Finite Group DatabasebetaFinite Group Databasebeta| order | 19110 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊(ΓL(1,𝔽8)⋊D91) |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊D455 |
| 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 | |
80 conjugacy classes of subgroups.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 1365 |
A minimal faithful permutation representation — 2 generators on 32 points:
(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(15,16)(17,18)(20,23,24,21,22,25)(27,28)(29,30)(31,32);(1,2,4,6,8,10,12,13,11,9,7,5,3)(14,15,17,18,16)(19,20,22,25,24,23,21)(26,27,29,31,32,30,28)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^21142 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19110, 148);