Finite Group DatabasebetaFinite Group Databasebeta| order | 19110 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊#16838449 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C72×C13 | C2×C3 |
| LCS | G ▷ C5×C72×C13 | |
| UCS | C1 | |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3185 |
Polycyclic presentation:
2,3,5,7^2,13|c^a=c^4,d^a=d^6,e^a=e^6,d^b=d^2,e^b=e^2,f^b=f^9548 conjugacy classes — view the full character table.
| maximal subgroup of | #50303826, #50303830, #50304097, … |
| maximal normal subgroup of | #50303826, #50303830, #50304097, … |
| maximal quotient of | #50303627, C2×C5⋊#16838449 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19110, 125);