Finite Group Databasebeta

← Group #13030064

Character table — Group #13030064

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size111122222222444444444555588888888888888810101010101010101010101010101010161616161616161616202020202020202020202020202020202020202020404040404040404040
order12222244444422244510101044442441010101010102020202020204444444488888888101010202020202020244448888888888888888444888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1
χ3111111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1iiii−i−i−i−i111111111-1-1-1-1-1ii−i−iiiiiii−i−i−i−i−i−i-1-1-1iii−i−i−i
χ4111111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii111111111-1-1-1-1-1−i−iii−i−i−i−i−i−iiiiiii-1-1-1−i−i−iiii
χ51111111111111-1-11111111111-1-1-111-1-1-1-111111111111111111111111-1-11-1-11-1-1111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1
χ61111111111111-1-11111111111-1-1-111-1-1-1-111111111111111-1-1-1-1-1-1-1-11-1-11-1-11-1-1111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ71111111111111-1-1111111-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1iiii−i−i−i−i1-1-11-1-11-1-1-1-1-111−i−iiiiiiiii−i−i−i−i−i−i111−i−i−iiii
χ81111111111111-1-1111111-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1−i−i−i−iiiii1-1-11-1-11-1-1-1-1-111ii−i−i−i−i−i−i−i−iiiiiii111iii−i−i−i
χ911111111-1-1-1-1-1111-1111111111-1-1111111-1-111-1-1-1-1-1-1111111111111-111-1-1-11-1-1-11-111111111-1-1-1-111-1-1-1-1-1-111-1-11-1-1
χ1011111111-1-1-1-1-1111-1111111111-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-11-1-1-11-111-1-1-1-1-1-11111-1-11111-1-11-111-111
χ1111111111-1-1-1-1-1111-11111-1-1-1-11-1-1111111-1-111-1-11111-1-1-1-1iiii−i−i−i−i-111-1-1-11-1-11-11-1-1ii−i−iii−i−i−i−i−i−iiiii11-1i−i−i−iii
χ1211111111-1-1-1-1-1111-11111-1-1-1-11-1-1111111-1-111-1-11111-1-1-1-1−i−i−i−iiiii-111-1-1-11-1-11-11-1-1−i−iii−i−iiiiiii−i−i−i−i11-1−iiii−i−i
χ1311111111-1-1-1-1-1-1-11-111111111-11111-1-1-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-111111-11-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111-1-111-111
χ1411111111-1-1-1-1-1-1-11-111111111-11111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111-11-1-1-11111-1-11111-1-1111111-11-1-11-1-1
χ1511111111-1-1-1-1-1-1-11-11111-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1iiii−i−i−i−i-1-1-1-1111111-1111−i−iiiii−i−i−i−i−i−iiiii-1-11−iiii−i−i
χ1611111111-1-1-1-1-1-1-11-11111-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1−i−i−i−iiiii-1-1-1-1111111-1111ii−i−i−i−iiiiiii−i−i−i−i-1-11i−i−i−iii
χ171111-1-11111-1-1111-1-111111111-11-1-1-11111-1-11111-1-111-1-111111111111-1-1-1-1-1-111-1-11111111-1-111-1-1-1-111-1-1-11-1-11-1-11-1
χ181111-1-11111-1-1111-1-111111111-11-1-1-11111-1-11111-1-111-1-111-1-1-1-1-1-1-1-11-1-1-1-1-1-111-1-1111-1-1-1-111-1-11111-1-111-11-11-111-11
χ191111-1-11111-1-1111-1-11111-1-1-1-1-11-1-1-11111-1-1111111-1-111-1-1iiii−i−i−i−i1-1-1-1-1-1-11111-1-1-1ii−i−i−i−iii−i−iii−i−iii1-11−ii−ii−ii
χ201111-1-11111-1-1111-1-11111-1-1-1-1-11-1-1-11111-1-1111111-1-111-1-1−i−i−i−iiiii1-1-1-1-1-1-11111-1-1-1−i−iiiii−i−iii−i−iii−i−i1-11i−ii−ii−i
χ211111-1-11111-1-11-1-1-1-1111111111-11-1-1-1-1-1-1-1-11111-1-111-1-11111111111111-111-1-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-111-1-11-111-111-11
χ221111-1-11111-1-11-1-1-1-1111111111-11-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-1111-111-1-1-1-1-11-1-1111111-1-11111-1-1111-11-11-1-11-1
χ231111-1-11111-1-11-1-1-1-11111-1-1-1-11-11-1-1-1-1-1-1-1-1111111-1-111-1-1iiii−i−i−i−i111-111-1-1-111-111−i−iii−i−iii−i−iii−i−iii-11-1i−ii−ii−i
χ241111-1-11111-1-11-1-1-1-11111-1-1-1-11-11-1-1-1-1-1-1-1-1111111-1-111-1-1−i−i−i−iiiii111-111-1-1-111-111ii−i−iii−i−iii−i−iii−i−i-11-1−ii−ii−ii
χ251111-1-111-1-111-111-1111111111-1-11-1-111111111-1-111-1-1-1-11111111111-1-1-1111-1-1-11-1-1111111-1-1-1-111-1-1-1-1111-1-1-1-11-1-11
χ261111-1-111-1-111-111-1111111111-1-11-1-111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1111-1-1-11-1-111-1-1-1-11111-1-11111-1-11-1-111-111-1
χ271111-1-111-1-111-111-111111-1-1-1-1-1-11-1-111111111-1-1-1-11111-1-1iiii−i−i−i−i-1-1-1111-1-1-1-111-1-1ii−i−i−i−i−i−iiiiiii−i−i-111−i−iiii−i
χ281111-1-111-1-111-111-111111-1-1-1-1-1-11-1-111111111-1-1-1-11111-1-1−i−i−i−iiiii-1-1-1111-1-1-1-111-1-1−i−iiiiiii−i−i−i−i−i−iii-111ii−i−i−ii
χ291111-1-111-1-111-1-1-1-111111111111-1-1-1-1-1-1-11111-1-111-1-1-1-11111111111-1111-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-11111-111-1
χ301111-1-111-1-111-1-1-1-111111111111-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1111-1-1-1111-1-1-1-111111111-1-11111-1-1-111-1-11-1-11
χ311111-1-111-1-111-1-1-1-111111-1-1-1-111-1-1-1-1-1-1-11111-1-1-1-11111-1-1iiii−i−i−i−i-1111-1-1-111-11111−i−iii−i−i−i−iiiiiii−i−i1-1-1ii−i−i−ii
χ321111-1-111-1-111-1-1-1-111111-1-1-1-111-1-1-1-1-1-1-11111-1-1-1-11111-1-1−i−i−i−iiiii-1111-1-1-111-11111ii−i−iiiii−i−i−i−i−i−iii1-1-1−i−iiii−i
χ33222222-2-22222-200-2-22222222200022000022-2-222222222-2-200000000-200-200-200-2-2-2000000000000000000000000000
χ34222222-2-22222-200-2-22222-2-2-2-200022000022-2-222-2-2-2-2-2-22200000000-200-200-200222000000000000000000000000000
χ35222222-2-2-2-2-2-2200-2222222222000220000-2-2-2-2-2-2-2-2-2-222-2-200000000200200-2002-22000000000000000000000000000
χ36222222-2-2-2-2-2-2200-222222-2-2-2-2000220000-2-2-2-2-2-22222-2-22200000000200200-200-22-2000000000000000000000000000
χ372222-2-2-2-222-2-2-2002222222222000-2-20000-2-2-2-222-2-222-2-2-2-200000000-20020020022-2000000000000000000000000000
χ382222-2-2-2-222-2-2-200222222-2-2-2-2000-2-20000-2-2-2-22222-2-2222200000000-200200200-2-22000000000000000000000000000
χ392222-2-2-2-2-2-2222002-222222222000-2-2000022-2-2-2-222-2-2-2-2-2-200000000200-200200-222000000000000000000000000000
χ402222-2-2-2-2-2-2222002-22222-2-2-2-2000-2-2000022-2-2-2-2-2-222222200000000200-2002002-2-2000000000000000000000000000
χ4122-2-2002-2000002-2002-2-222i2i−2i−2i0000022-2-2002-2000000002i−2i−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ390000000000002i−2i−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000000000000000000
χ4222-2-2002-2000002-2002-2-222i2i−2i−2i0000022-2-2002-2000000002i−2i2ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000000000002i−2i2ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000000000000000000
χ4322-2-2002-2000002-2002-2-22−2i−2i2i2i0000022-2-2002-200000000−2i2i−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37000000000000−2i2i−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000000000000000000
χ4422-2-2002-2000002-2002-2-22−2i−2i2i2i0000022-2-2002-200000000−2i2i2ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000000−2i2i2ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000000000000000
χ4522-2-2002-200000-22002-2-222i2i−2i−2i00000-2-222002-2000000002i−2i−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39000000000000−2i2i2ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000000000000000000
χ4622-2-2002-200000-22002-2-222i2i−2i−2i00000-2-222002-2000000002i−2i2ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000000000−2i2i−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000000000000000000
χ4722-2-2002-200000-22002-2-22−2i−2i2i2i00000-2-222002-200000000−2i2i−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ370000000000002i−2i2ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000000000000000
χ4822-2-2002-200000-22002-2-22−2i−2i2i2i00000-2-222002-200000000−2i2i2ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000000000002i−2i−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000000000000000000
χ492-2-222-2002i−2i2i−2i0000022-2-22-22-20002-200002i−2i002i−2i2i−2i2i−2i2-200i2−i2i2−i2i2−i2i2−i2000000000000000000i2−i22−22−2i2−i22−22−2000000000
χ502-2-222-2002i−2i2i−2i0000022-2-22-22-20002-200002i−2i002i−2i2i−2i2i−2i2-200−i2i2−i2i2−i2i2−i2i2000000000000000000−i2i2−22−22−i2i2−22−22000000000
χ512-2-222-2002i−2i2i−2i0000022-2-2-22-220002-200002i−2i002i−2i−2i2i−2i2i-22002−22−2−22−220000000000000000002−2−i2i2−i2i2−22i2−i2i2−i2000000000
χ522-2-222-2002i−2i2i−2i0000022-2-2-22-220002-200002i−2i002i−2i−2i2i−2i2i-2200−22−222−22−2000000000000000000−22i2−i2i2−i22−2−i2i2−i2i2000000000
χ532-2-222-200−2i2i−2i2i0000022-2-22-22-20002-20000−2i2i00−2i2i−2i2i−2i2i2-200i2−i2i2−i2i2−i2i2−i2000000000000000000i2−i2−22−22i2−i2−22−22000000000
χ542-2-222-200−2i2i−2i2i0000022-2-22-22-20002-20000−2i2i00−2i2i−2i2i−2i2i2-200−i2i2−i2i2−i2i2−i2i2000000000000000000−i2i22−22−2−i2i22−22−2000000000
χ552-2-222-200−2i2i−2i2i0000022-2-2-22-220002-20000−2i2i00−2i2i2i−2i2i−2i-22002−22−2−22−220000000000000000002−2i2−i2i2−i2−22−i2i2−i2i2000000000
χ562-2-222-200−2i2i−2i2i0000022-2-2-22-220002-20000−2i2i00−2i2i2i−2i2i−2i-2200−22−222−22−2000000000000000000−22−i2i2−i2i22−2i2−i2i2−i2000000000
χ572-2-22-22002i−2i−2i2i0000022-2-22-22-2000-220000−2i2i002i−2i−2i2i2i−2i-2200i2−i2i2−i2i2−i2i2−i2000000000000000000−i2i22−2−22−i2i22−2−22000000000
χ582-2-22-22002i−2i−2i2i0000022-2-22-22-2000-220000−2i2i002i−2i−2i2i2i−2i-2200−i2i2−i2i2−i2i2−i2i2000000000000000000i2−i2−222−2i2−i2−222−2000000000
χ592-2-22-22002i−2i−2i2i0000022-2-2-22-22000-220000−2i2i002i−2i2i−2i−2i2i2-2002−22−2−22−22000000000000000000−22−i2i2i2−i22−2i2−i2−i2i2000000000
χ602-2-22-22002i−2i−2i2i0000022-2-2-22-22000-220000−2i2i002i−2i2i−2i−2i2i2-200−22−222−22−20000000000000000002−2i2−i2−i2i2−22−i2i2i2−i2000000000
χ612-2-22-2200−2i2i2i−2i0000022-2-22-22-2000-2200002i−2i00−2i2i2i−2i−2i2i-2200i2−i2i2−i2i2−i2i2−i2000000000000000000−i2i2−222−2−i2i2−222−2000000000
χ622-2-22-2200−2i2i2i−2i0000022-2-22-22-2000-2200002i−2i00−2i2i2i−2i−2i2i-2200−i2i2−i2i2−i2i2−i2i2000000000000000000i2−i22−2−22i2−i22−2−22000000000
χ632-2-22-2200−2i2i2i−2i0000022-2-2-22-22000-2200002i−2i00−2i2i−2i2i2i−2i2-2002−22−2−22−22000000000000000000−22i2−i2−i2i22−2−i2i2i2−i2000000000
χ642-2-22-2200−2i2i2i−2i0000022-2-2-22-22000-2200002i−2i00−2i2i−2i2i2i−2i2-200−22−222−22−20000000000000000002−2−i2i2i2−i2−22i2−i2−i2i2000000000
χ6544444444444444444-1-1-1-10000444-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-1-1-1-1-1-1-1-1-1000000000000000000000000000000
χ664444444444444-4-444-1-1-1-10000-4-4-4-1-11111-1-1-1-1-1-10000000000000000-111-111-111000000000000000000000000000000
χ6744444444-4-4-4-4-4444-4-1-1-1-100004-4-4-1-1-1-1-1-111-1-11100000000000000001-1-1111-111000000000000000000000000000000
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χ69444444-4-44444-400-4-4-1-1-1-10000000-1-15−55−5-1-111-1-1000000000000000015−515−515−5000000000000000000000000000000
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χ794444-4-4-4-4-4-4444004-4-1-1-1-10000000115−55−5-1-111110000000000000000-1−5515−5-1−55000000000000000000000000000000
χ804444-4-4-4-4-4-4444004-4-1-1-1-1000000011−55−55-1-111110000000000000000-15−51−55-15−5000000000000000000000000000000
χ8144-4-400-440000000004-4-444i4i−4i−4i00000000000-4400000000−4i4i00000000000000000000000000000000000000000000000
χ8244-4-400-440000000004-4-44−4i−4i4i4i00000000000-44000000004i−4i00000000000000000000000000000000000000000000000
χ834-44-400000000000004-44-44i−4i−4i4i000000000000000000000002−2i−2+2i−2+2i2−2i2+2i−2−2i−2−2i2+2i000000000000000000000000000000000000000
χ844-44-400000000000004-44-44i−4i−4i4i00000000000000000000000−2+2i2−2i2−2i−2+2i−2−2i2+2i2+2i−2−2i000000000000000000000000000000000000000
χ854-44-400000000000004-44-4−4i4i4i−4i000000000000000000000002+2i−2−2i−2−2i2+2i2−2i−2+2i−2+2i2−2i000000000000000000000000000000000000000
χ864-44-400000000000004-44-4−4i4i4i−4i00000000000000000000000−2−2i2+2i2+2i−2−2i−2+2i2−2i2−2i−2+2i000000000000000000000000000000000000000
χ8788-8-8008-8000008-800-222-2000000000-2-22200-22000000000000000000000000000000000000000000000000000000000
χ8888-8-8008-800000-8800-222-200000000022-2-200-22000000000000000000000000000000000000000000000000000000000
χ8988-8-800-88000000000-222-200000000025−25−2525002-2000000000000000000000000000000000000000000000000000000000
χ9088-8-800-88000000000-222-2000000000−252525−25002-2000000000000000000000000000000000000000000000000000000000
χ918-8-888-8008i−8i8i−8i00000-2-2220000000-220000−2i2i00−2i2i0000000000000000000000000000000000000000000000000000000
χ928-8-888-800−8i8i−8i8i00000-2-2220000000-2200002i−2i002i−2i0000000000000000000000000000000000000000000000000000000
χ938-8-88-88008i−8i−8i8i00000-2-22200000002-200002i−2i00−2i2i0000000000000000000000000000000000000000000000000000000
χ948-8-88-8800−8i8i8i−8i00000-2-22200000002-20000−2i2i002i−2i0000000000000000000000000000000000000000000000000000000
χ9516-1616-160000000000000-44-4400000000000000000000000000000000000000000000000000000000000000000000000000

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