Finite Group DatabasebetaFinite Group Databasebeta| order | 33620 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic1681⋊C5 |
| derived, Sylow | C1681 ⋊ C4×C5 |
| Hall | C1681⋊C5 ⋊ C4 |
| Hall | Dic1681 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D1681⋊C5 |
| commutator, hypocenter | C1681 | C4×C5 |
| Frattini, socle | C2×C41 | D41⋊C5 |
| Fitting, cosocle | C2×C1681 | C2×C5 |
| prime radical | C2×C1681⋊C5 | C2 |
| LCS | G ▷ C1681 | |
| UCS | C1 ◁ C2 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6724 |
Polycyclic presentation:
2,5,41,2,41|a^2=d,c^41=e^40,c^a=c^40e,e^a=e^40,c^b=c^10e^40,e^b=e^10356 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33620, 2);