D₁₆₁₇₁ #44568962

order	32342
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₆₁₇₁
unambiguous semidirect product	C₁₀₃⋊D₁₅₇
unambiguous semidirect product	C₁₅₇⋊D₁₀₃

Splittings

Fitting, socle, derived, Hall	C₁₀₃×C₁₅₇ ⋊ C₂
Sylow	C₁₅₇ ⋊ D₁₀₃
Sylow	C₁₀₃ ⋊ D₁₅₇

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₀₃×C₁₅₇	C₂
LCS	G ▷ C₁₀₃×C₁₅₇
UCS	C₁

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 260
transitive degree	μ_t(G) = 16171

A minimal faithful permutation representation — 2 generators on 260 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)(104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260);(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)(105,260)(106,259)(107,258)(108,257)(109,256)(110,255)(111,254)(112,253)(113,252)(114,251)(115,250)(116,249)(117,248)(118,247)(119,246)(120,245)(121,244)(122,243)(123,242)(124,241)(125,240)(126,239)(127,238)(128,237)(129,236)(130,235)(131,234)(132,233)(133,232)(134,231)(135,230)(136,229)(137,228)(138,227)(139,226)(140,225)(141,224)(142,223)(143,222)(144,221)(145,220)(146,219)(147,218)(148,217)(149,216)(150,215)(151,214)(152,213)(153,212)(154,211)(155,210)(156,209)(157,208)(158,207)(159,206)(160,205)(161,204)(162,203)(163,202)(164,201)(165,200)(166,199)(167,198)(168,197)(169,196)(170,195)(171,194)(172,193)(173,192)(174,191)(175,190)(176,189)(177,188)(178,187)(179,186)(180,185)(181,184)(182,183)

Polycyclic presentation:

2,103,157|b^a=b^102,c^a=c^156

Conjugacy classes & character table

8087 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×D₁₆₁₇₁
maximal normal subgroup of	C₂×D₁₆₁₇₁
maximal quotient of	Dic₁₆₁₇₁, C₂×D₁₆₁₇₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32342, 3);

D16171 #44568962