Finite Group Databasebeta

← Group #13015495

Character table — Group #13015495

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size111111112222222222224444444455555555888888888888888810101010101010101010101010101010101010101010101010101010101010101010101010101010101010101616161616161616404040404040404040404040
order12222222222244444444510101010101010444444444444101010102020202020202020444444444444888888888888888888888888888888882020202020202020444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i11111111-1-1-1-1iiii−i−i−i−i
χ61111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii11111111-1-1-1-1−i−i−i−iiiii
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-11111−i−i−i−iiiii
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii-1-1-1-1-1-1-1-11111iiii−i−i−i−i
χ911111111-1-1-1-11111-1-1-1-1111111111111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-11111-1-1-1-1111111111111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-111-1-111
χ1111111111-1-1-1-11111-1-1-1-11111111111111111-1-111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-111
χ1211111111-1-1-1-11111-1-1-1-11111111111111111-1-111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-11111-1-111-1-1
χ1311111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1-1-111ii−i−i−i−iii
χ1411111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1-1-111−i−iiiii−i−i
χ1511111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-111111111-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1111111-1-1−i−iiiii−i−i
χ1611111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-111111111-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1111111-1-1ii−i−i−i−iii
χ1711-1-111-1-111-1-111-1-111-1-1111-1-11-1-11111-1-1-1-1i−ii−i11-1-111-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−ii−ii−ii−ii−ii−ii−i
χ1811-1-111-1-111-1-111-1-111-1-1111-1-11-1-11111-1-1-1-1i−ii−i11-1-111-1-111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111ii−i−iii−i−ii−ii−i−ii−ii−ii−ii
χ1911-1-111-1-111-1-111-1-111-1-1111-1-11-1-11111-1-1-1-1−ii−ii11-1-111-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iii−ii−ii−ii−ii−ii−ii
χ2011-1-111-1-111-1-111-1-111-1-1111-1-11-1-11111-1-1-1-1−ii−ii11-1-111-1-111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111−i−iii−i−iii−ii−iii−ii−ii−ii−i
χ2111-1-111-1-111-1-111-1-111-1-1111-1-11-1-1-1-1-1-11111i−ii−i11-1-111-1-111-1-111-1-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i−ii−ii-11-111-11-1
χ2211-1-111-1-111-1-111-1-111-1-1111-1-11-1-1-1-1-1-11111i−ii−i11-1-111-1-111-1-111-1-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i−ii−ii1-11-1-11-11
χ2311-1-111-1-111-1-111-1-111-1-1111-1-11-1-1-1-1-1-11111−ii−ii11-1-111-1-111-1-111-1-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iiii−ii−i1-11-1-11-11
χ2411-1-111-1-111-1-111-1-111-1-1111-1-11-1-1-1-1-1-11111−ii−ii11-1-111-1-111-1-111-1-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iiii−ii−i-11-111-11-1
χ2511-1-111-1-1-1-11111-1-1-1-111111-1-11-1-11111-1-1-1-1i−i−ii-1-11111-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111ii−i−i−i−iiii−i−iii−i−iii−i−ii
χ2611-1-111-1-1-1-11111-1-1-1-111111-1-11-1-11111-1-1-1-1i−i−ii-1-11111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1ii−i−i−i−iiii−i−ii−iii−i−iii−i
χ2711-1-111-1-1-1-11111-1-1-1-111111-1-11-1-11111-1-1-1-1−iii−i-1-11111-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111−i−iiiii−i−i−iii−i−iii−i−iii−i
χ2811-1-111-1-1-1-11111-1-1-1-111111-1-11-1-11111-1-1-1-1−iii−i-1-11111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1−i−iiiii−i−i−iii−ii−i−iii−i−ii
χ2911-1-111-1-1-1-11111-1-1-1-111111-1-11-1-1-1-1-1-11111i−i−ii-1-11111-1-1-1-111111111-1-1-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii−iii−i-111-11-1-11
χ3011-1-111-1-1-1-11111-1-1-1-111111-1-11-1-1-1-1-1-11111i−i−ii-1-11111-1-1-1-111111111-1-1-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii−iii−i1-1-11-111-1
χ3111-1-111-1-1-1-11111-1-1-1-111111-1-11-1-1-1-1-1-11111−iii−i-1-11111-1-1-1-111111111-1-1-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−ii−i−ii1-1-11-111-1
χ3211-1-111-1-1-1-11111-1-1-1-111111-1-11-1-1-1-1-1-11111−iii−i-1-11111-1-1-1-111111111-1-1-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−ii−i−ii-111-11-1-11
χ33222222222222-2-2-2-2-2-2-2-2222222222222222200002222-2-2-2-2-2-2-2-2-2-222-2-222-2-2-2-20000000000000000000000000000000000000000000000000000
χ34222222222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-200002222-2-2-2-2-2-2-2-222-2-222-2-222220000000000000000000000000000000000000000000000000000
χ3522222222-2-2-2-2-2-2-2-2222222222222222222220000-2-2-2-2-2-2-2-22222-2-2-2-222-2-222-2-20000000000000000000000000000000000000000000000000000
χ3622222222-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-20000-2-2-2-2-2-2-2-222222222-2-222-2-2220000000000000000000000000000000000000000000000000000
χ37222-2-2-22-200002-22-200002-2-22-222-22i2i−2i−2i2i2i−2i−2i000000002-22-200002i−2i000000002i−2i00000000−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ3700000000−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ3900000000000000000000
χ38222-2-2-22-200002-22-200002-2-22-222-22i2i−2i−2i2i2i−2i−2i000000002-22-200002i−2i000000002i−2i000000002ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000002ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900000000000000000000
χ39222-2-2-22-200002-22-200002-2-22-222-2−2i−2i2i2i−2i−2i2i2i000000002-22-20000−2i2i00000000−2i2i00000000−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ3900000000−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ3700000000000000000000
χ40222-2-2-22-200002-22-200002-2-22-222-2−2i−2i2i2i−2i−2i2i2i000000002-22-20000−2i2i00000000−2i2i000000002ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000002ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700000000000000000000
χ41222-2-2-22-20000-22-2200002-2-22-222-22i2i−2i−2i2i2i−2i−2i00000000-22-220000−2i2i00000000−2i2i−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ3900000000−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ370000000000000000000000000000
χ42222-2-2-22-20000-22-2200002-2-22-222-22i2i−2i−2i2i2i−2i−2i00000000-22-220000−2i2i00000000−2i2i2ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000002ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000000000000000000000000000
χ43222-2-2-22-20000-22-2200002-2-22-222-2−2i−2i2i2i−2i−2i2i2i00000000-22-2200002i−2i000000002i−2i−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ3700000000−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ390000000000000000000000000000
χ44222-2-2-22-20000-22-2200002-2-22-222-2−2i−2i2i2i−2i−2i2i2i00000000-22-2200002i−2i000000002i−2i2ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000002ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000000000000000000000000000
χ4522-22-2-2-2200002-2-2200002-2-2-222-222i2i−2i−2i−2i−2i2i2i000000002-2-220000−2i2i000000002i−2i00000000−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700000000−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900000000000000000000
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χ10244-4-444-4-4-4-44444-4-4-4-444-1-1-111-11100000000−4i4i4i−4i11-1-1-1-11111-1-100000000000000000000000000000000000000000000ii−i−i−i−iii000000000000
χ10344-4-444-4-4-4-444-4-44444-4-4-1-1-111-11100000000000011-1-111-1-1-1-11100000000000000000000000000000000000000000000i5−i5−i5i5−i5i5i5−i5000000000000
χ10444-4-444-4-4-4-444-4-44444-4-4-1-1-111-11100000000000011-1-111-1-1-1-11100000000000000000000000000000000000000000000−i5i5i5−i5i5−i5−i5i5000000000000
χ105888-8-8-88-800008-88-80000-222-22-2-220000000000000000-22-2200000000000000000000000000000000000000000000000000000000000000000000
χ106888-8-8-88-80000-88-880000-222-22-2-2200000000000000002-22-200000000000000000000000000000000000000000000000000000000000000000000
χ10788-88-8-8-8800008-8-880000-2222-2-22-20000000000000000-222-200000000000000000000000000000000000000000000000000000000000000000000
χ10888-88-8-8-880000-888-80000-2222-2-22-200000000000000002-2-2200000000000000000000000000000000000000000000000000000000000000000000
χ1098-8888-8-8-88-88-800000000-2-22222-2-2000000000000-22-22000000000000000000000000000000000000000000000000000000000000000000000000
χ1108-8888-8-8-8-88-8800000000-2-22222-2-20000000000002-22-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1118-88-8-88-88000000008i−8i8i−8i-22-22-22-2200000000000000000000−2i2i−2i2i0000000000000000000000000000000000000000000000000000000000000000
χ1128-88-8-88-8800000000−8i8i−8i8i-22-22-22-22000000000000000000002i−2i2i−2i0000000000000000000000000000000000000000000000000000000000000000
χ1138-8-88-888-8000000008i−8i−8i8i-22-2-2222-200000000000000000000−2i2i2i−2i0000000000000000000000000000000000000000000000000000000000000000
χ1148-8-88-888-800000000−8i8i8i−8i-22-2-2222-2000000000000000000002i−2i−2i2i0000000000000000000000000000000000000000000000000000000000000000
χ1158-8-8-88-8888-8-8800000000-2-22-2-2222000000000000-222-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1168-8-8-88-888-888-800000000-2-22-2-22220000000000002-2-22000000000000000000000000000000000000000000000000000000000000000000000000

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