Finite Group DatabasebetaFinite Group Databasebeta| order | 34138 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C101 · Schur multiplier (H2) = C1 |
| direct product | C101×D169 |
| unambiguous semidirect product | C169⋊(C2×C101) |
| Fitting, Hall | C101×C169 ⋊ C2 |
| derived, Sylow | C169 ⋊ C2×C101 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C101 | D169 |
| commutator, cosocle, hypocenter | C169 | C2×C101 |
| Frattini | C13 | D13×C101 |
| Fitting | C101×C169 | C2 |
| socle | C13×C101 | D13 |
| LCS | G ▷ C169 | |
| UCS | C1 ◁ C101 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17069 |
8686 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34138, 2);