Finite Group DatabasebetaFinite Group Databasebeta| order | 35226 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#26044109 |
| Fitting, socle, derived | C3×C19×C103 ⋊ C2×C3 |
| Hall | C3×#19154536 ⋊ C2 |
| Hall | C19×C103 ⋊ C3×D3 |
| Sylow | C103 ⋊ C3⋊(D19⋊C3) |
| Sylow | C19 ⋊ D3×C103⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C19×C103 | C2×C3 |
| LCS | G ▷ C3×C19×C103 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 125 |
| transitive degree | μt(G) = 5871 |
A minimal faithful permutation representation — 2 generators on 125 points:
(2,3)(5,9,10,6,7,11)(8,17,14,12,13,19)(15,20,22,21,18,16)(24,25,27)(26,29,34)(28,32,31)(30,36,44)(33,39,41)(35,42,38)(37,46,57)(40,49,54)(43,52,51)(45,55,48)(47,59,73)(50,62,70)(53,65,67)(56,68,64)(58,71,61)(60,75,91)(63,78,88)(66,76,85)(69,83,82)(72,86,80)(74,89,77)(79,94,106)(81,95,103)(84,99,100)(87,101,98)(90,104,96)(92,107,93)(97,110,116)(102,113,112)(105,114,111)(108,117,109)(115,121,120)(118,122,119)(123,125,124);(1,2,3)(4,5,8,14,20,17,21,7,11,16,22,10,9,15,13,18,19,12,6)(23,24,26,30,37,47,60,76,49,29,35,43,53,66,81,97,110,78,46,58,72,87,102,107,73,88,103,75,92,108,118,123,122,104,71,44,54,67,82,98,111,119,121,101,68,42,27,31,38,48,61,77,93,99,65,39,25,28,33,40,50,63,79,95,62,36,45,56,69,84,91,106,116,94,59,74,90,105,115,117,89,57,70,85,100,112,120,124,125,114,86,55,34,41,51,64,80,96,109,113,83,52,32)Polycyclic presentation:
2,3^2,19,103|c^a=c^2,d^a=d^18,d^b=d^7,e^b=e^561038 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35226, 60);