Finite Group DatabasebetaFinite Group Databasebeta| order | 20740 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | Dic17×C61⋊C5 |
| unambiguous semidirect product | (C61×Dic17)⋊C5 |
| derived, Hall | C17×C61 ⋊ C4×C5 |
| Hall | C17×C61⋊C5 ⋊ C4 |
| Hall | C61×Dic17 ⋊ C5 |
| Sylow | C61 ⋊ C5×Dic17 |
| Sylow | C17 ⋊ C4×C61⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D17×C61⋊C5 |
| commutator, hypocenter | C17×C61 | C4×C5 |
| Fitting, socle, cosocle | C2×C17×C61 | C2×C5 |
| prime radical | C2×C17×C61⋊C5 | C2 |
| LCS | G ▷ C17×C61 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4148 |
340 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20740, 11);