Finite Group DatabasebetaFinite Group Databasebeta| order | 34510 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊(C17⋊(D29⋊C7)) |
| unambiguous semidirect product | C17⋊(C5⋊(D29⋊C7)) |
| unambiguous semidirect product | (C29⋊C7)⋊D85 |
| unambiguous semidirect product | D2465⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C17×C29 | C2×C7 |
| LCS | G ▷ C5×C17×C29 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2465 |
Polycyclic presentation:
2,5,7,17,29|b^a=b^4,d^a=d^16,e^a=e^28,e^c=e^16478 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34510, 24);