Finite Group DatabasebetaFinite Group Databasebeta| order | 25740 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊(Dic65⋊C9) |
| unambiguous semidirect product | Dic715⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C3 | C5⋊(C11⋊(D13⋊C3)) |
| commutator, hypocenter | C5×C11×C13 | C4×C9 |
| Fitting, socle, prime radical, cosocle | C2×C3×C5×C11×C13 | C2×C3 |
| LCS | G ▷ C5×C11×C13 | |
| UCS | C1 ◁ C2×C3 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 25740 |
Polycyclic presentation:
2,3,5,11,13,2,3|a^2=f,b^3=g,c^a=c^4,d^a=d^10,e^a=e^12,e^b=e^31182 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25740, 33);