D₁₃₀₈₁ #39908560

order	26162
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₃₀₈₁
unambiguous semidirect product	C₁₀₃⋊D₁₂₇
unambiguous semidirect product	C₁₂₇⋊D₁₀₃

Splittings

Fitting, socle, derived, Hall	C₁₀₃×C₁₂₇ ⋊ C₂
Sylow	C₁₂₇ ⋊ D₁₀₃
Sylow	C₁₀₃ ⋊ D₁₂₇

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₀₃×C₁₂₇	C₂
LCS	G ▷ C₁₀₃×C₁₂₇
UCS	C₁

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 230
transitive degree	μ_t(G) = 13081

A minimal faithful permutation representation — 2 generators on 230 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);(2,103)(3,102)(4,101)(5,100)(6,99)(7,98)(8,97)(9,96)(10,95)(11,94)(12,93)(13,92)(14,91)(15,90)(16,89)(17,88)(18,87)(19,86)(20,85)(21,84)(22,83)(23,82)(24,81)(25,80)(26,79)(27,78)(28,77)(29,76)(30,75)(31,74)(32,73)(33,72)(34,71)(35,70)(36,69)(37,68)(38,67)(39,66)(40,65)(41,64)(42,63)(43,62)(44,61)(45,60)(46,59)(47,58)(48,57)(49,56)(50,55)(51,54)(52,53)(105,230)(106,229)(107,228)(108,227)(109,226)(110,225)(111,224)(112,223)(113,222)(114,221)(115,220)(116,219)(117,218)(118,217)(119,216)(120,215)(121,214)(122,213)(123,212)(124,211)(125,210)(126,209)(127,208)(128,207)(129,206)(130,205)(131,204)(132,203)(133,202)(134,201)(135,200)(136,199)(137,198)(138,197)(139,196)(140,195)(141,194)(142,193)(143,192)(144,191)(145,190)(146,189)(147,188)(148,187)(149,186)(150,185)(151,184)(152,183)(153,182)(154,181)(155,180)(156,179)(157,178)(158,177)(159,176)(160,175)(161,174)(162,173)(163,172)(164,171)(165,170)(166,169)(167,168)

Polycyclic presentation:

2,103,127|b^a=b^102,c^a=c^126

Conjugacy classes & character table

6542 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×D₁₃₀₈₁
maximal normal subgroup of	C₂×D₁₃₀₈₁
maximal quotient of	Dic₁₃₀₈₁, C₂×D₁₃₀₈₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26162, 3);

D13081 #39908560