Finite Group DatabasebetaFinite Group Databasebeta| order | 33620 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C1681 · Schur multiplier (H2) = C1 |
| direct product | AGL(1,𝔽5)×C1681 |
| Fitting, Hall | C5×C1681 ⋊ C4 |
| derived, Sylow | C5 ⋊ C4×C1681 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1681 | AGL(1,𝔽5) |
| commutator, hypocenter | C5 | C4×C1681 |
| Frattini | C41 | AGL(1,𝔽5)×C41 |
| Fitting | C5×C1681 | C4 |
| socle | C5×C41 | C4×C41 |
| prime radical, cosocle | D5×C41 | C2×C41 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C1681 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8405 |
8405 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33620, 12);