Finite Group DatabasebetaFinite Group Databasebeta| order | 37758 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C29⋊#13049958 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C29×C31 | C2×C3 |
| LCS | G ▷ C7×C29×C31 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6293 |
Polycyclic presentation:
2,3,7,29,31|c^a=c^6,d^a=d^28,c^b=c^2,e^b=e^51107 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37758, 53);