Finite Group DatabasebetaFinite Group Databasebeta| order | 20748 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(C19⋊#261) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C13×C19 | C3×C4 |
| prime radical | C19×ΓL(1,𝔽8)×D13 | C2 |
| cosocle | C7×C19×D13 | C2×C3 |
| LCS | G ▷ C7×C13×C19 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1729 |
Polycyclic presentation:
2,3,2,7,13,19|a^2=c,d^a=d^6,e^a=e^5,f^a=f^18,d^b=d^4,e^c=e^12389 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20748, 184);