Finite Group DatabasebetaFinite Group Databasebeta| order | 20650 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C59 · Schur multiplier (H2) = C5 |
| direct product | C59×C5⋊D35 |
| unambiguous semidirect product | C5⋊(C59×D35) |
| unambiguous semidirect product | C7⋊(C5⋊D5×C59) |
| Fitting, socle, Hall | C52×C7×C59 ⋊ C2 |
| derived, Hall | C52×C7 ⋊ C2×C59 |
| Hall | C52×C59 ⋊ D7 |
| Hall | C7×C59 ⋊ C5⋊D5 |
| Sylow | C52 ⋊ D7×C59 |
| Sylow | C7 ⋊ C5⋊D5×C59 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C59 | C5⋊D35 |
| commutator, cosocle, hypocenter | C52×C7 | C2×C59 |
| Frattini | C1 | G |
| Fitting, socle | C52×C7×C59 | C2 |
| LCS | G ▷ C52×C7 | |
| UCS | C1 ◁ C59 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10325 |
5251 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20650, 19);