Finite Group DatabasebetaFinite Group Databasebeta| order | 19950 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊(C19⋊#3874) |
| unambiguous semidirect product | C19⋊(C7⋊#3874) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C7×C19×C52⋊C3 | C2 |
| Fitting, socle | C52×C7×C19 | D3 |
| LCS | G ▷ C7×C19×C52⋊C3 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1995 |
Polycyclic presentation:
2,3,7,19,5^2|b^a=b^2,c^a=c^6,d^a=d^18,e^a=e^2f^4,f^a=e^3f^3,e^b=e^2f^4,f^b=e^2f^2739 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19950, 97);