Finite Group DatabasebetaFinite Group Databasebeta| order | 34645 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C169 · Schur multiplier (H2) = C1 |
| direct product | C169×C41⋊C5 |
| unambiguous semidirect product | C41⋊(C5×C169) |
| unambiguous semidirect product | (C41×C169)⋊C5 |
| Fitting, Hall | C41×C169 ⋊ C5 |
| derived, Sylow | C41 ⋊ C5×C169 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C169 | C41⋊C5 |
| commutator, hypocenter | C41 | C5×C169 |
| Frattini | C13 | C13×C41⋊C5 |
| Fitting | C41×C169 | C5 |
| socle, cosocle | C13×C41 | C5×C13 |
| prime radical | C13×C41⋊C5 | C13 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C169 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6929 |
2197 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34645, 2);