C₂×D₈₇₉₁ #47975911

order	35164
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₁₇₅₈₂
direct product	C₂×D₈₇₉₁
unambiguous semidirect product	(C₂×C₅₉)⋊D₁₄₉
unambiguous semidirect product	(C₂×C₁₄₉)⋊D₅₉

Splittings

Fitting, socle	C₂×C₅₉×C₁₄₉ ⋊ C₂
derived, Hall	C₅₉×C₁₄₉ ⋊ C₂²
Sylow	C₁₄₉ ⋊ C₂×D₅₉
Sylow	C₅₉ ⋊ C₂×D₁₄₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₈₇₉₁
commutator, cosocle, hypocenter	C₅₉×C₁₄₉	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₅₉×C₁₄₉	C₂
LCS	G ▷ C₅₉×C₁₄₉
UCS	C₁ ◁ C₂

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 210
transitive degree	μ_t(G) = 17582

A minimal faithful permutation representation — 2 generators on 210 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);(4,61)(5,60)(6,59)(7,58)(8,57)(9,56)(10,55)(11,54)(12,53)(13,52)(14,51)(15,50)(16,49)(17,48)(18,47)(19,46)(20,45)(21,44)(22,43)(23,42)(24,41)(25,40)(26,39)(27,38)(28,37)(29,36)(30,35)(31,34)(32,33)(63,210)(64,209)(65,208)(66,207)(67,206)(68,205)(69,204)(70,203)(71,202)(72,201)(73,200)(74,199)(75,198)(76,197)(77,196)(78,195)(79,194)(80,193)(81,192)(82,191)(83,190)(84,189)(85,188)(86,187)(87,186)(88,185)(89,184)(90,183)(91,182)(92,181)(93,180)(94,179)(95,178)(96,177)(97,176)(98,175)(99,174)(100,173)(101,172)(102,171)(103,170)(104,169)(105,168)(106,167)(107,166)(108,165)(109,164)(110,163)(111,162)(112,161)(113,160)(114,159)(115,158)(116,157)(117,156)(118,155)(119,154)(120,153)(121,152)(122,151)(123,150)(124,149)(125,148)(126,147)(127,146)(128,145)(129,144)(130,143)(131,142)(132,141)(133,140)(134,139)(135,138)(136,137)

Conjugacy classes & character table

8794 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35164, 11);

C2×D8791 #47975911