Finite Group DatabasebetaFinite Group Databasebeta| order | 22230 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊D3705 |
| unambiguous semidirect product | C5⋊(C3⋊D741) |
| unambiguous semidirect product | C13⋊(C3⋊D285) |
| unambiguous semidirect product | C19⋊(C3⋊D195) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C5×C13×C19 | C2 |
| LCS | G ▷ C32×C5×C13×C19 | |
| UCS | C1 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11115 |
Polycyclic presentation:
2,3^2,5,13,19|b^a=b^2,c^a=c^2,d^a=d^4,e^a=e^12,f^a=f^185559 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22230, 168);