Finite Group DatabasebetaFinite Group Databasebeta| order | 36036 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊#15692591 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C11⋊#11763984 |
| commutator, hypocenter | C7×C11×C13 | C4×C9 |
| Fitting, socle | C3×C7×C11×C13 | C3×C4 |
| prime radical, cosocle | C3×C7×C11×D13 | C2×C3 |
| LCS | G ▷ C7×C11×C13 | |
| UCS | C1 ◁ C3 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9009 |
Polycyclic presentation:
2,3,2,7,11,13,3|a^2=c,b^3=g,d^a=d^6,e^a=e^10,f^a=f^5,d^b=d^2,f^b=f^9,f^c=f^12423 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36036, 72);