Finite Group DatabasebetaFinite Group Databasebeta| order | 20740 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | #595×C61⋊C5 |
| unambiguous semidirect product | (C61×#595)⋊C5 |
| Fitting, socle, derived, Hall | C17×C61 ⋊ C4×C5 |
| Hall | C17×C61⋊C5 ⋊ C4 |
| Hall | C61×#595 ⋊ C5 |
| Sylow | C61 ⋊ C5×#595 |
| Sylow | C17 ⋊ C4×C61⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C17×C61 | C4×C5 |
| prime radical | D17×C61⋊C5 | C2 |
| cosocle | D17×C61 | C2×C5 |
| LCS | G ▷ C17×C61 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1037 |
136 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20740, 18);