Finite Group DatabasebetaFinite Group Databasebeta| order | 36270 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #20299829⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #14559030⋊C5 |
| commutator, hypocenter | C13×C31 | C2×C5×C9 |
| Fitting, socle, cosocle | C3×C13×C31 | C2×C3×C5 |
| prime radical | C3×C13⋊(D31⋊C5) | C3 |
| LCS | G ▷ C13×C31 | |
| UCS | C1 ◁ C3 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3627 |
Polycyclic presentation:
2,3,5,13,31,3|b^3=f,d^a=d^12,e^a=e^30,d^b=d^3,e^b=e^25,e^c=e^16159 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36270, 71);