Finite Group DatabasebetaFinite Group Databasebeta| order | 34138 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C169 · Schur multiplier (H2) = C1 |
| direct product | C169×D101 |
| unambiguous semidirect product | C101⋊(C2×C169) |
| Fitting, Hall | C101×C169 ⋊ C2 |
| derived, Sylow | C101 ⋊ C2×C169 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C169 | D101 |
| commutator, hypocenter | C101 | C2×C169 |
| Frattini | C13 | C13×D101 |
| Fitting | C101×C169 | C2 |
| socle, cosocle | C13×C101 | C2×C13 |
| prime radical | C13×D101 | C13 |
| LCS | G ▷ C101 | |
| UCS | C1 ◁ C169 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17069 |
8788 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34138, 3);