D₈₇₉₁ #31798458

order	17582
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₈₇₉₁
unambiguous semidirect product	C₅₉⋊D₁₄₉
unambiguous semidirect product	C₁₄₉⋊D₅₉

Splittings

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

Subgroups

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

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 208
transitive degree	μ_t(G) = 8791

A minimal faithful permutation representation — 2 generators on 208 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);(2,59)(3,58)(4,57)(5,56)(6,55)(7,54)(8,53)(9,52)(10,51)(11,50)(12,49)(13,48)(14,47)(15,46)(16,45)(17,44)(18,43)(19,42)(20,41)(21,40)(22,39)(23,38)(24,37)(25,36)(26,35)(27,34)(28,33)(29,32)(30,31)(61,208)(62,207)(63,206)(64,205)(65,204)(66,203)(67,202)(68,201)(69,200)(70,199)(71,198)(72,197)(73,196)(74,195)(75,194)(76,193)(77,192)(78,191)(79,190)(80,189)(81,188)(82,187)(83,186)(84,185)(85,184)(86,183)(87,182)(88,181)(89,180)(90,179)(91,178)(92,177)(93,176)(94,175)(95,174)(96,173)(97,172)(98,171)(99,170)(100,169)(101,168)(102,167)(103,166)(104,165)(105,164)(106,163)(107,162)(108,161)(109,160)(110,159)(111,158)(112,157)(113,156)(114,155)(115,154)(116,153)(117,152)(118,151)(119,150)(120,149)(121,148)(122,147)(123,146)(124,145)(125,144)(126,143)(127,142)(128,141)(129,140)(130,139)(131,138)(132,137)(133,136)(134,135)

Polycyclic presentation:

2,59,149|b^a=b^58,c^a=c^148

Conjugacy classes & character table

4397 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₅₉×D₁₄₉, C₂×D₈₇₉₁
maximal normal subgroup of	D₅₉×D₁₄₉, C₂×D₈₇₉₁
maximal quotient of	Dic₈₇₉₁, C₂×D₈₇₉₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17582, 3);

D8791 #31798458