C2×C5×C11×C19 ⋊ C2×C5 |
| 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 ⋊ C2×D5×C11⋊C5 |
| Sylow | C11 ⋊ C2×C5×D95 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C11⋊C5×D95 |
| commutator, cosocle, hypocenter | C5×C11×C19 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C11×C19 | C2×C5 |
| LCS | G ▷ C5×C11×C19 | |
| UCS | C1 ◁ C2 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2090 |
686 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20900, 75);