Finite Group DatabasebetaFinite Group Databasebeta| order | 11970 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊(#4296⋊D7) |
| unambiguous semidirect product | #4296⋊D35 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C7×C19 | C2×C9 |
| prime radical | C5⋊((C19⋊C3)⋊D7) | C3 |
| cosocle | C5×C7×C19⋊C3 | C2×C3 |
| LCS | G ▷ C5×C7×C19 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,5,7,19|b^3=c,d^a=d^4,e^a=e^6,f^a=f^18,f^b=f^4,f^c=f^7206 conjugacy classes — view the full character table.
| maximal subgroup of | D35×AGL(1,𝔽19), D7×C5⋊AGL(1,𝔽19), D5×#4296⋊D7, … |
| maximal normal subgroup of | D35×AGL(1,𝔽19), D7×C5⋊AGL(1,𝔽19), D5×#4296⋊D7, … |
| maximal quotient of | #4296⋊Dic35, C2×C5⋊(#4296⋊D7) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11970, 76);