Finite Group DatabasebetaFinite Group Databasebeta| order | 29602 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C41 · Schur multiplier (H2) = C1 |
| direct product | C41×D361 |
| unambiguous semidirect product | C361⋊(C2×C41) |
| Fitting, Hall | C41×C361 ⋊ C2 |
| derived, Sylow | C361 ⋊ C2×C41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C41 | D361 |
| commutator, cosocle, hypocenter | C361 | C2×C41 |
| Frattini | C19 | D19×C41 |
| Fitting | C41×C361 | C2 |
| socle | C19×C41 | D19 |
| LCS | G ▷ C361 | |
| UCS | C1 ◁ C41 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 14801 |
7462 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29602, 2);