Finite Group DatabasebetaFinite Group Databasebeta| order | 22050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3×C5 |
| unambiguous semidirect product | C3⋊(C3⋊(C5⋊D245)) |
| unambiguous semidirect product | C5⋊(C3⋊D735) |
| unambiguous semidirect product | C49⋊(C3⋊(C3⋊(C5⋊D5))) |
| Fitting, derived, Hall | C32×C52×C49 ⋊ C2 |
| Hall | C52×C49 ⋊ C3⋊D3 |
| Hall | C32×C49 ⋊ C5⋊D5 |
| Hall | C32×C52 ⋊ D49 |
| Sylow | C49 ⋊ C3⋊(C3⋊(C5⋊D5)) |
| Sylow | C52 ⋊ C3⋊D147 |
| Sylow | C32 ⋊ C5⋊D245 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C32×C52×C49 | C2 |
| Frattini | C7 | C3⋊(C3⋊(C5⋊D35)) |
| socle | C32×C52×C7 | D7 |
| LCS | G ▷ C32×C52×C49 | |
| UCS | C1 | |
288 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11025 |
Polycyclic presentation:
2,3^2,5^2,7^2|f^7=g^6,b^a=b^2,c^a=c^2,d^a=d^4,e^a=e^4,f^a=f^6g,g^a=g^65514 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22050, 150);