D₁₆₄₉₁ #45682245

order	32982
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₆₄₉₁
unambiguous semidirect product	C₃⋊D₅₄₉₇
unambiguous semidirect product	C₂₃⋊D₇₁₇
unambiguous semidirect product	C₂₃₉⋊D₆₉

Splittings

Fitting, socle, derived, Hall	C₃×C₂₃×C₂₃₉ ⋊ C₂
Hall	C₂₃×C₂₃₉ ⋊ D₃
Hall	C₃×C₂₃₉ ⋊ D₂₃
Sylow	C₂₃₉ ⋊ D₆₉
Hall	C₃×C₂₃ ⋊ D₂₃₉
Sylow	C₂₃ ⋊ D₇₁₇
Sylow	C₃ ⋊ D₅₄₉₇

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₂₃×C₂₃₉	C₂
LCS	G ▷ C₃×C₂₃×C₂₃₉
UCS	C₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 265
transitive degree	μ_t(G) = 16491

A minimal faithful permutation representation — 2 generators on 265 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)(27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265);(2,3)(5,26)(6,25)(7,24)(8,23)(9,22)(10,21)(11,20)(12,19)(13,18)(14,17)(15,16)(28,265)(29,264)(30,263)(31,262)(32,261)(33,260)(34,259)(35,258)(36,257)(37,256)(38,255)(39,254)(40,253)(41,252)(42,251)(43,250)(44,249)(45,248)(46,247)(47,246)(48,245)(49,244)(50,243)(51,242)(52,241)(53,240)(54,239)(55,238)(56,237)(57,236)(58,235)(59,234)(60,233)(61,232)(62,231)(63,230)(64,229)(65,228)(66,227)(67,226)(68,225)(69,224)(70,223)(71,222)(72,221)(73,220)(74,219)(75,218)(76,217)(77,216)(78,215)(79,214)(80,213)(81,212)(82,211)(83,210)(84,209)(85,208)(86,207)(87,206)(88,205)(89,204)(90,203)(91,202)(92,201)(93,200)(94,199)(95,198)(96,197)(97,196)(98,195)(99,194)(100,193)(101,192)(102,191)(103,190)(104,189)(105,188)(106,187)(107,186)(108,185)(109,184)(110,183)(111,182)(112,181)(113,180)(114,179)(115,178)(116,177)(117,176)(118,175)(119,174)(120,173)(121,172)(122,171)(123,170)(124,169)(125,168)(126,167)(127,166)(128,165)(129,164)(130,163)(131,162)(132,161)(133,160)(134,159)(135,158)(136,157)(137,156)(138,155)(139,154)(140,153)(141,152)(142,151)(143,150)(144,149)(145,148)(146,147)

Polycyclic presentation:

2,3,23,239|b^a=b^2,c^a=c^22,d^a=d^238

Conjugacy classes & character table

8247 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32982, 8);

D16491 #45682245