Finite Group DatabasebetaFinite Group Databasebeta| order | 19620 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C5×C109 ⋊ C4×C9 |
| Hall | C5×#11758281 ⋊ C4 |
| Hall | #14546128 ⋊ C9 |
| Hall | #11758281 ⋊ AGL(1,𝔽5) |
| Sylow | C109 ⋊ C9×AGL(1,𝔽5) |
| Sylow | C5 ⋊ #16840993 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C109 | C4×C9 |
| prime radical, cosocle | D5×C109⋊C3 | C2×C3 |
| LCS | G ▷ C5×C109 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 545 |
Polycyclic presentation:
2,3,2,3,5,109|a^2=c,b^3=d,e^a=e^2,f^a=f^108,f^b=f^16,e^c=e^4,f^d=f^6369 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19620, 81);