Finite Group DatabasebetaFinite Group Databasebeta| order | 34340 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic1717⋊C5 |
| derived, Hall | C17×C101 ⋊ C4×C5 |
| Hall | C17×C101⋊C5 ⋊ C4 |
| Hall | Dic1717 ⋊ C5 |
| Hall | C101⋊C5 ⋊ Dic17 |
| Sylow | C101 ⋊ C5×Dic17 |
| Sylow | C17 ⋊ Dic101⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C17⋊(D101⋊C5) |
| commutator, hypocenter | C17×C101 | C4×C5 |
| Fitting, socle, cosocle | C2×C17×C101 | C2×C5 |
| prime radical | C2×C17×C101⋊C5 | C2 |
| LCS | G ▷ C17×C101 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6868 |
Polycyclic presentation:
2,5,17,101,2|a^2=e,c^a=c^16,d^a=d^100,d^b=d^95440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34340, 12);