Finite Group DatabasebetaFinite Group Databasebeta| order | 35028 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #19154246⋊D3 |
| Fitting, socle, derived | C3×C7×C139 ⋊ C22×C3 |
| Hall | C3×#15668588 ⋊ C22 |
| Hall | C7×C139 ⋊ C2×C3×D3 |
| Sylow | C139 ⋊ C2×C3⋊AGL(1,𝔽7) |
| Sylow | C7 ⋊ D3×D139⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C7×C139 | C22×C3 |
| LCS | G ▷ C3×C7×C139 | |
| UCS | C1 | |
88 conjugacy classes of subgroups.
| minimal degree | μ(G) = 149 |
| transitive degree | μt(G) = 2919 |
A minimal faithful permutation representation — 2 generators on 149 points:
(2,3)(5,8,9,6,7,10)(11,12,18)(13,22,34)(14,16,23)(15,26,17)(19,35,51)(20,36,33)(21,39,25)(24,48,30)(27,52,74)(28,53,47)(29,58,38)(31,49,32)(37,71,43)(40,75,103)(41,76,66)(42,81,57)(44,69,55)(45,50,72)(46,54,67)(56,100,62)(59,104,133)(60,105,89)(61,110,80)(63,94,78)(64,73,101)(65,92,91)(68,77,96)(70,98,90)(79,131,85)(82,129,143)(83,134,117)(84,127,109)(86,122,107)(87,102,132)(88,124,119)(93,106,128)(95,126,112)(97,120,111)(99,130,118)(108,148,113)(114,141,136)(115,116,146)(121,135,147)(123,145,138)(125,139,137)(140,144,149);(1,2,3)(4,5,7,10,9,8,6)(12,13)(14,16)(15,19)(17,18)(20,24)(21,27)(22,30)(23,32)(25,34)(26,36)(28,37)(29,40)(31,43)(33,45)(35,46)(38,51)(39,54)(41,56)(42,59)(44,62)(47,64)(48,55)(49,53)(50,68)(52,65)(57,74)(58,77)(60,79)(61,82)(63,85)(66,87)(67,90)(69,92)(70,93)(71,78)(72,76)(73,97)(75,88)(80,103)(81,106)(83,108)(84,111)(86,113)(89,115)(91,118)(94,120)(95,121)(96,112)(98,124)(99,125)(100,107)(101,105)(102,129)(104,116)(109,133)(110,135)(114,137)(117,119)(122,139)(123,140)(126,143)(127,144)(128,138)(130,146)(131,136)(132,134)(141,149)(142,147)(145,148)Polycyclic presentation:
2^2,3^2,7,139|f^a=f^138,d^b=d^2,e^b=e^6,e^c=e^2,f^c=f^42300 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35028, 123);