Finite Group DatabasebetaFinite Group Databasebeta| order | 34086 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C23⋊#13093367 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C13×C19×C23 | C2×C3 |
| LCS | G ▷ C13×C19×C23 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 5681 |
A minimal faithful permutation representation — 2 generators on 55 points:
(2,6,7,3,4,8)(5,12,11,9,10,13)(15,19,20,16,17,21)(18,26,27,22,23,31)(24,32,30,29,28,25)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(54,55);(1,2,5,4,8,11,10,12,13,7,6,9,3)(14,15,18,23,28,31,30,20,19,24,29,17,21,25,27,32,26,22,16)(33,34,36,38,40,42,44,46,48,50,52,54,55,53,51,49,47,45,43,41,39,37,35)Polycyclic presentation:
2,3,13,19,23|c^a=c^12,d^a=d^18,e^a=e^22,c^b=c^3,d^b=d^11982 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34086, 48);