Finite Group Databasebeta

← Group #14304918

Character table — Group #14304918

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1111222222444444555588888888810101010101012121616161616161616202020202020202020202020202024242424244040404040404040404848606060606060120120120
order1222344666510101012124444412121520203030302212121212882020606060606060668888242424242424242444040404026688242424242020444488488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1111-1-1
χ311111111111111111111111111111111111-1-11111111111111111111111-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-11111-1-1-111
χ511111111111111111111-1-1-111111111111111-1-111-1-1-1-111111111111111-11111-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1
χ611111111111111111111-1-1-111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1111111-1-1-1-1-1-111-111
χ711111111111111111111-1-1-1111111111111-1-1-1-111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111
χ811111111111111111111-1-1-1111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1111111111111-1-11-1-1
χ91111111111111111-1-1-1-1111111111-1-1-1-1-1-11111111111-1-1ii−i−iiiii−i−i−i−i11111-1-1-1i−iii−i−i11ii−i−i-1-1-1i−i
χ101111111111111111-1-1-1-1111111111-1-1-1-1-1-11111111111-1-1−i−iii−i−i−i−iiiii11111-1-1-1−ii−i−iii11−i−iii-1-1-1−ii
χ111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-111111111-1-1ii−i−iiiii−i−i−i−i-1-1-1-1-1-1-1-1i−iii−i−i-1-1−i−iii111−ii
χ121111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-111111111-1-1−i−iii−i−i−i−iiiii-1-1-1-1-1-1-1-1−ii−i−iii-1-1ii−i−i111i−i
χ131111111111111111-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1ii−i−iiiii−i−i−i−i-11111111−ii−i−iii-1-1ii−i−i-1-11−ii
χ141111111111111111-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1−i−iii−i−i−i−iiiii-11111111i−iii−i−i-1-1−i−iii-1-11i−i
χ151111111111111111-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1ii−i−iiiii−i−i−i−i1-1-1-1-1111−ii−i−iii11−i−iii11-1i−i
χ161111111111111111-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1−i−iii−i−i−i−iiiii1-1-1-1-1111i−iii−i−i11ii−i−i11-1−ii
χ1722222-2-22222222-2-222220002-2-2222-2-222220000-2-20000-2-22-22-222-2-222-2-20000000000000000000000000
χ1822222-2-22222222-2-222220002-2-2222-2-222220000-2-20000-2-2-22-22-2-222-2-2220000000000000000000000000
χ1922222-2-22222222-2-2-2-2-2-20002-2-222222-2-2-2-20000-2-20000222i−2i−2i2i2i2i−2i−2i−2i−2i2i2i0000000000000000000000000
χ2022222-2-22222222-2-2-2-2-2-20002-2-222222-2-2-2-20000-2-2000022−2i2i2i−2i−2i−2i2i2i2i2i−2i−2i0000000000000000000000000
χ212222-122-1-1-12222-1-122222-1-1-122-1-1-122-1-1-1-10022-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000002-1-122-1-1-1-100000000000
χ222222-122-1-1-12222-1-122222-1-1-122-1-1-122-1-1-1-10022-1-1-1-1-1-1-1-1-2-2-2-211111111000002-1-1-2-2111100000000000
χ232222-122-1-1-12222-1-12222-211-122-1-1-122-1-1-1-100-2-2-1-11111-1-12222-1-1-1-1-1-1-1-100000-211-2-2111100000000000
χ242222-122-1-1-12222-1-12222-211-122-1-1-122-1-1-1-100-2-2-1-11111-1-1-2-2-2-21111111100000-21122-1-1-1-100000000000
χ252222-122-1-1-12222-1-1-2-2-2-22-1-1-122-1-1-1-2-211110022-1-1-1-1-1-1112i2i−2i−2i−i−i−i−iiiii00000-2112i−2i−i−iii00000000000
χ262222-122-1-1-12222-1-1-2-2-2-22-1-1-122-1-1-1-2-211110022-1-1-1-1-1-111−2i−2i2i2iiiii−i−i−i−i00000-211−2i2iii−i−i00000000000
χ272222-122-1-1-12222-1-1-2-2-2-2-211-122-1-1-1-2-2111100-2-2-1-11111112i2i−2i−2i−i−i−i−iiiii000002-1-1−2i2iii−i−i00000000000
χ282222-122-1-1-12222-1-1-2-2-2-2-211-122-1-1-1-2-2111100-2-2-1-1111111−2i−2i2i2iiiii−i−i−i−i000002-1-12i−2i−i−iii00000000000
χ292222-1-2-2-1-1-122221122220−i3i3-1-2-2-1-1-1-2-2-1-1-1-1000011−i3−i3i3i3112-22-2-1-111-1-111000000−i3i300−i3i3−i3i300000000000
χ302222-1-2-2-1-1-122221122220−i3i3-1-2-2-1-1-1-2-2-1-1-1-1000011−i3−i3i3i311-22-2211-1-111-1-1000000−i3i300i3−i3i3−i300000000000
χ312222-1-2-2-1-1-122221122220i3−i3-1-2-2-1-1-1-2-2-1-1-1-1000011i3i3−i3−i3112-22-2-1-111-1-111000000i3−i300i3−i3i3−i300000000000
χ322222-1-2-2-1-1-122221122220i3−i3-1-2-2-1-1-1-2-2-1-1-1-1000011i3i3−i3−i311-22-2211-1-111-1-1000000i3−i300−i3i3−i3i300000000000
χ332222-1-2-2-1-1-1222211-2-2-2-20−i3i3-1-2-2-1-1-1221111000011−i3−i3i3i3-1-12i−2i−2i2i−i−iiiii−i−i000000i3−i3003−3−3300000000000
χ342222-1-2-2-1-1-1222211-2-2-2-20−i3i3-1-2-2-1-1-1221111000011−i3−i3i3i3-1-1−2i2i2i−2iii−i−i−i−iii000000i3−i300−333−300000000000
χ352222-1-2-2-1-1-1222211-2-2-2-20i3−i3-1-2-2-1-1-1221111000011i3i3−i3−i3-1-12i−2i−2i2i−i−iiiii−i−i000000−i3i300−333−300000000000
χ362222-1-2-2-1-1-1222211-2-2-2-20i3−i3-1-2-2-1-1-1221111000011i3i3−i3−i3-1-1−2i2i2i−2iii−i−i−i−iii000000−i3i3003−3−3300000000000
χ372-22-222-2-2-222-22-22-222-2-200022-2-2-22-2222-2-22i−2i002-200002-200000000000002i2i−2i−2i0000000000000002i−2i000
χ382-22-222-2-2-222-22-22-222-2-200022-2-2-22-2222-2-2−2i2i002-200002-20000000000000−2i−2i2i2i000000000000000−2i2i000
χ392-22-222-2-2-222-22-22-2-2-22200022-2-2-222-2-2-2222i−2i002-20000-2200000000000002i2i−2i−2i000000000000000−2i2i000
χ402-22-222-2-2-222-22-22-2-2-22200022-2-2-222-2-2-222−2i2i002-20000-220000000000000−2i−2i2i2i0000000000000002i−2i000
χ412-22-22-22-2-222-22-2-2222-2-20002-22-2-222-222-2-20000-220000-2200000000000000000000000000002i−2i2i−2i00000
χ422-22-22-22-2-222-22-2-2222-2-20002-22-2-222-222-2-20000-220000-220000000000000000000000000000−2i2i−2i2i00000
χ432-22-22-22-2-222-22-2-22-2-2220002-22-2-22-22-2-2220000-2200002-200000000000000000000000000002-2-2200000
χ442-22-22-22-2-222-22-2-22-2-2220002-22-2-22-22-2-2220000-2200002-20000000000000000000000000000-222-200000
χ454444444444-1-1-1-1440000444-1-1-1-1-1-100000044-1-1-1-1-1-1-1-1000000000000004-1-1-1-1000000000-1-1000000000
χ464444444444-1-1-1-1440000444-1-1-1-1-1-1000000-4-4-1-1-1-1-1-1-1-100000000000000-4111100000000011000000000
χ474444444444-1-1-1-1440000-4-4-4-1-1-1-1-1-10000004411-1-1111100000000000000-4-1-1-1-100000000011000000000
χ484444444444-1-1-1-1440000-4-4-4-1-1-1-1-1-1000000-4-411-1-111110000000000000041111000000000-1-1000000000
χ4944-4-44004-4-44-4-44004i−4i4i−4i0004004-4-4004i−4i4i−4i0000000000000000000000000000000000000000000000000
χ5044-4-44004-4-44-4-4400−4i4i−4i4i0004004-4-400−4i4i−4i4i0000000000000000000000000000000000000000000000000
χ5144-4-4-200-2224-4-44004i−4i4i−4i000-200-22200−2i2i−2i2i0000000000000000002ζ13−2ζ29+2ζ37−2ζ53+2ζ61−2ζ77−2ζ101+2ζ109−2ζ13+2ζ29−2ζ37+2ζ53−2ζ61+2ζ77+2ζ101−2ζ109002ζ7−2ζ23+2ζ31−2ζ47−2ζ71+2ζ79+2ζ103−2ζ119−2ζ7+2ζ23−2ζ31+2ζ47+2ζ71−2ζ79−2ζ103+2ζ1190000000000000000000000000
χ5244-4-4-200-2224-4-44004i−4i4i−4i000-200-22200−2i2i−2i2i000000000000000000−2ζ13+2ζ29−2ζ37+2ζ53−2ζ61+2ζ77+2ζ101−2ζ1092ζ13−2ζ29+2ζ37−2ζ53+2ζ61−2ζ77−2ζ101+2ζ10900−2ζ7+2ζ23−2ζ31+2ζ47+2ζ71−2ζ79−2ζ103+2ζ1192ζ7−2ζ23+2ζ31−2ζ47−2ζ71+2ζ79+2ζ103−2ζ1190000000000000000000000000
χ5344-4-4-200-2224-4-4400−4i4i−4i4i000-200-222002i−2i2i−2i0000000000000000002ζ7−2ζ23+2ζ31−2ζ47−2ζ71+2ζ79+2ζ103−2ζ119−2ζ7+2ζ23−2ζ31+2ζ47+2ζ71−2ζ79−2ζ103+2ζ119002ζ13−2ζ29+2ζ37−2ζ53+2ζ61−2ζ77−2ζ101+2ζ109−2ζ13+2ζ29−2ζ37+2ζ53−2ζ61+2ζ77+2ζ101−2ζ1090000000000000000000000000
χ5444-4-4-200-2224-4-4400−4i4i−4i4i000-200-222002i−2i2i−2i000000000000000000−2ζ7+2ζ23−2ζ31+2ζ47+2ζ71−2ζ79−2ζ103+2ζ1192ζ7−2ζ23+2ζ31−2ζ47−2ζ71+2ζ79+2ζ103−2ζ11900−2ζ13+2ζ29−2ζ37+2ζ53−2ζ61+2ζ77+2ζ101−2ζ1092ζ13−2ζ29+2ζ37−2ζ53+2ζ61−2ζ77−2ζ101+2ζ1090000000000000000000000000
χ554-44-444-4-4-44-11-114-40000000-1-1111-10000004i−4i−55-11−55−55000000000000000−i−iii000000000−i5i5000000000
χ564-44-444-4-4-44-11-114-40000000-1-1111-10000004i−4i5−5-115−55−5000000000000000−i−iii000000000i5−i5000000000
χ574-44-444-4-4-44-11-114-40000000-1-1111-1000000−4i4i−55-11−55−55000000000000000ii−i−i000000000i5−i5000000000
χ584-44-444-4-4-44-11-114-40000000-1-1111-1000000−4i4i5−5-115−55−5000000000000000ii−i−i000000000−i5i5000000000
χ594-44-4-24-422-24-44-4-2244-4-4000-24-422-2-44-2-2220000-220000-220000000000000000000000000000000000000
χ604-44-4-24-422-24-44-4-22-4-444000-24-422-24-422-2-20000-2200002-20000000000000000000000000000000000000
χ614-44-4-2-4422-24-44-42-244-4-4000-2-4422-24-4-2-22200002-200002-20000000000000000000000000000000000000
χ624-44-4-2-4422-24-44-42-2-4-444000-2-4422-2-4422-2-200002-20000-220000000000000000000000000000000000000
χ634-4-44400-44-444-4-4004i−4i−4i4i000400-44-4004i−4i−4i4i0000000000000000000000000000000000000000000000000
χ644-4-44400-44-444-4-400−4i4i4i−4i000400-44-400−4i4i4i−4i0000000000000000000000000000000000000000000000000
χ654-4-44-2002-2244-4-4004i−4i−4i4i000-2002-2200−2i2i2i−2i00000000000000002ζ13−2ζ29+2ζ37−2ζ53+2ζ61−2ζ77−2ζ101+2ζ109−2ζ13+2ζ29−2ζ37+2ζ53−2ζ61+2ζ77+2ζ101−2ζ109002ζ7−2ζ23+2ζ31−2ζ47−2ζ71+2ζ79+2ζ103−2ζ119−2ζ7+2ζ23−2ζ31+2ζ47+2ζ71−2ζ79−2ζ103+2ζ119000000000000000000000000000
χ664-4-44-2002-2244-4-4004i−4i−4i4i000-2002-2200−2i2i2i−2i0000000000000000−2ζ13+2ζ29−2ζ37+2ζ53−2ζ61+2ζ77+2ζ101−2ζ1092ζ13−2ζ29+2ζ37−2ζ53+2ζ61−2ζ77−2ζ101+2ζ10900−2ζ7+2ζ23−2ζ31+2ζ47+2ζ71−2ζ79−2ζ103+2ζ1192ζ7−2ζ23+2ζ31−2ζ47−2ζ71+2ζ79+2ζ103−2ζ119000000000000000000000000000
χ674-4-44-2002-2244-4-400−4i4i4i−4i000-2002-22002i−2i−2i2i00000000000000002ζ7−2ζ23+2ζ31−2ζ47−2ζ71+2ζ79+2ζ103−2ζ119−2ζ7+2ζ23−2ζ31+2ζ47+2ζ71−2ζ79−2ζ103+2ζ119002ζ13−2ζ29+2ζ37−2ζ53+2ζ61−2ζ77−2ζ101+2ζ109−2ζ13+2ζ29−2ζ37+2ζ53−2ζ61+2ζ77+2ζ101−2ζ109000000000000000000000000000
χ684-4-44-2002-2244-4-400−4i4i4i−4i000-2002-22002i−2i−2i2i0000000000000000−2ζ7+2ζ23−2ζ31+2ζ47+2ζ71−2ζ79−2ζ103+2ζ1192ζ7−2ζ23+2ζ31−2ζ47−2ζ71+2ζ79+2ζ103−2ζ11900−2ζ13+2ζ29−2ζ37+2ζ53−2ζ61+2ζ77+2ζ101−2ζ1092ζ13−2ζ29+2ζ37−2ζ53+2ζ61−2ζ77−2ζ101+2ζ109000000000000000000000000000
χ6988888-8-8888-2-2-2-2-8-80000000-222-2-2-20000000000220000000000000000000000000000000000000000000
χ708888-488-4-4-4-2-2-2-2-4-400008-4-41-2-211100000000-2-2111111000000000000000000000000000000000000000
χ718888-488-4-4-4-2-2-2-2-4-40000-8441-2-2111000000002211-1-1-1-1000000000000000000000000000000000000000
χ728888-4-8-8-4-4-4-2-2-2-24400000−4i34i31221110000000000-1-1i3i3−i3−i3000000000000000000000000000000000000000
χ738888-4-8-8-4-4-4-2-2-2-244000004i3−4i31221110000000000-1-1−i3−i3i3i3000000000000000000000000000000000000000
χ7488-8-88008-8-8-222-2000000000-200-2220000000000000000000000000000000i10−i10i10−i1000000000000000000000
χ7588-8-88008-8-8-222-2000000000-200-2220000000000000000000000000000000−i10i10−i10i1000000000000000000000
χ768-88-88-88-8-88-22-22-880000000-22-222-200000000002-20000000000000000000000000000000000000000000
χ778-88-8-48-844-4-22-22-4400000001-22-1-1100000000−25251-15−55−5000000000000000000000000000000000000000
χ788-88-8-48-844-4-22-22-4400000001-22-1-110000000025−251-1−55−55000000000000000000000000000000000000000
χ798-88-8-4-8844-4-22-224-4000000012-2-1-110000000000-11−i15i15i15−i15000000000000000000000000000000000000000
χ808-88-8-4-8844-4-22-224-4000000012-2-1-110000000000-11i15−i15−i15i15000000000000000000000000000000000000000
χ818-8-88800-88-8-2-222000000000-2002-22000000000000000000000000000000010−10−101000000000000000000000
χ828-8-88800-88-8-2-222000000000-2002-220000000000000000000000000000000−101010−1000000000000000000000
χ831616-16-16-800-888-444-40000000002002-2-20000000000000000000000000000000000000000000000000000000
χ8416-16-1616-8008-88-4-444000000000200-22-20000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 120 (ζ120 = 1); i = ζ30.