C₂×D₉₀₇₁ #49136792

order	36284
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₁₈₁₄₂
direct product	C₂×D₉₀₇₁
unambiguous semidirect product	(C₂×C₄₇)⋊D₁₉₃
unambiguous semidirect product	(C₂×C₁₉₃)⋊D₄₇

Splittings

Fitting, socle	C₂×C₄₇×C₁₉₃ ⋊ C₂
derived, Hall	C₄₇×C₁₉₃ ⋊ C₂²
Sylow	C₁₉₃ ⋊ C₂×D₄₇
Sylow	C₄₇ ⋊ C₂×D₁₉₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₉₀₇₁
commutator, cosocle, hypocenter	C₄₇×C₁₉₃	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₄₇×C₁₉₃	C₂
LCS	G ▷ C₄₇×C₁₉₃
UCS	C₁ ◁ C₂

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 242
transitive degree	μ_t(G) = 18142

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

Conjugacy classes & character table

9074 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36284, 11);

C2×D9071 #49136792