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#30655953

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

Aliases

No aliases for this group.

Splittings

Subgroups

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 434 points:

(2,3,5)(4,7,12)(6,10,9)(8,14,22)(11,17,19)(13,20,16)(15,24,35)(18,27,32)(21,30,29)(23,33,26)(25,37,51)(28,40,48)(31,43,45)(34,46,42)(36,49,39)(38,53,70)(41,56,67)(44,59,64)(47,62,61)(50,65,58)(52,68,55)(54,72,92)(57,75,89)(60,78,86)(63,81,83)(66,84,80)(69,87,77)(71,90,74)(73,94,117)(76,97,114)(79,100,111)(82,103,108)(85,106,105)(88,109,102)(91,112,99)(93,115,96)(95,119,145)(98,122,142)(101,125,139)(104,128,136)(107,131,133)(110,134,130)(113,137,127)(116,140,124)(118,143,121)(120,147,176)(123,150,173)(126,153,170)(129,156,167)(132,159,164)(135,162,161)(138,165,158)(141,168,155)(144,171,152)(146,174,149)(148,178,210)(151,181,207)(154,184,204)(157,187,201)(160,190,198)(163,193,195)(166,196,192)(169,199,189)(172,202,186)(175,205,183)(177,208,180)(179,212,247)(182,215,244)(185,218,241)(188,221,238)(191,224,235)(194,227,232)(197,230,229)(200,233,226)(203,236,223)(206,239,220)(209,242,217)(211,245,214)(213,249,286)(216,252,283)(219,255,280)(222,258,277)(225,261,274)(228,264,271)(231,250,268)(234,269,266)(237,272,263)(240,275,260)(243,278,257)(246,281,254)(248,284,251)(253,289,322)(256,292,319)(259,295,316)(262,298,313)(265,301,310)(267,290,307)(270,306,305)(273,308,303)(276,311,300)(279,314,297)(282,317,294)(285,320,291)(287,323,288)(293,326,353)(296,329,350)(299,332,347)(302,335,344)(304,327,341)(309,340,339)(312,342,337)(315,345,334)(318,348,331)(321,351,328)(324,354,325)(330,357,378)(333,360,375)(336,363,372)(338,358,369)(343,368,367)(346,370,365)(349,373,362)(352,376,359)(355,379,356)(361,382,397)(364,385,394)(366,383,391)(371,390,389)(374,392,387)(377,395,384)(380,398,381)(386,401,410)(388,402,407)(393,406,405)(396,408,403)(399,411,400)(404,414,417)(409,416,415)(412,418,413)(419,421,420)(423,424,426)(425,428,432)(427,430,429)(431,433,434);(1,2,4,8,15,25,38,54,73,95,120,148,179,213,250,193,131,81,43,17,3,6,11,18,28,41,57,76,98,123,151,182,216,253,290,227,159,103,59,27,7,13,21,31,44,60,79,101,126,154,185,219,256,293,327,264,190,128,78,40,14,23,34,47,63,82,104,129,157,188,222,259,296,330,358,301,224,156,100,56,24,36,50,66,85,107,132,160,191,225,262,299,333,361,383,335,261,187,125,75,37,52,69,88,110,135,163,194,228,265,302,336,364,386,402,363,298,221,153,97,53,71,91,113,138,166,197,231,267,304,338,366,388,404,414,385,332,258,184,122,72,93,116,141,169,200,234,270,286,322,353,378,397,410,417,401,360,295,218,150,94,118,144,172,203,237,273,309,323,247,283,319,350,375,394,407,382,329,255,181,119,146,175,206,240,276,312,343,354,284,210,244,280,316,347,372,391,357,292,215,147,177,209,243,279,315,346,371,379,320,245,176,207,241,277,313,344,369,326,252,178,211,246,282,318,349,374,393,398,351,281,208,145,173,204,238,274,310,341,289,212,248,285,321,352,377,396,409,411,376,317,242,174,117,142,170,201,235,271,307,249,287,324,355,380,399,412,419,418,395,348,278,205,143,92,114,139,167,198,232,268,305,339,367,389,405,415,420,421,408,373,314,239,171,115,70,89,111,136,164,195,229,266,303,337,365,387,403,413,416,392,345,275,202,140,90,51,67,86,108,133,161,192,226,263,300,334,362,384,400,406,370,311,236,168,112,68,35,48,64,83,105,130,158,189,223,260,297,331,359,381,390,342,272,199,137,87,49,22,32,45,61,80,102,127,155,186,220,257,294,328,356,368,308,233,165,109,65,33,12,19,29,42,58,77,99,124,152,183,217,254,291,325,340,269,196,134,84,46,20,5,9,16,26,39,55,74,96,121,149,180,214,251,288,306,230,162,106,62,30,10)(422,423,425,426,429,428,432,434,433,424,427,431,430)

Polycyclic presentation:

3,13,421|b^a=b^9,c^a=c^20

Conjugacy classes & character table

1827 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16419, 4);