D₁₃₀₆₇ #39908449

order	26134
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₃₀₆₇
unambiguous semidirect product	C₇₃⋊D₁₇₉
unambiguous semidirect product	C₁₇₉⋊D₇₃

Splittings

Fitting, socle, derived, Hall	C₇₃×C₁₇₉ ⋊ C₂
Sylow	C₁₇₉ ⋊ D₇₃
Sylow	C₇₃ ⋊ D₁₇₉

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇₃×C₁₇₉	C₂
LCS	G ▷ C₇₃×C₁₇₉
UCS	C₁

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 252
transitive degree	μ_t(G) = 13067

A minimal faithful permutation representation — 2 generators on 252 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);(2,73)(3,72)(4,71)(5,70)(6,69)(7,68)(8,67)(9,66)(10,65)(11,64)(12,63)(13,62)(14,61)(15,60)(16,59)(17,58)(18,57)(19,56)(20,55)(21,54)(22,53)(23,52)(24,51)(25,50)(26,49)(27,48)(28,47)(29,46)(30,45)(31,44)(32,43)(33,42)(34,41)(35,40)(36,39)(37,38)(75,252)(76,251)(77,250)(78,249)(79,248)(80,247)(81,246)(82,245)(83,244)(84,243)(85,242)(86,241)(87,240)(88,239)(89,238)(90,237)(91,236)(92,235)(93,234)(94,233)(95,232)(96,231)(97,230)(98,229)(99,228)(100,227)(101,226)(102,225)(103,224)(104,223)(105,222)(106,221)(107,220)(108,219)(109,218)(110,217)(111,216)(112,215)(113,214)(114,213)(115,212)(116,211)(117,210)(118,209)(119,208)(120,207)(121,206)(122,205)(123,204)(124,203)(125,202)(126,201)(127,200)(128,199)(129,198)(130,197)(131,196)(132,195)(133,194)(134,193)(135,192)(136,191)(137,190)(138,189)(139,188)(140,187)(141,186)(142,185)(143,184)(144,183)(145,182)(146,181)(147,180)(148,179)(149,178)(150,177)(151,176)(152,175)(153,174)(154,173)(155,172)(156,171)(157,170)(158,169)(159,168)(160,167)(161,166)(162,165)(163,164)

Polycyclic presentation:

2,73,179|b^a=b^72,c^a=c^178

Conjugacy classes & character table

6535 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×D₁₃₀₆₇
maximal normal subgroup of	C₂×D₁₃₀₆₇
maximal quotient of	Dic₁₃₀₆₇, C₂×D₁₃₀₆₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26134, 3);

D13067 #39908449