Finite Group DatabasebetaFinite Group Databasebeta| order | 34138 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C13×C101 · Schur multiplier (H2) = C1 |
| direct product | C13×D13×C101 |
| unambiguous semidirect product | C13⋊(C2×C13×C101) |
| Fitting, socle, Hall | C132×C101 ⋊ C2 |
| derived | C13 ⋊ C2×C13×C101 |
| Sylow | C132 ⋊ C2×C101 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13×C101 | D13 |
| commutator, cosocle, hypocenter | C13 | C2×C13×C101 |
| Frattini | C1 | G |
| Fitting, socle | C132×C101 | C2 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C13×C101 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2626 |
10504 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34138, 7);