Finite Group DatabasebetaFinite Group Databasebeta| order | 19110 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊#16838460 |
| 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 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 910 |
Polycyclic presentation:
2,3,5,7^2,13|c^a=c^4,d^a=d^6,f^a=f^12,d^b=d^2,e^b=e^2625 conjugacy classes — view the full character table.
| maximal subgroup of | D13×C5⋊#64423, D65×#64423, D5×#16838460, … |
| maximal normal subgroup of | D13×C5⋊#64423, D65×#64423, D5×#16838460, … |
| maximal quotient of | #50303638, C2×C5⋊#16838460 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19110, 136);