C₂×#23756587 #34095258

order	20032
automorphism	?
homology	Abelianization (H₁) = C₂×C₃₂ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₂×#23756587

Splittings

derived, Sylow

C₃₁₃ ⋊ C₂×C₃₂

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₄	#14578818
commutator, hypocenter	C₃₁₃	C₂×C₃₂
Frattini	C₄	C₂×#14578818
Fitting	C₂×C₄×C₃₁₃	C₈
socle, prime radical	C₂²×C₃₁₃	C₁₆
cosocle	#19097564	C₂²
LCS	G ▷ C₃₁₃
UCS	C₁ ◁ C₂×C₄

34 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 347
transitive degree	μ_t(G) = 20032

A minimal faithful permutation representation — 2 generators on 347 points:

(2,3,4,7,5,8,10,16)(6,12,13,28,14,29,31,61)(9,19,20,43,21,44,46,37)(11,24,25,54,26,55,23,52)(15,33,34,73,35,74,76,62)(17,36,38,78,39,18,41,42)(22,48,49,97,50,98,100,120)(27,57,58,114,59,115,68,133)(30,64,65,124,66,125,127,79)(32,69,70,135,71,136,53,106)(40,81,82,157,83,63,122,123)(45,88,89,167,90,168,92,105)(47,93,94,175,95,109,85,162)(51,102,103,190,104,191,193,121)(56,110,111,164,112,87,166,86)(60,117,118,210,119,211,147,137)(67,129,130,222,131,214,132,213)(72,138,139,228,140,141,134,224)(75,143,144,200,145,230,232,153)(77,148,149,236,150,206,107,197)(80,154,155,108,156,198,152,199)(84,159,160,184,161,142,229,128)(91,170,171,256,172,179,185,223)(96,176,177,259,178,207,215,281)(99,181,182,261,183,205,221,195)(101,186,187,262,188,227,163,248)(113,202,203,278,204,180,260,216)(116,208,209,249,189,217,263,165)(126,218,219,268,220,173,174,196)(146,233,234,280,235,295,194,269)(151,237,238,297,239,290,225,240)(158,243,244,226,245,287,241,288)(169,253,254,304,255,252,251,247)(192,264,265,289,266,308,294,271)(201,274,275,258,276,273,242,299)(212,283,284,305,285,291,301,250)(231,292,277,310,293,306,257,272)(246,267,302,296,303,282,298,270)(279,311,309,307,286,312,300,313)(316,317,318,322,319,323,326,332,320,324,327,333,329,335,338,342,321,325,328,334,330,336,339,343,331,337,340,344,341,345,346,347);(1,2,6,15,36,3,9,22,51,81,12,30,67,132,159,33,75,146,187,94,38,80,149,70,25,4,11,27,60,110,19,45,91,173,202,48,99,184,127,221,102,192,267,263,177,82,158,238,139,58,13,32,72,141,208,64,126,210,136,227,129,190,73,61,120,213,269,148,133,223,160,246,237,224,118,34,77,151,240,283,143,231,284,287,312,233,265,144,123,216,262,307,292,281,304,175,258,305,249,164,78,152,241,298,274,154,242,300,308,310,236,296,234,193,268,135,226,289,261,167,54,108,200,124,43,7,17,40,84,93,24,56,113,205,176,57,116,188,100,185,117,212,286,260,254,111,201,277,219,89,20,47,96,179,253,88,169,255,168,252,170,178,95,46,92,174,257,276,166,251,203,279,285,211,171,49,101,189,115,207,181,204,112,55,109,161,83,39,16,37,79,153,199,52,105,195,271,288,106,196,103,194,270,197,272,264,309,275,198,273,302,244,155,42,86,165,250,299,162,247,259,306,313,248,278,157,232,294,295,311,243,301,293,230,291,297,239,150,76,147,228,290,303,229,256,114,206,280,222,97,28,62,121,214,186,69,137,220,125,217,138,140,71,31,68,134,225,245,122,215,209,282,266,191,182,65,128,183,98,180,218,172,90,44,87,119,59,26,10,23,53,107,156,41,85,163,235,145,74,142,130,131,66,29,63,104,50,21,8,18,35,14,5)(314,315)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20032, 1655);

C2×#23756587 #34095258