Finite Group Databasebeta

← Group #14300285

Character table — Group #14300285

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size1111222222444444444444555588888810101010101010101010101010101010101012121616161616161616202020202020202020202020202020202020202020202020202024242424244848606060606060120120120
order12223446662256666101010121244441520203030302288881212121224242424242424248810103030303060604466888888121212122424242424242424242424244404040402020444488488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-11111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1111-1-1
χ41111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111
χ51111111111111111111111-1-1-1-1111111-1-1ii−i−i-1-1-1-1iiii−i−i−i−i1111111111-1-1-1-1iii−i−i−i-1-1-1-1iiiiii−i−i−i−i−i−i1111111ii−i−i-1-1-1i−i
χ61111111111111111111111-1-1-1-1111111-1-1ii−i−i-1-1-1-1iiii−i−i−i−i-1-111111111-1-1-1-1iii−i−i−i-1-1-1-1iiiiii−i−i−i−i−i−i-1-1-1-1-1-1-1−i−iii111−ii
χ71111111111111111111111-1-1-1-1111111-1-1−i−iii-1-1-1-1−i−i−i−iiiii1111111111-1-1-1-1−i−i−iiii-1-1-1-1−i−i−i−i−i−iiiiiii1111111−i−iii-1-1-1−ii
χ81111111111111111111111-1-1-1-1111111-1-1−i−iii-1-1-1-1−i−i−i−iiiii-1-111111111-1-1-1-1−i−i−iiii-1-1-1-1−i−i−i−i−i−iiiiiii-1-1-1-1-1-1-1ii−i−i111i−i
χ91111111111-1-11-1-1-1-111111111111111111111111111111111111-1-1-1-1-1-111-1-1111-1-11-1-1-1-1-1-111-1-1-1-111-1-1-1-1-11111-1-1111111-1-1-1
χ101111111111-1-11-1-1-1-1111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1111-1-11-1-1-1-1-1-111-1-1-1-111-1-1-1-11-1-1-1-111-1-1-1-1-1-1111
χ111111111111-1-11-1-1-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-111-111-111-1-1-1-1-1-11111-1-11111-11111-1-1-1-1-1-111-111
χ121111111111-1-11-1-1-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-111-111-1-1-1-1-1-11111-1-111111-1-1-1-1111111-1-11-1-1
χ131111111111-1-11-1-1-1-111111-1-1-1-1111111-1-1ii−i−i-1-1-1-1iiii−i−i−i−i11-1-1-1-1-1-11111-1-1i−i−i−iii1111ii−i−i−i−i−i−iiiii-11111-1-1ii−i−i-1-11−ii
χ141111111111-1-11-1-1-1-111111-1-1-1-1111111-1-1ii−i−i-1-1-1-1iiii−i−i−i−i-1-1-1-1-1-1-1-11111-1-1i−i−i−iii1111ii−i−i−i−i−i−iiiii1-1-1-1-111−i−iii11-1i−i
χ151111111111-1-11-1-1-1-111111-1-1-1-1111111-1-1−i−iii-1-1-1-1−i−i−i−iiiii11-1-1-1-1-1-11111-1-1−iiii−i−i1111−i−iiiiiii−i−i−i−i-11111-1-1−i−iii-1-11i−i
χ161111111111-1-11-1-1-1-111111-1-1-1-1111111-1-1−i−iii-1-1-1-1−i−i−i−iiiii-1-1-1-1-1-1-1-11111-1-1−iiii−i−i1111−i−iiiiiii−i−i−i−i1-1-1-1-111ii−i−i11-1−ii
χ1722222-2-22220020000222-2-222222-2-2222-2-2222222222222222200000000-2-200-2-2-200-2000000-2-20000-2-200000000000000000000
χ1822222-2-22220020000222-2-222222-2-2222-2-2-2-2-2-22222-2-2-2-2-2-2-2-200000000-2-200-2-220020000002200002200000000000000000000
χ1922222-2-22220020000222-2-2-2-2-2-22-2-2222222i2i−2i−2i-2-2-2-22i2i2i2i−2i−2i−2i−2i00000000-2-20022−2i002i000000−2i−2i00002i2i00000000000000000000
χ2022222-2-22220020000222-2-2-2-2-2-22-2-222222−2i−2i2i2i-2-2-2-2−2i−2i−2i−2i2i2i2i2i00000000-2-200222i00−2i0000002i2i0000−2i−2i00000000000000000000
χ212222-122-1-1-1222-1-1-1-1222-1-12222-122-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-10022-1-1-1-1-1-122-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ222222-122-1-1-1222-1-1-1-1222-1-12222-122-1-1-122-2-2-2-2-1-1-1-1111111110022-1-1-1-1-1-122-1-1-2-2-2-2-2-2-1-1-1-11111111111110000000000000000
χ232222-122-1-1-1222-1-1-1-1222-1-1-2-2-2-2-122-1-1-1-2-22i2i−2i−2i1111−i−i−i−iiiii0022-1-1-1-1-1-1-2-2112i2i2i−2i−2i−2i1111−i−i−i−i−i−iiiiiii0000000000000000
χ242222-122-1-1-1222-1-1-1-1222-1-1-2-2-2-2-122-1-1-1-2-2−2i−2i2i2i1111iiii−i−i−i−i0022-1-1-1-1-1-1-2-211−2i−2i−2i2i2i2i1111iiiiii−i−i−i−i−i−i0000000000000000
χ252222-122-1-1-1-2-221111222-1-12222-122-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-100-2-21111-1-1-2-2-1-12-2-22-2-21111-1-11111-1-111110000000000000000
χ262222-122-1-1-1-2-221111222-1-12222-122-1-1-122-2-2-2-2-1-1-1-11111111100-2-21111-1-1-2-2-1-1-222-222111111-1-1-1-111-1-1-1-10000000000000000
χ272222-122-1-1-1-2-221111222-1-1-2-2-2-2-122-1-1-1-2-22i2i−2i−2i1111−i−i−i−iiiii00-2-21111-1-122112i−2i−2i−2i2i2i-1-1-1-1−i−iiiiiii−i−i−i−i0000000000000000
χ282222-122-1-1-1-2-221111222-1-1-2-2-2-2-122-1-1-1-2-2−2i−2i2i2i1111iiii−i−i−i−i00-2-21111-1-12211−2i2i2i2i−2i−2i-1-1-1-1ii−i−i−i−i−i−iiiii0000000000000000
χ292222-1-2-2-1-1-1002−i3−i3i3i3222112222-1-2-2-1-1-1-2-22222-1-1-1-1-1-1-1-1-1-1-1-10000−i3−i3i3i3110011-200-200−i3−i3i3i311−i3−i3i3i311−i3−i3i3i30000000000000000
χ302222-1-2-2-1-1-1002−i3−i3i3i3222112222-1-2-2-1-1-1-2-2-2-2-2-2-1-1-1-1111111110000−i3−i3i3i3110011200200−i3−i3i3i3-1-1i3i3−i3−i3-1-1i3i3−i3−i30000000000000000
χ312222-1-2-2-1-1-1002−i3−i3i3i322211-2-2-2-2-1-2-2-1-1-1222i2i−2i−2i1111−i−i−i−iiiii0000−i3−i3i3i31100-1-1−2i002i00i3i3−i3−i3ii33−3−3−i−i−3−3330000000000000000
χ322222-1-2-2-1-1-1002−i3−i3i3i322211-2-2-2-2-1-2-2-1-1-122−2i−2i2i2i1111iiii−i−i−i−i0000−i3−i3i3i31100-1-12i00−2i00i3i3−i3−i3−i−i−3−333ii33−3−30000000000000000
χ332222-1-2-2-1-1-1002i3i3−i3−i3222112222-1-2-2-1-1-1-2-22222-1-1-1-1-1-1-1-1-1-1-1-10000i3i3−i3−i3110011-200-200i3i3−i3−i311i3i3−i3−i311i3i3−i3−i30000000000000000
χ342222-1-2-2-1-1-1002i3i3−i3−i3222112222-1-2-2-1-1-1-2-2-2-2-2-2-1-1-1-1111111110000i3i3−i3−i3110011200200i3i3−i3−i3-1-1−i3−i3i3i3-1-1−i3−i3i3i30000000000000000
χ352222-1-2-2-1-1-1002i3i3−i3−i322211-2-2-2-2-1-2-2-1-1-1222i2i−2i−2i1111−i−i−i−iiiii0000i3i3−i3−i31100-1-1−2i002i00−i3−i3i3i3ii−3−333−i−i33−3−30000000000000000
χ362222-1-2-2-1-1-1002i3i3−i3−i322211-2-2-2-2-1-2-2-1-1-122−2i−2i2i2i1111iiii−i−i−i−i0000i3i3−i3−i31100-1-12i00−2i00−i3−i3i3i3−i−i33−3−3ii−3−3330000000000000000
χ372-22-222-2-2-222-222-22-2-22-22-222-2-222-2-2-222-2000022-2-200000000002-22-22-22-22-22-20000002-22-20000000000000000000000000000
χ382-22-222-2-2-222-222-22-2-22-22-2-2-22222-2-2-22-220000-2-22200000000002-22-22-22-2-22-22000000-22-220000000000000000000000000000
χ392-22-222-2-2-22-222-22-22-22-22-222-2-222-2-2-222-2000022-2-20000000000-22-22-222-2-222-2000000-22-220000000000000000000000000000
χ402-22-222-2-2-22-222-22-22-22-22-2-2-22222-2-2-22-220000-2-2220000000000-22-22-222-22-2-220000002-22-20000000000000000000000000000
χ412-22-22-22-2-220020000-22-2-2222-2-22-22-2-22-22000022-2-20000000000000000-2200-2202i−2i02i−2i0000002i−2i2i−2i002i−2i2i−2i0000000000000000
χ422-22-22-22-2-220020000-22-2-2222-2-22-22-2-22-22000022-2-20000000000000000-2200-220−2i2i0−2i2i000000−2i2i−2i2i00−2i2i−2i2i0000000000000000
χ432-22-22-22-2-220020000-22-2-22-2-2222-22-2-222-20000-2-2220000000000000000-22002-202-20-220000002-22-200-22-220000000000000000
χ442-22-22-22-2-220020000-22-2-22-2-2222-22-2-222-20000-2-2220000000000000000-22002-20-2202-2000000-22-22002-22-20000000000000000
χ452-22-2-12-211-12-22-11-11-22-2-1122-2-2-12-211-12-20000-1-11133−3−333−3−3002-2-11-11-112-2-11000000-11-113−33−3−333−33−3−330000000000000000
χ462-22-2-12-211-12-22-11-11-22-2-1122-2-2-12-211-12-20000-1-111−3−333−3−333002-2-11-11-112-2-11000000-11-11−33−333−3−33−333−30000000000000000
χ472-22-2-12-211-12-22-11-11-22-2-11-2-222-12-211-1-22000011-1-1−i3−i3i3i3i3i3−i3−i3002-2-11-11-11-221-10000001-11-1−i3i3−i3i3i3−i3i3−i3i3−i3−i3i30000000000000000
χ482-22-2-12-211-12-22-11-11-22-2-11-2-222-12-211-1-22000011-1-1i3i3−i3−i3−i3−i3i3i3002-2-11-11-11-221-10000001-11-1i3−i3i3−i3−i3i3−i3i3−i3i3i3−i30000000000000000
χ492-22-2-12-211-1-2221-11-1-22-2-1122-2-2-12-211-12-20000-1-11133−3−333−3−300-221-11-1-11-22-110000001-11-13−3−333−33−3−333−30000000000000000
χ502-22-2-12-211-1-2221-11-1-22-2-1122-2-2-12-211-12-20000-1-111−3−333−3−33300-221-11-1-11-22-110000001-11-1−333−3−33−333−3−330000000000000000
χ512-22-2-12-211-1-2221-11-1-22-2-11-2-222-12-211-1-22000011-1-1−i3−i3i3i3i3i3−i3−i300-221-11-1-112-21-1000000-11-11−i3i3i3−i3−i3i3i3−i3−i3i3i3−i30000000000000000
χ522-22-2-12-211-1-2221-11-1-22-2-11-2-222-12-211-1-22000011-1-1i3i3−i3−i3−i3−i3i3i300-221-11-1-112-21-1000000-11-11i3−i3−i3i3i3−i3−i3i3i3−i3−i3i30000000000000000
χ532-22-2-1-2211-1002−i3i3i3−i3-22-21-122-2-2-1-2211-1-220000-1-11133−3−333−3−30000−i3i3i3−i31-1001-102i−2i02i−2i−i3i3i3−i3−33−ii−ii−33−ii−ii0000000000000000
χ542-22-2-1-2211-1002−i3i3i3−i3-22-21-122-2-2-1-2211-1-220000-1-111−3−333−3−3330000−i3i3i3−i31-1001-10−2i2i0−2i2i−i3i3i3−i33−3i−ii−i3−3i−ii−i0000000000000000
χ552-22-2-1-2211-1002−i3i3i3−i3-22-21-1-2-222-1-2211-12-2000011-1-1−i3−i3i3i3i3i3−i3−i30000−i3i3i3−i31-100-1102-20-22i3−i3−i3i3i3−i3-11-11−i3i31-11-10000000000000000
χ562-22-2-1-2211-1002−i3i3i3−i3-22-21-1-2-222-1-2211-12-2000011-1-1i3i3−i3−i3−i3−i3i3i30000−i3i3i3−i31-100-110-2202-2i3−i3−i3i3−i3i31-11-1i3−i3-11-110000000000000000
χ572-22-2-1-2211-1002i3−i3−i3i3-22-21-122-2-2-1-2211-1-220000-1-11133−3−333−3−30000i3−i3−i3i31-1001-10−2i2i0−2i2ii3−i3−i3i3−33i−ii−i−33i−ii−i0000000000000000
χ582-22-2-1-2211-1002i3−i3−i3i3-22-21-122-2-2-1-2211-1-220000-1-111−3−333−3−3330000i3−i3−i3i31-1001-102i−2i02i−2ii3−i3−i3i33−3−ii−ii3−3−ii−ii0000000000000000
χ592-22-2-1-2211-1002i3−i3−i3i3-22-21-1-2-222-1-2211-12-2000011-1-1−i3−i3i3i3i3i3−i3−i30000i3−i3−i3i31-100-110-2202-2−i3i3i3−i3i3−i31-11-1−i3i3-11-110000000000000000
χ602-22-2-1-2211-1002i3−i3−i3i3-22-21-1-2-222-1-2211-12-2000011-1-1i3i3−i3−i3−i3−i3i3i30000i3−i3−i3i31-100-1102-20-22−i3i3i3−i3−i3i3-11-11i3−i31-11-10000000000000000
χ612-2-222002-2-200200002-2-2002i−2i2i−2i2002-2-2002ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ119−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1092i−2i2i−2i2ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ119−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−i2i200000000000000000000000000000000000−i2−i2i2i2001−i−1+i1+i−1−i2−2000
χ622-2-222002-2-200200002-2-2002i−2i2i−2i2002-2-2002ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ119−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1092i−2i2i−2i2ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ119−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109i2−i200000000000000000000000000000000000i2i2−i2−i200−1+i1−i−1−i1+i−22000
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χ642-2-222002-2-200200002-2-2002i−2i2i−2i2002-2-200−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ1192ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092i−2i2i−2i−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ1192ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ109i2−i200000000000000000000000000000000000i2i2−i2−i2001−i−1+i1+i−1−i−22000
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Here ζ is a primitive root of unity of order 120 (ζ120 = 1); i = ζ30.