Finite Group DatabasebetaFinite Group Databasebeta| order | 34188 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊(ΓL(1,𝔽8)⋊#3866) |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(C11⋊#3866) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C11×C37 | C3×C4 |
| prime radical | C11×ΓL(1,𝔽8)×D37 | C2 |
| cosocle | C7×C11×D37 | C2×C3 |
| LCS | G ▷ C7×C11×C37 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2849 |
Polycyclic presentation:
2,3,2,7,11,37|a^2=c,d^a=d^6,e^a=e^10,f^a=f^31,d^b=d^2,f^c=f^36559 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34188, 75);