D₉₀₇₃ #31827498

order	18146
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₉₀₇₃
unambiguous semidirect product	C₄₃⋊D₂₁₁
unambiguous semidirect product	C₂₁₁⋊D₄₃

Splittings

Fitting, socle, derived, Hall	C₄₃×C₂₁₁ ⋊ C₂
Sylow	C₂₁₁ ⋊ D₄₃
Sylow	C₄₃ ⋊ D₂₁₁

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₄₃×C₂₁₁	C₂
LCS	G ▷ C₄₃×C₂₁₁
UCS	C₁

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 254
transitive degree	μ_t(G) = 9073

A minimal faithful permutation representation — 2 generators on 254 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)(44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254);(2,43)(3,42)(4,41)(5,40)(6,39)(7,38)(8,37)(9,36)(10,35)(11,34)(12,33)(13,32)(14,31)(15,30)(16,29)(17,28)(18,27)(19,26)(20,25)(21,24)(22,23)(45,254)(46,253)(47,252)(48,251)(49,250)(50,249)(51,248)(52,247)(53,246)(54,245)(55,244)(56,243)(57,242)(58,241)(59,240)(60,239)(61,238)(62,237)(63,236)(64,235)(65,234)(66,233)(67,232)(68,231)(69,230)(70,229)(71,228)(72,227)(73,226)(74,225)(75,224)(76,223)(77,222)(78,221)(79,220)(80,219)(81,218)(82,217)(83,216)(84,215)(85,214)(86,213)(87,212)(88,211)(89,210)(90,209)(91,208)(92,207)(93,206)(94,205)(95,204)(96,203)(97,202)(98,201)(99,200)(100,199)(101,198)(102,197)(103,196)(104,195)(105,194)(106,193)(107,192)(108,191)(109,190)(110,189)(111,188)(112,187)(113,186)(114,185)(115,184)(116,183)(117,182)(118,181)(119,180)(120,179)(121,178)(122,177)(123,176)(124,175)(125,174)(126,173)(127,172)(128,171)(129,170)(130,169)(131,168)(132,167)(133,166)(134,165)(135,164)(136,163)(137,162)(138,161)(139,160)(140,159)(141,158)(142,157)(143,156)(144,155)(145,154)(146,153)(147,152)(148,151)(149,150)

Polycyclic presentation:

2,43,211|b^a=b^42,c^a=c^210

Conjugacy classes & character table

4538 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₄₃×D₂₁₁, C₂×D₉₀₇₃
maximal normal subgroup of	D₄₃×D₂₁₁, C₂×D₉₀₇₃
maximal quotient of	Dic₉₀₇₃, C₂×D₉₀₇₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18146, 3);

D9073 #31827498