Finite Group DatabasebetaFinite Group Databasebeta| order | 20740 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C61 · Schur multiplier (H2) = C1 |
| direct product | C61×#66776 |
| Fitting, socle, Hall | C5×C17×C61 ⋊ C4 |
| derived, Hall | C5×C17 ⋊ C4×C61 |
| Hall | C17×C61 ⋊ AGL(1,𝔽5) |
| Hall | C5×C61 ⋊ #595 |
| Sylow | C17 ⋊ AGL(1,𝔽5)×C61 |
| Sylow | C5 ⋊ C61×#595 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C61 | #66776 |
| commutator, hypocenter | C5×C17 | C4×C61 |
| Frattini | C1 | G |
| Fitting, socle | C5×C17×C61 | C4 |
| prime radical | C61×D85 | C2 |
| cosocle | D85 | C2×C61 |
| LCS | G ▷ C5×C17 | |
| UCS | C1 ◁ C61 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5185 |
1525 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20740, 40);