Finite Group DatabasebetaFinite Group Databasebeta| order | 19110 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊#16838417 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C5×C13×C49 | C2×C3 |
| Frattini | C7 | C5⋊#10587720 |
| socle | C5×C7×C13 | AGL(1,𝔽7) |
| LCS | G ▷ C5×C13×C49 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3185 |
Polycyclic presentation:
2,3,5,7,13,7|d^7=f^6,c^a=c^4,d^a=d^6f,f^a=f^6,d^b=d^2f^3,e^b=e^3,f^b=f^2548 conjugacy classes — view the full character table.
| maximal subgroup of | #16838413⋊D5, #16838419⋊D5, D5×#16838417, … |
| maximal normal subgroup of | #16838413⋊D5, #16838419⋊D5, D5×#16838417, … |
| maximal quotient of | #50303357, C2×C5⋊#16838417 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19110, 43);