Finite Group DatabasebetaFinite Group Databasebeta| order | 33620 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×Dic1681 |
| derived, Sylow | C1681 ⋊ C4×C5 |
| Hall | C5×C1681 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D1681 |
| commutator, hypocenter | C1681 | C4×C5 |
| Frattini | C2×C41 | C5×D41 |
| Fitting | C2×C5×C1681 | C2 |
| socle, prime radical | C2×C5×C41 | D41 |
| cosocle | C2×C1681 | C2×C5 |
| LCS | G ▷ C1681 | |
| UCS | C1 ◁ C2×C5 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 33620 |
8420 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33620, 5);