Finite Group DatabasebetaFinite Group Databasebeta| order | 33620 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C22×C1681⋊C5 |
| unambiguous semidirect product | (C22×C1681)⋊C5 |
| Fitting, Hall | C22×C1681 ⋊ C5 |
| derived, Sylow | C1681 ⋊ C22×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | C1681⋊C5 |
| commutator, cosocle, hypocenter | C1681 | C22×C5 |
| Frattini | C41 | C22×C41⋊C5 |
| Fitting | C22×C1681 | C5 |
| socle | C22×C41 | C41⋊C5 |
| LCS | G ▷ C1681 | |
| UCS | C1 ◁ C22 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6724 |
1364 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33620, 10);