Finite Group Databasebeta

← Group #13032944

Character table — Group #13032944

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size11112222222244444445555888888888888888888101010101010101010101010101010102020202020202020202020202020202020202020202020323232324040404040404040
order12224444888825881010104444224410102020202040404040404040404444888888888888488888888888888888888881010202044448888
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
χ911111111-1-1-1-111-1-111111111-11-1111111-1-1-1-1-1-1-1-11111-1-1-1-1111111111-1-1111111-1-111-1-1-1-1-1-1-1-1-1-11-11-11-11-11-11-1
χ1011111111-1-1-1-111-1-111111111-11-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111-1-111111111111-11-11-11-1-11-11
χ1111111111-1-1-1-111-1-11111111-11-11111111-1-1-1-1-1-1-1-11111-1-1-1-1111111111-1-11111-1-111-1-111-1-1-1-1-1-1-1-1-11-11-11-11-11-11
χ1211111111-1-1-1-111-1-11111111-11-11111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-111-1-111-1-111111111-11-11-11-111-11-1
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−iiiii1-11-1-11-11i−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−i1-11-1-11-11−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-11-111-11-1−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-11-111-11-1i−i−ii
χ171111-1-1111111-11-1-111111111-1-11-1-11-1-111111-1-1-1-1-1-111111111-1-111-1-1-1-1-11-11-11111111111-1-111-1-11-1-11-111-1-1-1-1-1
χ181111-1-1111111-11-1-111111111-1-11-1-11-1-111111-1-1-1-1-1-1111111-1-111-1-111-1-1-1-11-11-1-1-1-1-1-1-1-1-1-111-1-1111-1-11-111-11111
χ191111-1-1111111-11-1-11111111-111-1-1-11-1-111111-1-1-1-1-1-111111111-1-111-1-1-1-1-11-11-1-1-1-1-1-1-1-1-111-1-111-1-1-111-11-1-111111
χ201111-1-1111111-11-1-11111111-111-1-1-11-1-111111-1-1-1-1-1-1111111-1-111-1-111-1-1-1-11-1111111111-1-111-1-111-111-11-1-11-1-1-1-1
χ211111-1-1111111-11-1-1111-1-1-1-11-1-11-1-11-1-111111-1-1-1-111-1-1-1-1-1-1ii−i−i−i−iii111i−i−iiiiii−i−i−i−iii−i−i−i−iii1-1-111-1-11−i−iii
χ221111-1-1111111-11-1-1111-1-1-1-11-1-11-1-11-1-111111-1-1-1-111-1-1-1-1-1-1−i−iiiii−i−i111−iii−i−i−i−i−iiiii−i−iiiii−i−i1-1-111-1-11ii−i−i
χ231111-1-1111111-11-1-1111-1-1-1-1-111-1-1-11-1-111111-1-1-1-111-1-1-1-1-1-1ii−i−i−i−iii111i−i−ii−i−i−i−iiiiiii−i−i−i−iii-111-1-111-1ii−i−i
χ241111-1-1111111-11-1-1111-1-1-1-1-111-1-1-11-1-111111-1-1-1-111-1-1-1-1-1-1−i−iiiii−i−i111−iii−iiiii−i−i−i−i−i−iiiii−i−i-111-1-111-1−i−iii
χ251111-1-111-1-1-1-1-1111111111111-1-1-1-11-1-11-1-1-1-11111-1-111-1-1-1-111-1-111-1-1-1111-11-111-1-111-1-1-1-111-1-11111-1-1-1-111-11-11
χ261111-1-111-1-1-1-1-1111111111111-1-1-1-11-1-11-1-1-1-11111-1-111-1-1-1-1-1-111-1-111-111-11-11-1-111-1-11111-1-111-1-111-1-1-1-1111-11-1
χ271111-1-111-1-1-1-1-11111111111-1-111-1-11-1-11-1-1-1-11111-1-111-1-1-1-111-1-111-1-1-1111-11-1-1-111-1-111-1-111-1-111-1-11111-1-11-11-1
χ281111-1-111-1-1-1-1-11111111111-1-111-1-11-1-11-1-1-1-11111-1-111-1-1-1-1-1-111-1-111-111-11-1111-1-111-1-111-1-111-1-1-1-11111-1-1-11-11
χ291111-1-111-1-1-1-1-1111111-1-1-1-111-1-1-1-11-1-11-1-1-1-1111111-1-11111ii−i−i−i−iii1-1-1i−i−iiii−i−i−i−iii−i−iiiii−i−i11-1-111-1-1−iii−i
χ301111-1-111-1-1-1-1-1111111-1-1-1-111-1-1-1-11-1-11-1-1-1-1111111-1-11111−i−iiiii−i−i1-1-1−iii−i−i−iiiii−i−iii−i−i−i−iii11-1-111-1-1i−i−ii
χ311111-1-111-1-1-1-1-1111111-1-1-1-1-1-111-1-11-1-11-1-1-1-1111111-1-11111ii−i−i−i−iii1-1-1i−i−ii−i−iiiii−i−i−i−iiiii−i−i-1-111-1-111i−i−ii
χ321111-1-111-1-1-1-1-1111111-1-1-1-1-1-111-1-11-1-11-1-1-1-1111111-1-11111−i−iiiii−i−i1-1-1−iii−iii−i−i−i−iiiii−i−i−i−iii-1-111-1-111−iii−i
χ33222222-2-20000-220022222220000-2-2-222-20000000022-2-2000022222222-200-2-2-2-20000000000000000000000000000
χ34222222-2-20000-220022222220000-2-2-222-20000000022-2-20000-2-2-2-2-2-2-2-2-20022220000000000000000000000000000
χ35222222-2-20000-2200222-2-2-2-20000-2-2-222-200000000-2-22200002i2i2i2i−2i−2i−2i−2i200−2i−2i2i2i0000000000000000000000000000
χ36222222-2-20000-2200222-2-2-2-20000-2-2-222-200000000-2-2220000−2i−2i−2i−2i2i2i2i2i2002i2i−2i−2i0000000000000000000000000000
χ372222-2-2-2-2000022002222222000022-2-2-2-200000000-2-2-2-2000022-2-222-2-2200-22-220000000000000000000000000000
χ382222-2-2-2-2000022002222222000022-2-2-2-200000000-2-2-2-20000-2-222-2-2222002-22-20000000000000000000000000000
χ392222-2-2-2-200002200222-2-2-2-2000022-2-2-2-200000000222200002i2i−2i−2i−2i−2i2i2i-200−2i2i2i−2i0000000000000000000000000000
χ402222-2-2-2-200002200222-2-2-2-2000022-2-2-2-20000000022220000−2i−2i2i2i2i2i−2i−2i-2002i−2i−2i2i0000000000000000000000000000
χ412-22-200-222i2i−2i−2i0200-22-22i2i−2i−2i000000200-22i2i−2i−2i0000002i−2i22-2-2000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700000000000000000000
χ422-22-200-222i2i−2i−2i0200-22-22i2i−2i−2i000000200-22i2i−2i−2i0000002i−2i22-2-20000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700000000000000000000
χ432-22-200-222i2i−2i−2i0200-22-2−2i−2i2i2i000000200-22i2i−2i−2i000000−2i2i-2-222000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900000000000000000000
χ442-22-200-222i2i−2i−2i0200-22-2−2i−2i2i2i000000200-22i2i−2i−2i000000−2i2i-2-2220000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900000000000000000000
χ452-22-200-22−2i−2i2i2i0200-22-22i2i−2i−2i000000200-2−2i−2i2i2i0000002i−2i-2-222000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700000000000000000000
χ462-22-200-22−2i−2i2i2i0200-22-22i2i−2i−2i000000200-2−2i−2i2i2i0000002i−2i-2-2220000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700000000000000000000
χ472-22-200-22−2i−2i2i2i0200-22-2−2i−2i2i2i000000200-2−2i−2i2i2i000000−2i2i22-2-2000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900000000000000000000
χ482-22-200-22−2i−2i2i2i0200-22-2−2i−2i2i2i000000200-2−2i−2i2i2i000000−2i2i22-2-20000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900000000000000000000
χ492-2-222i−2i00i2−i2i2−i2022−22-2-22-22-200000002i−2i0i2−i2i2−i222−2−22i−2i00i2−i2i2−i22-22i−2i2-22i−2i02−2000000000000i2−i22−2i2−i22−2000000000000
χ502-2-222i−2i00i2−i2i2−i2022−22-2-22-22-200000002i−2i0i2−i2i2−i222−2−22i−2i00i2−i2i2−i2-22−2i2i-22−2i2i02−2000000000000−i2i2−22−i2i2−22000000000000
χ512-2-222i−2i00i2−i2i2−i2022−22-2-2-22-2200000002i−2i0i2−i2i2−i222−2−2−2i2i00−i2i2−i2i22i−2i-22−2i2i2-20−22000000000000−22i2−i22−2−i2i2000000000000
χ522-2-222i−2i00i2−i2i2−i2022−22-2-2-22-2200000002i−2i0i2−i2i2−i222−2−2−2i2i00−i2i2−i2i2−2i2i2-22i−2i-220−220000000000002−2−i2i2−22i2−i2000000000000
χ532-2-222i−2i00−i2i2−i2i202−222-2-22-22-200000002i−2i0−i2i2−i2i2−2−2222i−2i00−i2i2−i2i22-22i−2i2-22i−2i0−22000000000000−i2i2−22−i2i2−22000000000000
χ542-2-222i−2i00−i2i2−i2i202−222-2-22-22-200000002i−2i0−i2i2−i2i2−2−2222i−2i00−i2i2−i2i2-22−2i2i-22−2i2i0−22000000000000i2−i22−2i2−i22−2000000000000
χ552-2-222i−2i00−i2i2−i2i202−222-2-2-22-2200000002i−2i0−i2i2−i2i2−2−222−2i2i00i2−i2i2−i22i−2i-22−2i2i2-202−20000000000002−2−i2i2−22i2−i2000000000000
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χ612-2-22−2i2i00−i2i2−i2i2022−22-2-22-22-20000000−2i2i0−i2i2−i2i222−2−2−2i2i00−i2i2−i2i22-2−2i2i2-2−2i2i02−2000000000000−i2i22−2−i2i22−2000000000000
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χ908-8-888i−8i00−4i24i2−4i24i20-2−4242-22200000000000−2i2i0i2−i2i2−i222−2−2000000000000000000000000000000000000000000000000000
χ918-8-88−8i8i004i2−4i24i2−4i20-2−4242-222000000000002i−2i0−i2i2−i2i222−2−2000000000000000000000000000000000000000000000000000
χ928-8-88−8i8i00−4i24i2−4i24i20-242−42-222000000000002i−2i0i2−i2i2−i2−2−222000000000000000000000000000000000000000000000000000

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