D₁₆₂₄₁ #44570378

order	32482
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₆₂₄₁
unambiguous semidirect product	C₁₀₉⋊D₁₄₉
unambiguous semidirect product	C₁₄₉⋊D₁₀₉

Splittings

Fitting, socle, derived, Hall	C₁₀₉×C₁₄₉ ⋊ C₂
Sylow	C₁₄₉ ⋊ D₁₀₉
Sylow	C₁₀₉ ⋊ D₁₄₉

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₀₉×C₁₄₉	C₂
LCS	G ▷ C₁₀₉×C₁₄₉
UCS	C₁

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 258
transitive degree	μ_t(G) = 16241

A minimal faithful permutation representation — 2 generators on 258 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);(2,109)(3,108)(4,107)(5,106)(6,105)(7,104)(8,103)(9,102)(10,101)(11,100)(12,99)(13,98)(14,97)(15,96)(16,95)(17,94)(18,93)(19,92)(20,91)(21,90)(22,89)(23,88)(24,87)(25,86)(26,85)(27,84)(28,83)(29,82)(30,81)(31,80)(32,79)(33,78)(34,77)(35,76)(36,75)(37,74)(38,73)(39,72)(40,71)(41,70)(42,69)(43,68)(44,67)(45,66)(46,65)(47,64)(48,63)(49,62)(50,61)(51,60)(52,59)(53,58)(54,57)(55,56)(111,258)(112,257)(113,256)(114,255)(115,254)(116,253)(117,252)(118,251)(119,250)(120,249)(121,248)(122,247)(123,246)(124,245)(125,244)(126,243)(127,242)(128,241)(129,240)(130,239)(131,238)(132,237)(133,236)(134,235)(135,234)(136,233)(137,232)(138,231)(139,230)(140,229)(141,228)(142,227)(143,226)(144,225)(145,224)(146,223)(147,222)(148,221)(149,220)(150,219)(151,218)(152,217)(153,216)(154,215)(155,214)(156,213)(157,212)(158,211)(159,210)(160,209)(161,208)(162,207)(163,206)(164,205)(165,204)(166,203)(167,202)(168,201)(169,200)(170,199)(171,198)(172,197)(173,196)(174,195)(175,194)(176,193)(177,192)(178,191)(179,190)(180,189)(181,188)(182,187)(183,186)(184,185)

Polycyclic presentation:

2,109,149|b^a=b^108,c^a=c^148

Conjugacy classes & character table

8122 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×D₁₆₂₄₁
maximal normal subgroup of	C₂×D₁₆₂₄₁
maximal quotient of	Dic₁₆₂₄₁, C₂×D₁₆₂₄₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32482, 3);

D16241 #44570378