Finite Group DatabasebetaFinite Group Databasebeta| order | 38130 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#27163269 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C31×C41 | C2×C5 |
| LCS | G ▷ C3×C31×C41 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3813 |
Polycyclic presentation:
2,3,5,31,41|b^a=b^2,d^a=d^30,d^c=d^16,e^c=e^37408 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38130, 65);