Finite Group DatabasebetaFinite Group Databasebeta| order | 34450 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C5⋊D3445 |
| unambiguous semidirect product | C13⋊(C5⋊D265) |
| unambiguous semidirect product | C53⋊(C5⋊D65) |
| Fitting, socle, derived, Hall | C52×C13×C53 ⋊ C2 |
| Hall | C52×C53 ⋊ D13 |
| Hall | C13×C53 ⋊ C5⋊D5 |
| Hall | C52×C13 ⋊ D53 |
| Sylow | C53 ⋊ C5⋊D65 |
| Sylow | C52 ⋊ D689 |
| Sylow | C13 ⋊ C5⋊D265 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C13×C53 | C2 |
| LCS | G ▷ C52×C13×C53 | |
| UCS | C1 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17225 |
Polycyclic presentation:
2,5^2,13,53|b^a=b^4,c^a=c^4,d^a=d^12,e^a=e^528614 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34450, 30);