D₁₃₄₃₉ #41001856

order	26878
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₃₄₃₉
unambiguous semidirect product	C₈₉⋊D₁₅₁
unambiguous semidirect product	C₁₅₁⋊D₈₉

Splittings

Fitting, socle, derived, Hall	C₈₉×C₁₅₁ ⋊ C₂
Sylow	C₁₅₁ ⋊ D₈₉
Sylow	C₈₉ ⋊ D₁₅₁

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₈₉×C₁₅₁	C₂
LCS	G ▷ C₈₉×C₁₅₁
UCS	C₁

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 240
transitive degree	μ_t(G) = 13439

A minimal faithful permutation representation — 2 generators on 240 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);(2,89)(3,88)(4,87)(5,86)(6,85)(7,84)(8,83)(9,82)(10,81)(11,80)(12,79)(13,78)(14,77)(15,76)(16,75)(17,74)(18,73)(19,72)(20,71)(21,70)(22,69)(23,68)(24,67)(25,66)(26,65)(27,64)(28,63)(29,62)(30,61)(31,60)(32,59)(33,58)(34,57)(35,56)(36,55)(37,54)(38,53)(39,52)(40,51)(41,50)(42,49)(43,48)(44,47)(45,46)(91,240)(92,239)(93,238)(94,237)(95,236)(96,235)(97,234)(98,233)(99,232)(100,231)(101,230)(102,229)(103,228)(104,227)(105,226)(106,225)(107,224)(108,223)(109,222)(110,221)(111,220)(112,219)(113,218)(114,217)(115,216)(116,215)(117,214)(118,213)(119,212)(120,211)(121,210)(122,209)(123,208)(124,207)(125,206)(126,205)(127,204)(128,203)(129,202)(130,201)(131,200)(132,199)(133,198)(134,197)(135,196)(136,195)(137,194)(138,193)(139,192)(140,191)(141,190)(142,189)(143,188)(144,187)(145,186)(146,185)(147,184)(148,183)(149,182)(150,181)(151,180)(152,179)(153,178)(154,177)(155,176)(156,175)(157,174)(158,173)(159,172)(160,171)(161,170)(162,169)(163,168)(164,167)(165,166)

Polycyclic presentation:

2,89,151|b^a=b^88,c^a=c^150

Conjugacy classes & character table

6721 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×D₁₃₄₃₉
maximal normal subgroup of	C₂×D₁₃₄₃₉
maximal quotient of	Dic₁₃₄₃₉, C₂×D₁₃₄₃₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26878, 3);

D13439 #41001856