Finite Group DatabasebetaFinite Group Databasebeta| order | 19220 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C31 |
No aliases for this group.
| Fitting, socle, derived, Hall | C5×C312 ⋊ C4 |
| Sylow | C312 ⋊ Dic5 |
| Sylow | C5 ⋊ #16838652 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C312 | C4 |
| prime radical, cosocle | C5×C31⋊D31 | C2 |
| LCS | G ▷ C5×C312 | |
| UCS | C1 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 310 |
Polycyclic presentation:
2^2,5,31^2|a^2=b,c^a=c^4,d^a=d^27e^4,e^a=d^19e^4,d^b=d^30,e^b=e^301208 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19220, 66);