Finite Group DatabasebetaFinite Group Databasebeta| order | 33620 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C41 · Schur multiplier (H2) = C1 |
| direct product | C41×Dic41⋊C5 |
| unambiguous semidirect product | Dic41⋊(C5×C41) |
| derived | C41 ⋊ C4×C5×C41 |
| Hall | C41×C41⋊C5 ⋊ C4 |
| Hall | C41×Dic41 ⋊ C5 |
| Sylow | C412 ⋊ C4×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C41 | D41⋊C5 |
| commutator, hypocenter | C41 | C4×C5×C41 |
| Frattini | C2 | C41×D41⋊C5 |
| Fitting, socle | C2×C412 | C2×C5 |
| prime radical | C2×C41×C41⋊C5 | C2 |
| cosocle | C2×C41 | C2×C5×C41 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C2×C41 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 820 |
1148 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33620, 23);