Finite Group DatabasebetaFinite Group Databasebeta| order | 19110 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊(C13⋊#64418) |
| unambiguous semidirect product | C13⋊(C5⋊#64418) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C5×C13×#3862 | C2 |
| Fitting, socle | C5×C72×C13 | D3 |
| LCS | G ▷ C5×C13×#3862 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 910 |
Polycyclic presentation:
2,3,5,13,7^2|b^a=b^2,c^a=c^4,d^a=d^12,e^a=e^4f,f^a=e^6f^3,e^b=e^2f^6,f^b=f^4628 conjugacy classes — view the full character table.
| maximal subgroup of | D13×C5⋊#64418, D65×#64418, D5×C13⋊#64418, … |
| maximal normal subgroup of | D13×C5⋊#64418, D65×#64418, D5×C13⋊#64418, … |
| maximal quotient of | #50303670, C2×C5⋊(C13⋊#64418) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19110, 168);