Finite Group DatabasebetaFinite Group Databasebeta| order | 19716 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(C31⋊#6157) |
| unambiguous semidirect product | C31⋊(C3⋊#6157) |
| Fitting, socle, derived, Hall | C3×C31×C53 ⋊ C4 |
| Hall | C31×C53 ⋊ Dic3 |
| Hall | C3×C53 ⋊ Dic31 |
| Hall | C3×C31 ⋊ #6157 |
| Sylow | C53 ⋊ Dic93 |
| Sylow | C31 ⋊ C3⋊#6157 |
| Sylow | C3 ⋊ C31⋊#6157 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C31×C53 | C4 |
| prime radical, cosocle | C3×C31×D53 | C2 |
| LCS | G ▷ C3×C31×C53 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4929 |
Polycyclic presentation:
2^2,3,31,53|a^2=b,c^a=c^2,d^a=d^30,e^a=e^30,e^b=e^521305 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19716, 25);