Finite Group Databasebeta

?

← Prev (#44501902) Next (#44501904) →

D₁₅₃₄₇ #44501903

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

Aliases

Splittings

Subgroups

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 252 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103)(104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252);(2,103)(3,102)(4,101)(5,100)(6,99)(7,98)(8,97)(9,96)(10,95)(11,94)(12,93)(13,92)(14,91)(15,90)(16,89)(17,88)(18,87)(19,86)(20,85)(21,84)(22,83)(23,82)(24,81)(25,80)(26,79)(27,78)(28,77)(29,76)(30,75)(31,74)(32,73)(33,72)(34,71)(35,70)(36,69)(37,68)(38,67)(39,66)(40,65)(41,64)(42,63)(43,62)(44,61)(45,60)(46,59)(47,58)(48,57)(49,56)(50,55)(51,54)(52,53)(105,252)(106,251)(107,250)(108,249)(109,248)(110,247)(111,246)(112,245)(113,244)(114,243)(115,242)(116,241)(117,240)(118,239)(119,238)(120,237)(121,236)(122,235)(123,234)(124,233)(125,232)(126,231)(127,230)(128,229)(129,228)(130,227)(131,226)(132,225)(133,224)(134,223)(135,222)(136,221)(137,220)(138,219)(139,218)(140,217)(141,216)(142,215)(143,214)(144,213)(145,212)(146,211)(147,210)(148,209)(149,208)(150,207)(151,206)(152,205)(153,204)(154,203)(155,202)(156,201)(157,200)(158,199)(159,198)(160,197)(161,196)(162,195)(163,194)(164,193)(165,192)(166,191)(167,190)(168,189)(169,188)(170,187)(171,186)(172,185)(173,184)(174,183)(175,182)(176,181)(177,180)(178,179)

Polycyclic presentation:

2,103,149|b^a=b^102,c^a=c^148

Conjugacy classes & character table

7675 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30694, 3);