C₂×C₇⋊(D₂₇₁⋊C₅) #49182008

order	37940
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₇⋊(D₂₇₁⋊C₅)
unambiguous semidirect product	(C₂×C₇)⋊(D₂₇₁⋊C₅)
unambiguous semidirect product	(C₂×C₂₇₁⋊C₅)⋊D₇
unambiguous semidirect product	(C₂×D₁₈₉₇)⋊C₅

Splittings

Fitting, socle	C₂×C₇×C₂₇₁ ⋊ C₂×C₅
derived, Hall	C₇×C₂₇₁ ⋊ C₂²×C₅
Hall	C₇×C₂₇₁⋊C₅ ⋊ C₂²
Hall	C₂×D₁₈₉₇ ⋊ C₅
Hall	C₂₇₁⋊C₅ ⋊ C₂×D₇
Sylow	C₂₇₁ ⋊ C₂×C₅×D₇
Sylow	C₇ ⋊ C₂×D₂₇₁⋊C₅

Subgroups

	subgroup	G/H
center, hypercenter	C₂	C₇⋊(D₂₇₁⋊C₅)
commutator, cosocle, hypocenter	C₇×C₂₇₁	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₂₇₁	C₂×C₅
LCS	G ▷ C₇×C₂₇₁
UCS	C₁ ◁ C₂

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 280
transitive degree	μ_t(G) = 3794

A minimal faithful permutation representation — 2 generators on 280 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37940, 16);

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