Finite Group DatabasebetaFinite Group Databasebeta| order | 20804 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic743⋊C7 |
| unambiguous semidirect product | (C743⋊C7)⋊C4 |
| derived, Sylow | C743 ⋊ C4×C7 |
| Hall | C743⋊C7 ⋊ C4 |
| Hall | Dic743 ⋊ C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D743⋊C7 |
| commutator, hypocenter | C743 | C4×C7 |
| Fitting, socle, cosocle | C2×C743 | C2×C7 |
| prime radical | C2×C743⋊C7 | C2 |
| LCS | G ▷ C743 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2972 |
Polycyclic presentation:
2,7,743,2|a^2=d,c^a=c^742,c^b=c^433134 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20804, 2);