Finite Group Databasebeta

← Group #13032943

Character table — Group #13032943

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size11112222222244444445555888888888888888888101010101010101010101010101010102020202020202020202020202020202020202020202020323232324040404040404040
order12224444888845881010104444224420202020202040404040404040404444888888888888288888888888888888888881010202044448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ311111111111111111111111-1-1-1-11111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-1-1ii−i−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1ii−i−i
χ61111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii-1-1-1−i−iii−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1−i−iii
χ71111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-1-1ii−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111−i−iii
χ81111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii-1-1-1−i−iiiiiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111ii−i−i
χ911111111-1-1-1-111-1-111111111-11-1111111-1-1-1-1-1-1-1-11111-1-1-1-1111111111-1-1111111-1-111-1-1-1-1-1-1-1-1-1-11-11-111-1-11-11-1
χ1011111111-1-1-1-111-1-111111111-11-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111-1-111111111111-11-111-1-1-11-11
χ1111111111-1-1-1-111-1-11111111-11-11111111-1-1-1-1-1-1-1-11111-1-1-1-1111111111-1-11111-1-111-1-111-1-1-1-1-1-1-1-1-11-11-1-111-11-11
χ1211111111-1-1-1-111-1-11111111-11-11111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-111-1-111-1-111111111-11-11-1-1111-11-1
χ1311111111-1-1-1-111-1-1111-1-1-1-11-11-1111111-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i-111ii−i−iii−i−i−i−iii−i−i−i−iiiii1-11-1-1-111i−i−ii
χ1411111111-1-1-1-111-1-1111-1-1-1-11-11-1111111-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiii-111−i−iii−i−iiiii−i−iiiii−i−i−i−i1-11-1-1-111−iii−i
χ1511111111-1-1-1-111-1-1111-1-1-1-1-11-11111111-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i-111ii−i−i−i−iiiii−i−i−i−i−i−iiiii-11-1111-1-1−iii−i
χ1611111111-1-1-1-111-1-1111-1-1-1-1-11-11111111-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiii-111−i−iiiii−i−i−i−iiiiiii−i−i−i−i-11-1111-1-1i−i−ii
χ171111-1-1111111-11-1-111111111-1-11-1-1-1-1111111-1-1-1-1-1-111111111-1-111-1-1-1-1-11-11-11111111111-1-111-1-11-1-111-11-1-1-1-1-1
χ181111-1-1111111-11-1-111111111-1-11-1-1-1-1111111-1-1-1-1-1-1111111-1-111-1-111-1-1-1-11-11-1-1-1-1-1-1-1-1-1-111-1-1111-1-111-11-11111
χ191111-1-1111111-11-1-11111111-111-1-1-1-1-1111111-1-1-1-1-1-111111111-1-111-1-1-1-1-11-11-1-1-1-1-1-1-1-1-111-1-111-1-1-111-1-11-111111
χ201111-1-1111111-11-1-11111111-111-1-1-1-1-1111111-1-1-1-1-1-1111111-1-111-1-111-1-1-1-11-1111111111-1-111-1-111-111-1-11-11-1-1-1-1
χ211111-1-1111111-11-1-1111-1-1-1-11-1-11-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1ii−i−i−i−iii111i−i−iiiiii−i−i−i−iii−i−i−i−iii1-1-11-11-11−i−iii
χ221111-1-1111111-11-1-1111-1-1-1-11-1-11-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1−i−iiiii−i−i111−iii−i−i−i−i−iiiii−i−iiiii−i−i1-1-11-11-11ii−i−i
χ231111-1-1111111-11-1-1111-1-1-1-1-111-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1ii−i−i−i−iii111i−i−ii−i−i−i−iiiiiii−i−i−i−iii-111-11-11-1ii−i−i
χ241111-1-1111111-11-1-1111-1-1-1-1-111-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1−i−iiiii−i−i111−iii−iiiii−i−i−i−i−i−iiiii−i−i-111-11-11-1−i−iii
χ251111-1-111-1-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-111-1-111-1-1-1111-11-111-1-111-1-1-1-111-1-11111-1-11-1-11-11-11
χ261111-1-111-1-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-111-1-111-111-11-11-1-111-1-11111-1-111-1-111-1-11-1-111-11-1
χ271111-1-111-1-1-1-1-11111111111-1-111-1-1-1-111-1-1-1-11111-1-111-1-1-1-111-1-111-1-1-1111-11-1-1-111-1-111-1-111-1-111-1-111-111-11-11-1
χ281111-1-111-1-1-1-1-11111111111-1-111-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-111-1-111-111-11-1111-1-111-1-111-1-111-1-1-1-111-111-1-11-11
χ291111-1-111-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1111111-1-11111ii−i−i−i−iii1-1-1i−i−iiii−i−i−i−iii−i−iiiii−i−i11-1-1-111-1−iii−i
χ301111-1-111-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1111111-1-11111−i−iiiii−i−i1-1-1−iii−i−i−iiiii−i−iii−i−i−i−iii11-1-1-111-1i−i−ii
χ311111-1-111-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111-1-11111ii−i−i−i−iii1-1-1i−i−ii−i−iiiii−i−i−i−iiiii−i−i-1-1111-1-11i−i−ii
χ321111-1-111-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111-1-11111−i−iiiii−i−i1-1-1−iii−iii−i−i−i−iiiii−i−i−i−iii-1-1111-1-11−iii−i
χ33222222-2-20000-22002222222000022-2-2-2-20000000022-2-2000022222222-200-2-2-2-20000000000000000000000000000
χ34222222-2-20000-22002222222000022-2-2-2-20000000022-2-20000-2-2-2-2-2-2-2-2-20022220000000000000000000000000000
χ35222222-2-20000-2200222-2-2-2-2000022-2-2-2-200000000-2-22200002i2i2i2i−2i−2i−2i−2i200−2i−2i2i2i0000000000000000000000000000
χ36222222-2-20000-2200222-2-2-2-2000022-2-2-2-200000000-2-2220000−2i−2i−2i−2i2i2i2i2i2002i2i−2i−2i0000000000000000000000000000
χ372222-2-2-2-20000220022222220000-2-222-2-200000000-2-2-2-2000022-2-222-2-2200-22-220000000000000000000000000000
χ382222-2-2-2-20000220022222220000-2-222-2-200000000-2-2-2-20000-2-222-2-2222002-22-20000000000000000000000000000
χ392222-2-2-2-200002200222-2-2-2-20000-2-222-2-200000000222200002i2i−2i−2i−2i−2i2i2i-200−2i2i2i−2i0000000000000000000000000000
χ402222-2-2-2-200002200222-2-2-2-20000-2-222-2-20000000022220000−2i−2i2i2i2i2i−2i−2i-2002i−2i−2i2i0000000000000000000000000000
χ4122-2-2002-222-2-20200-2-222i2i−2i−2i000000002-222-2-20000002i−2i2i2i−2i−2i000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900000000000000000000
χ4222-2-2002-222-2-20200-2-222i2i−2i−2i000000002-222-2-20000002i−2i2i2i−2i−2i0000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900000000000000000000
χ4322-2-2002-222-2-20200-2-22−2i−2i2i2i000000002-222-2-2000000−2i2i−2i−2i2i2i000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700000000000000000000
χ4422-2-2002-222-2-20200-2-22−2i−2i2i2i000000002-222-2-2000000−2i2i−2i−2i2i2i0000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700000000000000000000
χ4522-2-2002-2-2-2220200-2-222i2i−2i−2i000000002-2-2-2220000002i−2i−2i−2i2i2i000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900000000000000000000
χ4622-2-2002-2-2-2220200-2-222i2i−2i−2i000000002-2-2-2220000002i−2i−2i−2i2i2i0000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900000000000000000000
χ4722-2-2002-2-2-2220200-2-22−2i−2i2i2i000000002-2-2-222000000−2i2i2i2i−2i−2i000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700000000000000000000
χ4822-2-2002-2-2-2220200-2-22−2i−2i2i2i000000002-2-2-222000000−2i2i2i2i−2i−2i0000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700000000000000000000
χ492-22-22i−2i00i2−i2i2−i2022−22-2-22-22-200002i−2i0000i2−i2i2−i222−2−22i−2i00i2−i2i2−i22-22i−2i2-22i−2i02−2000000000000i2−i22−2i2−i22−2000000000000
χ502-22-22i−2i00i2−i2i2−i2022−22-2-22-22-200002i−2i0000i2−i2i2−i222−2−22i−2i00i2−i2i2−i2-22−2i2i-22−2i2i02−2000000000000−i2i2−22−i2i2−22000000000000
χ512-22-22i−2i00i2−i2i2−i2022−22-2-2-22-2200002i−2i0000i2−i2i2−i222−2−2−2i2i00−i2i2−i2i22i−2i-22−2i2i2-20−22000000000000−22i2−i22−2−i2i2000000000000
χ522-22-22i−2i00i2−i2i2−i2022−22-2-2-22-2200002i−2i0000i2−i2i2−i222−2−2−2i2i00−i2i2−i2i2−2i2i2-22i−2i-220−220000000000002−2−i2i2−22i2−i2000000000000
χ532-22-22i−2i00−i2i2−i2i202−222-2-22-22-200002i−2i0000−i2i2−i2i2−2−2222i−2i00−i2i2−i2i22-22i−2i2-22i−2i0−22000000000000−i2i2−22−i2i2−22000000000000
χ542-22-22i−2i00−i2i2−i2i202−222-2-22-22-200002i−2i0000−i2i2−i2i2−2−2222i−2i00−i2i2−i2i2-22−2i2i-22−2i2i0−22000000000000i2−i22−2i2−i22−2000000000000
χ552-22-22i−2i00−i2i2−i2i202−222-2-2-22-2200002i−2i0000−i2i2−i2i2−2−222−2i2i00i2−i2i2−i22i−2i-22−2i2i2-202−20000000000002−2−i2i2−22i2−i2000000000000
χ562-22-22i−2i00−i2i2−i2i202−222-2-2-22-2200002i−2i0000−i2i2−i2i2−2−222−2i2i00i2−i2i2−i2−2i2i2-22i−2i-2202−2000000000000−22i2−i22−2−i2i2000000000000
χ572-22-2−2i2i00i2−i2i2−i202−222-2-22-22-20000−2i2i0000i2−i2i2−i2−2−222−2i2i00i2−i2i2−i22-2−2i2i2-2−2i2i0−22000000000000i2−i2−22i2−i2−22000000000000
χ582-22-2−2i2i00i2−i2i2−i202−222-2-22-22-20000−2i2i0000i2−i2i2−i2−2−222−2i2i00i2−i2i2−i2-222i−2i-222i−2i0−22000000000000−i2i22−2−i2i22−2000000000000
χ592-22-2−2i2i00i2−i2i2−i202−222-2-2-22-220000−2i2i0000i2−i2i2−i2−2−2222i−2i00−i2i2−i2i22i−2i2-2−2i2i-2202−2000000000000−22−i2i22−2i2−i2000000000000
χ602-22-2−2i2i00i2−i2i2−i202−222-2-2-22-220000−2i2i0000i2−i2i2−i2−2−2222i−2i00−i2i2−i2i2−2i2i-222i−2i2-202−20000000000002−2i2−i2−22−i2i2000000000000
χ612-22-2−2i2i00−i2i2−i2i2022−22-2-22-22-20000−2i2i0000−i2i2−i2i222−2−2−2i2i00−i2i2−i2i22-2−2i2i2-2−2i2i02−2000000000000−i2i22−2−i2i22−2000000000000
χ622-22-2−2i2i00−i2i2−i2i2022−22-2-22-22-20000−2i2i0000−i2i2−i2i222−2−2−2i2i00−i2i2−i2i2-222i−2i-222i−2i02−2000000000000i2−i2−22i2−i2−22000000000000
χ632-22-2−2i2i00−i2i2−i2i2022−22-2-2-22-220000−2i2i0000−i2i2−i2i222−2−22i−2i00i2−i2i2−i22i−2i2-2−2i2i-220−220000000000002−2i2−i2−22−i2i2000000000000
χ642-22-2−2i2i00−i2i2−i2i2022−22-2-2-22-220000−2i2i0000−i2i2−i2i222−2−22i−2i00i2−i2i2−i2−2i2i-222i−2i2-20−22000000000000−22−i2i22−2i2−i2000000000000
χ654444444444444-144-1-1-100004444-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000000000000000000-1-1-1-100000000
χ664444444444444-144-1-1-10000-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000000000000000000111100000000
χ6744444444-4-4-4-44-1-4-4-1-1-100004-44-4-1-1-1-1-1-111111111000000000000000000000000000000000000000-11-1100000000
χ6844444444-4-4-4-44-1-4-4-1-1-10000-44-44-1-1-1-1-1-1111111110000000000000000000000000000000000000001-11-100000000
χ694444-4-4444444-4-1-4-4-1-1-100004-4-441111-1-1-1-1-1-11111000000000000000000000000000000000000000-111-100000000
χ704444-4-4444444-4-1-4-4-1-1-10000-444-41111-1-1-1-1-1-111110000000000000000000000000000000000000001-1-1100000000
χ714444-4-444-4-4-4-4-4-144-1-1-1000044-4-41111-1-11111-1-1-1-1000000000000000000000000000000000000000-1-11100000000
χ724444-4-444-4-4-4-4-4-144-1-1-10000-4-4441111-1-11111-1-1-1-100000000000000000000000000000000000000011-1-100000000
χ7344-4-400-4400000400-4-444i4i−4i−4i00000000-440000000000−4i4i00000000000000000000000000000000000000000000000
χ7444-4-400-4400000400-4-44−4i−4i4i4i00000000-4400000000004i−4i00000000000000000000000000000000000000000000000
χ754-4-4400002i2−2i2−2i22i20400-44-44i−4i−4i4i00000000002i2−2i2−2i22i200000000−222222−220000000000000000000000000000000000000000000
χ764-4-4400002i2−2i2−2i22i20400-44-4−4i4i4i−4i00000000002i2−2i2−2i22i20000000022−22−22220000000000000000000000000000000000000000000
χ774-4-440000−2i22i22i2−2i20400-44-44i−4i−4i4i0000000000−2i22i22i2−2i20000000022−22−22220000000000000000000000000000000000000000000
χ784-4-440000−2i22i22i2−2i20400-44-4−4i4i4i−4i0000000000−2i22i22i2−2i200000000−222222−220000000000000000000000000000000000000000000
χ79888888-8-80000-8-200-2-2-200000000-2-2222200000000000000000000000000000000000000000000000000000000000
χ808888-8-8-8-800008-200-2-2-20000000022-2-22200000000000000000000000000000000000000000000000000000000000
χ8188-8-8008-888-8-80-20022-2000000000000-22-2-2220000000000000000000000000000000000000000000000000000000
χ8288-8-8008-8-8-8880-20022-2000000000000-2222-2-20000000000000000000000000000000000000000000000000000000
χ8388-8-800-8800000-20022-20000000000002-2000025−2525−25000000000000000000000000000000000000000000000000000
χ8488-8-800-8800000-20022-20000000000002-20000−2525−2525000000000000000000000000000000000000000000000000000
χ858-88-88i−8i004i2−4i24i2−4i20-242−42-22200000000−2i2i0000−i2i2−i2i2−2−222000000000000000000000000000000000000000000000000000
χ868-88-88i−8i00−4i24i2−4i24i20-2−4242-22200000000−2i2i0000i2−i2i2−i222−2−2000000000000000000000000000000000000000000000000000
χ878-88-8−8i8i004i2−4i24i2−4i20-2−4242-222000000002i−2i0000−i2i2−i2i222−2−2000000000000000000000000000000000000000000000000000
χ888-88-8−8i8i00−4i24i2−4i24i20-242−42-222000000002i−2i0000i2−i2i2−i2−2−222000000000000000000000000000000000000000000000000000
χ898-8-8800004i2−4i2−4i24i20-2002-2200000000002i5−2i500−i2i2i2−i210−10−1010000000000000000000000000000000000000000000000000000
χ908-8-8800004i2−4i2−4i24i20-2002-220000000000−2i52i500−i2i2i2−i2−101010−10000000000000000000000000000000000000000000000000000
χ918-8-880000−4i24i24i2−4i20-2002-2200000000002i5−2i500i2−i2−i2i2−101010−10000000000000000000000000000000000000000000000000000
χ928-8-880000−4i24i24i2−4i20-2002-220000000000−2i52i500i2−i2−i2i210−10−1010000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.