Finite Group DatabasebetaFinite Group Databasebeta| order | 19950 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | (C5⋊D5)⋊#87704 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C7×C19 | C2×C3 |
| LCS | G ▷ C52×C7×C19 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1995 |
Polycyclic presentation:
2,3,5^2,7,19|c^a=c^4,d^a=d^4,c^b=cd^3,d^b=c^4d^3,e^b=e^2,f^b=f^7626 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19950, 111);