Finite Group DatabasebetaFinite Group Databasebeta| order | 19110 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊#16838446 |
| 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.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 3185 |
A minimal faithful permutation representation — 3 generators on 32 points:
(2,6,7,3,4,8)(5,12,11,9,10,13)(15,16)(17,18)(20,23,24,21,22,25)(27,30,31,28,29,32);(1,2,5,4,8,11,10,12,13,7,6,9,3)(14,15,17,18,16)(26,27,29,32,31,30,28);(19,20,22,25,24,23,21)Polycyclic presentation:
2,3,5,7^2,13|c^a=c^4,d^a=d^6,e^a=e^6,f^a=f^12,d^b=d^2,e^b=e^2,f^b=f^3542 conjugacy classes — view the full character table.
| maximal subgroup of | #50303821, #50303822, #50304096, … |
| maximal normal subgroup of | #50303821, #50303822, #50304096, … |
| maximal quotient of | #50303624, C2×C5⋊#16838446 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19110, 122);