Finite Group DatabasebetaFinite Group Databasebeta| order | 34340 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C101 · Schur multiplier (H2) = C1 |
| direct product | C101×#66774 |
| Fitting, socle, Hall | C5×C17×C101 ⋊ C4 |
| derived, Hall | C5×C17 ⋊ C4×C101 |
| Hall | C17×C101 ⋊ AGL(1,𝔽5) |
| Hall | C5×C101 ⋊ Dic17 |
| Sylow | C17 ⋊ AGL(1,𝔽5)×C101 |
| Sylow | C5 ⋊ Dic17×C101 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C101 | #66774 |
| commutator, hypocenter | C5×C17 | C4×C101 |
| Frattini | C1 | G |
| Fitting, socle | C5×C17×C101 | C4 |
| prime radical | D5×C17×C101 | C2 |
| cosocle | D5×C17 | C2×C101 |
| LCS | G ▷ C5×C17 | |
| UCS | C1 ◁ C101 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8585 |
3737 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34340, 44);