Finite Group DatabasebetaFinite Group Databasebeta| order | 33620 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C41 · Schur multiplier (H2) = C2 |
| direct product | D5×C41×D41 |
| unambiguous semidirect product | (D5×C41)⋊(C2×C41) |
| unambiguous semidirect product | (C5×D41)⋊(C2×C41) |
| unambiguous semidirect product | D205⋊(C2×C41) |
| Fitting, socle, Hall | C5×C412 ⋊ C22 |
| derived | C5×C41 ⋊ C22×C41 |
| Sylow | C412 ⋊ C2×D5 |
| Sylow | C5 ⋊ C2×C41×D41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C41 | D5×D41 |
| commutator, cosocle, hypocenter | C5×C41 | C22×C41 |
| Frattini | C1 | G |
| Fitting, socle | C5×C412 | C22 |
| LCS | G ▷ C5×C41 | |
| UCS | C1 ◁ C41 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 410 |
3608 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33620, 99);