Finite Group Databasebeta

← Group #13030075

Character table — Group #13030075

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size111122222222444444444555588888888888888810101010101010101010101010101010161616161616161616202020202020202020202020202020202020202020404040404040404040
order12224444444422444510101044442242020202020202020202020202244444488888888101010101010202020444448888888888888888444888888
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
χ511111111111111-1-1111111111-1-1-111111111-1-1-1-1111111111111111111-1-1-1-11-1-11-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1
χ611111111111111-1-1111111111-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11-1-11-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ711111111111111-1-111111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i11-1-1-1-11-1-1-111-1-1−i−iiiiiiiii−i−i−i−i−i−i111−i−i−iiii
χ811111111111111-1-111111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii11-1-1-1-11-1-1-111-1-1ii−i−i−i−i−i−i−i−iiiiiii111iii−i−i−i
χ911111111-1-1-1-11-111-1111111111-1-1-1-11111-1-11111-1-111-1-111111111111-111-1-1-1-1-1-1111-1111111-1-1-1-111-1-1-1-1-11-11-1-11-1-1
χ1011111111-1-1-1-11-111-1111111111-1-1-1-11111-1-11111-1-111-1-111-1-1-1-1-1-1-1-11-111-1-1-1-1-1-1111-1-1-1-1-1-1-11111-1-11111-11-1-111-111
χ1111111111-1-1-1-11-111-11111-1-1-1-11-1-1-1-11111-1-1111111-1-111-1-1iiii−i−i−i−i1-111-1-1-1-1-11-1-1-11ii−i−iii−i−i−i−i−i−iiiii1-11i−i−i−iii
χ1211111111-1-1-1-11-111-11111-1-1-1-11-1-1-1-11111-1-1111111-1-111-1-1−i−i−i−iiiii1-111-1-1-1-1-11-1-1-11−i−iii−i−iiiiiii−i−i−i−i1-11−iiii−i−i
χ1311111111-1-1-1-11-1-1-1-111111111-111-1-11111-1-1-1-1-1-1-1-111-1-111111111111-1-1-111-111-1-1-11-1-1-1-1-111-1-1-1-111-1-1-1-11-11-111-111
χ1411111111-1-1-1-11-1-1-1-111111111-111-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11-1-1-111-111-1-1-11-11111-1-11111-1-111111-111-1-11-1-1
χ1511111111-1-1-1-11-1-1-1-11111-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-111-1-1iiii−i−i−i−i1-1-1-111-111111-11−i−iiiii−i−i−i−i−i−iiiii-11-1−iiii−i−i
χ1611111111-1-1-1-11-1-1-1-11111-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-111-1-1−i−i−i−iiiii1-1-1-111-111111-11ii−i−i−i−iiiiiii−i−i−i−i-11-1i−i−i−iii
χ17111111-1-111-1-1-1111-111111111-11-1-1-111-1-1111111-1-1-1-1111111111111-11-1-111-1-1-1-111-111111-1-111-1-1-1-111-1-1-1-11-11-1-11-1
χ18111111-1-111-1-1-1111-111111111-11-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-111-1-1-1-111-11-1-1-1-111-1-11111-1-111-1-111-111-11
χ19111111-1-111-1-1-1111-11111-1-1-1-1-11-1-1-111-1-11111111111-1-1-1-1iiii−i−i−i−i-11-1-111-1-1-11-1-11-1ii−i−i−i−iii−i−iii−i−iii11-1−ii−ii−ii
χ20111111-1-111-1-1-1111-11111-1-1-1-1-11-1-1-111-1-11111111111-1-1-1-1−i−i−i−iiiii-11-1-111-1-1-11-1-11-1−i−iiiii−i−iii−i−iii−i−i11-1i−ii−ii−i
χ21111111-1-111-1-1-11-1-1-1111111111-11-1-111-1-111-1-1-1-1-1-1-1-1111111111111-1111-1-1-111-1-1-1-11-1-1-1-1-1-111-1-1-1-111-1-111-11-111-11
χ22111111-1-111-1-1-11-1-1-1111111111-11-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1111-1-1-111-1-1-1-11111111-1-11111-1-11111-1-11-1-11-1
χ23111111-1-111-1-1-11-1-1-11111-1-1-1-11-11-1-111-1-111-1-1-1-11111-1-1-1-1iiii−i−i−i−i-1111-1-1-1111111-1−i−iii−i−iii−i−iii−i−iii-1-11i−ii−ii−i
χ24111111-1-111-1-1-11-1-1-11111-1-1-1-11-11-1-111-1-111-1-1-1-11111-1-1-1-1−i−i−i−iiiii-1111-1-1-1111111-1ii−i−iii−i−iii−i−iii−i−i-1-11−ii−ii−ii
χ25111111-1-1-1-111-1-111111111111-1-111111-1-1-1-1111111-1-1-1-11111111111-1-1-1-1-1-1111111-1-11111-1-1-1-111-1-1-1-1111-1-1-1-11-1-11
χ26111111-1-1-1-111-1-111111111111-1-111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-11111-1-11-1-111-111-1
χ27111111-1-1-1-111-1-11111111-1-1-1-1-1-111111-1-1-1-11111-1-11111-1-1iiii−i−i−i−i-1-1-1-1-1-1111-1-1-111ii−i−i−i−i−i−iiiiiii−i−i-111−i−iiii−i
χ28111111-1-1-1-111-1-11111111-1-1-1-1-1-111111-1-1-1-11111-1-11111-1-1−i−i−i−iiiii-1-1-1-1-1-1111-1-1-111−i−iiiiiii−i−i−i−i−i−iii-111ii−i−i−ii
χ29111111-1-1-1-111-1-1-1-111111111111-11111-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-111111-1-11-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-11111-111-1
χ30111111-1-1-1-111-1-1-1-111111111111-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111-1-11-1-1-1-111111111-1-11111-1-1-111-1-11-1-11
χ31111111-1-1-1-111-1-1-1-111111-1-1-1-111-11111-1-1-1-1-1-1-1-1-1-11111-1-1iiii−i−i−i−i-1-111111-1-1-11111−i−iii−i−i−i−iiiiiii−i−i1-1-1ii−i−i−ii
χ32111111-1-1-1-111-1-1-1-111111-1-1-1-111-11111-1-1-1-1-1-1-1-1-1-11111-1-1−i−i−i−iiiii-1-111111-1-1-11111ii−i−iiiii−i−i−i−i−i−iii1-1-1−i−iiii−i
χ332222-2-2222222-2-200-22222222200022-2-222220000222222-2-200000000-2-20000-200-200-2-20000000000000000000000000
χ342222-2-2222222-2-200-22222-2-2-2-200022-2-222220000-2-2-2-2-2-22200000000-2-20000-200200220000000000000000000000000
χ352222-2-222-2-2-2-2-2200222222222000-2-2-2-222-2-20000-2-222-2-2-2-200000000-220000200200-220000000000000000000000000
χ362222-2-222-2-2-2-2-220022222-2-2-2-2000-2-2-2-222-2-2000022-2-2222200000000-220000200-2002-20000000000000000000000000
χ372222-2-2-2-222-2-22-200222222222000-2-2-2-2-2-2220000-2-2-2-222-2-2000000002-200002002002-20000000000000000000000000
χ382222-2-2-2-222-2-22-20022222-2-2-2-2000-2-2-2-2-2-22200002222-2-222000000002-20000200-200-220000000000000000000000000
χ392222-2-2-2-2-2-2222200-22222222200022-2-2-2-2-2-2000022-2-2-2-2-2-200000000220000-200-200220000000000000000000000000
χ402222-2-2-2-2-2-2222200-22222-2-2-2-200022-2-2-2-2-2-20000-2-222222200000000220000-200200-2-20000000000000000000000000
χ4122-2-22-2000000002-202-2-222i2i−2i−2i000002-2000022-2-20000002i−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+2ζ3900000000002i−2i00−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000000000000000000
χ4222-2-22-2000000002-202-2-222i2i−2i−2i000002-2000022-2-20000002i−2i2ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900000000002i−2i002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000000000000000000
χ4322-2-22-2000000002-202-2-22−2i−2i2i2i000002-2000022-2-2000000−2i2i−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+2ζ370000000000−2i2i00−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000000000000000000
χ4422-2-22-2000000002-202-2-22−2i−2i2i2i000002-2000022-2-2000000−2i2i2ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000000000−2i2i002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000000000000000
χ4522-2-22-200000000-2202-2-222i2i−2i−2i000002-20000-2-2220000002i−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+2ζ390000000000−2i2i002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000000000000000000
χ4622-2-22-200000000-2202-2-222i2i−2i−2i000002-20000-2-2220000002i−2i2ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000000000−2i2i00−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000000000000000000
χ4722-2-22-200000000-2202-2-22−2i−2i2i2i000002-20000-2-222000000−2i2i−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+2ζ3700000000002i−2i002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000000000000000
χ4822-2-22-200000000-2202-2-22−2i−2i2i2i000002-20000-2-222000000−2i2i2ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700000000002i−2i00−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000000000000000000
χ492-2-22002i−2i2i−2i2-20000022-2-22-22-20002-2002i−2i2i−2i00002-22i−2i2i−2i00i2−i2i2−i2i2−i2i2−i20000000000000000002−22−2i2−i22−22−2i2−i2000000000
χ502-2-22002i−2i2i−2i2-20000022-2-22-22-20002-2002i−2i2i−2i00002-22i−2i2i−2i00−i2i2−i2i2−i2i2−i2i2000000000000000000−22−22−i2i2−22−22−i2i2000000000
χ512-2-22002i−2i2i−2i2-20000022-2-2-22-220002-2002i−2i2i−2i0000-22−2i2i−2i2i002−22−2−22−22000000000000000000−i2i2−i2i22−2i2−i2i2−i2−22000000000
χ522-2-22002i−2i2i−2i2-20000022-2-2-22-220002-2002i−2i2i−2i0000-22−2i2i−2i2i00−22−222−22−2000000000000000000i2−i2i2−i2−22−i2i2−i2i22−2000000000
χ532-2-22002i−2i−2i2i-220000022-2-22-22-2000-22002i−2i−2i2i0000-222i−2i−2i2i00i2−i2i2−i2i2−i2i2−i20000000000000000002−2−22−i2i22−2−22−i2i2000000000
χ542-2-22002i−2i−2i2i-220000022-2-22-22-2000-22002i−2i−2i2i0000-222i−2i−2i2i00−i2i2−i2i2−i2i2−i2i2000000000000000000−222−2i2−i2−222−2i2−i2000000000
χ552-2-22002i−2i−2i2i-220000022-2-2-22-22000-22002i−2i−2i2i00002-2−2i2i2i−2i002−22−2−22−22000000000000000000−i2i2i2−i2−22i2−i2−i2i22−2000000000
χ562-2-22002i−2i−2i2i-220000022-2-2-22-22000-22002i−2i−2i2i00002-2−2i2i2i−2i00−22−222−22−2000000000000000000i2−i2−i2i22−2−i2i2i2−i2−22000000000
χ572-2-2200−2i2i2i−2i-220000022-2-22-22-2000-2200−2i2i2i−2i0000-22−2i2i2i−2i00i2−i2i2−i2i2−i2i2−i2000000000000000000−222−2−i2i2−222−2−i2i2000000000
χ582-2-2200−2i2i2i−2i-220000022-2-22-22-2000-2200−2i2i2i−2i0000-22−2i2i2i−2i00−i2i2−i2i2−i2i2−i2i20000000000000000002−2−22i2−i22−2−22i2−i2000000000
χ592-2-2200−2i2i2i−2i-220000022-2-2-22-22000-2200−2i2i2i−2i00002-22i−2i−2i2i002−22−2−22−22000000000000000000i2−i2−i2i2−22−i2i2i2−i22−2000000000
χ602-2-2200−2i2i2i−2i-220000022-2-2-22-22000-2200−2i2i2i−2i00002-22i−2i−2i2i00−22−222−22−2000000000000000000−i2i2i2−i22−2i2−i2−i2i2−22000000000
χ612-2-2200−2i2i−2i2i2-20000022-2-22-22-20002-200−2i2i−2i2i00002-2−2i2i−2i2i00i2−i2i2−i2i2−i2i2−i2000000000000000000−22−22i2−i2−22−22i2−i2000000000
χ622-2-2200−2i2i−2i2i2-20000022-2-22-22-20002-200−2i2i−2i2i00002-2−2i2i−2i2i00−i2i2−i2i2−i2i2−i2i20000000000000000002−22−2−i2i22−22−2−i2i2000000000
χ632-2-2200−2i2i−2i2i2-20000022-2-2-22-220002-200−2i2i−2i2i0000-222i−2i2i−2i002−22−2−22−22000000000000000000i2−i2i2−i22−2−i2i2−i2i2−22000000000
χ642-2-2200−2i2i−2i2i2-20000022-2-2-22-220002-200−2i2i−2i2i0000-222i−2i2i−2i00−22−222−22−2000000000000000000−i2i2−i2i2−22i2−i2i2−i22−2000000000
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
χ6644444444444444-4-44-1-1-1-10000-4-4-4-1-1-1-1-1-1-1-111110000000000000000-1-11111-111000000000000000000000000000000
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χ784444-4-4-4-444-4-44-4004-1-1-1-10000000111111-1-1−55−550000000000000000-115−5−55-15−5000000000000000000000000000000
χ794444-4-4-4-4-4-4444400-4-1-1-1-10000000-1-11111115−55−50000000000000000-1-1−55−5515−5000000000000000000000000000000
χ804444-4-4-4-4-4-4444400-4-1-1-1-10000000-1-1111111−55−550000000000000000-1-15−55−51−55000000000000000000000000000000
χ8144-4-4-44000000000004-4-444i4i−4i−4i00000-4400000000000000−4i4i00000000000000000000000000000000000000000000000
χ8244-4-4-44000000000004-4-44−4i−4i4i4i00000-44000000000000004i−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
χ8788-8-88-8000000008-80-222-2000000000-220000-2-2220000000000000000000000000000000000000000000000000000000
χ8888-8-88-800000000-880-222-2000000000-22000022-2-20000000000000000000000000000000000000000000000000000000
χ8988-8-8-8800000000000-222-20000000002-2000025−25−25250000000000000000000000000000000000000000000000000000000
χ9088-8-8-8800000000000-222-20000000002-20000−252525−250000000000000000000000000000000000000000000000000000000
χ918-8-88008i−8i8i−8i8-800000-2-2220000000-2200−2i2i−2i2i00000000000000000000000000000000000000000000000000000000000
χ928-8-88008i−8i−8i8i-8800000-2-22200000002-200−2i2i2i−2i00000000000000000000000000000000000000000000000000000000000
χ938-8-8800−8i8i8i−8i-8800000-2-22200000002-2002i−2i−2i2i00000000000000000000000000000000000000000000000000000000000
χ948-8-8800−8i8i−8i8i8-800000-2-2220000000-22002i−2i2i−2i00000000000000000000000000000000000000000000000000000000000
χ9516-1616-160000000000000-44-4400000000000000000000000000000000000000000000000000000000000000000000000000

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