Finite Group DatabasebetaFinite Group Databasebeta| order | 19220 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #16838652⋊C5 |
| Fitting, socle, derived, Sylow | C312 ⋊ C4×C5 |
| Hall | #18012456 ⋊ C4 |
| Hall | #16838652 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C312 | C4×C5 |
| prime radical | #23751212 | C2 |
| cosocle | C31⋊D31 | C2×C5 |
| LCS | G ▷ C312 | |
| UCS | C1 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 62 |
Polycyclic presentation:
2,5,2,31^2|a^2=c,d^a=d^18e^14,e^a=d^10e^13,d^b=d^16,e^b=e^16,d^c=d^30,e^c=e^3068 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19220, 40);