Finite Group DatabasebetaFinite Group Databasebeta| order | 20748 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊#19104444 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C22×C7×C13×C19 | C3 |
| LCS | G ▷ C22×C7×C13×C19 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6916 |
Polycyclic presentation:
3,2^2,7,13,19|b^a=c,c^a=bc,d^a=d^2,e^a=e^9,f^a=f^112308 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20748, 412);