Finite Group DatabasebetaFinite Group Databasebeta| order | 34340 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C17 · Schur multiplier (H2) = C2 |
| direct product | D5×C17×D101 |
| unambiguous semidirect product | (D5×C101)⋊(C2×C17) |
| unambiguous semidirect product | (C5×D101)⋊(C2×C17) |
| unambiguous semidirect product | D505⋊(C2×C17) |
| Fitting, socle, Hall | C5×C17×C101 ⋊ C22 |
| derived, Hall | C5×C101 ⋊ C22×C17 |
| Hall | C17×C101 ⋊ C2×D5 |
| Sylow | C101 ⋊ C2×D5×C17 |
| Hall | C5×C17 ⋊ C2×D101 |
| Sylow | C5 ⋊ C2×C17×D101 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | D5×D101 |
| commutator, cosocle, hypocenter | C5×C101 | C22×C17 |
| Frattini | C1 | G |
| Fitting, socle | C5×C17×C101 | C22 |
| LCS | G ▷ C5×C101 | |
| UCS | C1 ◁ C17 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8585 |
3536 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34340, 49);