Finite Group Databasebeta

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D₁₇₅₉ #16812919

• metacyclic
• supersolvable
• metabelian
• solvable
• monolithic
• monomial
• stem
• Frobenius
• ambivalent

Aliases

Splittings

Subgroups

4 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 1759 points:

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018)(744,1017)(745,1016)(746,1015)(747,1014)(748,1013)(749,1012)(750,1011)(751,1010)(752,1009)(753,1008)(754,1007)(755,1006)(756,1005)(757,1004)(758,1003)(759,1002)(760,1001)(761,1000)(762,999)(763,998)(764,997)(765,996)(766,995)(767,994)(768,993)(769,992)(770,991)(771,990)(772,989)(773,988)(774,987)(775,986)(776,985)(777,984)(778,983)(779,982)(780,981)(781,980)(782,979)(783,978)(784,977)(785,976)(786,975)(787,974)(788,973)(789,972)(790,971)(791,970)(792,969)(793,968)(794,967)(795,966)(796,965)(797,964)(798,963)(799,962)(800,961)(801,960)(802,959)(803,958)(804,957)(805,956)(806,955)(807,954)(808,953)(809,952)(810,951)(811,950)(812,949)(813,948)(814,947)(815,946)(816,945)(817,944)(818,943)(819,942)(820,941)(821,940)(822,939)(823,938)(824,937)(825,936)(826,935)(827,934)(828,933)(829,932)(830,931)(831,930)(832,929)(833,928)(834,927)(835,926)(836,925)(837,924)(838,923)(839,922)(840,921)(841,920)(842,919)(843,918)(844,917)(845,916)(846,915)(847,914)(848,913)(849,912)(850,911)(851,910)(852,909)(853,908)(854,907)(855,906)(856,905)(857,904)(858,903)(859,902)(860,901)(861,900)(862,899)(863,898)(864,897)(865,896)(866,895)(867,894)(868,893)(869,892)(870,891)(871,890)(872,889)(873,888)(874,887)(875,886)(876,885)(877,884)(878,883)(879,882)(880,881)

Polycyclic presentation:

2,1759|b^a=b^1758

Conjugacy classes & character table

881 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3518, 1);