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C2×D15235 #72295779

order60940
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD30470
direct productC2×D15235

Splittings

Fitting, socleC2×C5×C11×C277 ⋊ C2
derived, HallC5×C11×C277 ⋊ C22
HallC11×C277 ⋊ C2×D5
HallC5×C277 ⋊ C2×D11
SylowC277 ⋊ C2×D55
HallC5×C11 ⋊ C2×D277
SylowC11 ⋊ C2×D1385
SylowC5 ⋊ C2×D3047

Subgroups

subgroupG/H
center, hypercenterC2D15235
commutator, cosocle, hypocenterC5×C11×C277C22
FrattiniC1G
Fitting, socleC2×C5×C11×C277C2
LCSG ▷ C5×C11×C277
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 295
transitive degreeμt(G) = 30470

A minimal faithful permutation representation — 2 generators on 295 points:

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

Conjugacy classes & character table

15238 conjugacy classes. The character table is too large to display.

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

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