Finite Group Databasebeta

← Group #13030079

Character table — Group #13030079

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size111122222222444444444555588888888888888810101010101010101010101010101010161616161616161616202020202020202020202020202020202020202020404040404040404040
order12224444444444444510101044442242020202020202020202020202244444488888888101010102020202020224448888888888888888444888888
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
χ51111111111111-1-11111111111-1-1-111111111-1-1-1-11111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1
χ61111111111111-1-11111111111-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ71111111111111-1-1111111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-1-1-111-1-11-1-1-111−i−iiiiiiiii−i−i−i−i−i−i111−i−i−iiii
χ81111111111111-1-1111111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii-1-1-1-111-1-11-1-1-111ii−i−i−i−i−i−i−i−iiiiiii111iii−i−i−i
χ9111111-1-111-1-1-1111-1111111111-1-111-1-111-1-11111-1-111-1-1111111111111-1-11-1-1-1-11-1-111111111-1-1-1-111-1-1-1-1-11-11-1-11-1-1
χ10111111-1-111-1-1-1111-1111111111-1-111-1-111-1-11111-1-111-1-111-1-1-1-1-1-1-1-111-1-11-1-1-1-11-1-111-1-1-1-1-1-11111-1-11111-11-1-111-111
χ11111111-1-111-1-1-1111-11111-1-1-1-11-1-111-1-111-1-1111111-1-111-1-1iiii−i−i−i−i11-1-11-1-1-1-1-111-1-1ii−i−iii−i−i−i−i−i−iiiii1-11i−i−i−iii
χ12111111-1-111-1-1-1111-11111-1-1-1-11-1-111-1-111-1-1111111-1-111-1-1−i−i−i−iiiii11-1-11-1-1-1-1-111-1-1−i−iii−i−iiiiiii−i−i−i−i1-11−iiii−i−i
χ13111111-1-111-1-1-1-1-11-111111111-11111-1-111-1-1-1-1-1-1-1-111-1-11111111111-1-1111-111-11-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11-11-111-111
χ14111111-1-111-1-1-1-1-11-111111111-11111-1-111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1111-111-11-1-1-1-11111-1-11111-1-111111-111-1-11-1-1
χ15111111-1-111-1-1-1-1-11-11111-1-1-1-1-11111-1-111-1-1-1-1-1-111-1-111-1-1iiii−i−i−i−i-1-1111-111-1-11111−i−iiiii−i−i−i−i−i−iiiii-11-1−iiii−i−i
χ16111111-1-111-1-1-1-1-11-11111-1-1-1-1-11111-1-111-1-1-1-1-1-111-1-111-1-1−i−i−i−iiiii-1-1111-111-1-11111ii−i−i−i−iiiiiii−i−i−i−i-11-1i−i−i−iii
χ171111-1-11111-1-1-111-1111111111-11-111-1-1-1-1111111-1-1-1-1111111111111-1-111-11-1-1-1-11-1111111-1-111-1-1-1-111-1-1-1-11-11-1-11-1
χ181111-1-11111-1-1-111-1111111111-11-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-11-1-1-1-11-111-1-1-1-111-1-11111-1-111-1-111-111-11
χ191111-1-11111-1-1-111-111111-1-1-1-1-11-111-1-1-1-11111111111-1-1-1-1iiii−i−i−i−i-1-111-11-1-1-11-11-1-1ii−i−i−i−iii−i−iii−i−iii11-1−ii−ii−ii
χ201111-1-11111-1-1-111-111111-1-1-1-1-11-111-1-1-1-11111111111-1-1-1-1−i−i−i−iiiii-1-111-11-1-1-11-11-1-1−i−iiiii−i−iii−i−iii−i−i11-1i−ii−ii−i
χ211111-1-11111-1-1-1-1-1-11111111111-1111-1-1-1-111-1-1-1-1-1-1-1-111111111111111-1-1-1111-1-11-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111-11-111-11
χ221111-1-11111-1-1-1-1-1-11111111111-1111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1111-1-11-1-1-1111111-1-11111-1-11111-1-11-1-11-1
χ231111-1-11111-1-1-1-1-1-111111-1-1-1-11-1111-1-1-1-111-1-1-1-11111-1-1-1-1iiii−i−i−i−i11-1-1-1111-11-1111−i−iii−i−iii−i−iii−i−iii-1-11i−ii−ii−i
χ241111-1-11111-1-1-1-1-1-111111-1-1-1-11-1111-1-1-1-111-1-1-1-11111-1-1-1-1−i−i−i−iiiii11-1-1-1111-11-1111ii−i−iii−i−iii−i−iii−i−i-1-11−ii−ii−ii
χ251111-1-1-1-11111111-1-111111111-1-111111-1-1-1-1111111-1-1-1-11111111111-1-1-1-1-1-1111-1-11111111-1-1-1-111-1-1-1-1111-1-1-1-11-1-11
χ261111-1-1-1-11111111-1-111111111-1-111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1111-1-1-1-11111-1-11111-1-11-1-111-111-1
χ271111-1-1-1-11111111-1-11111-1-1-1-1-1-111111-1-1-1-11111-1-11111-1-1iiii−i−i−i−i-1-1-1-1-1-111111-1-1-1ii−i−i−i−i−i−iiiiiii−i−i-111−i−iiii−i
χ281111-1-1-1-11111111-1-11111-1-1-1-1-1-111111-1-1-1-11111-1-11111-1-1−i−i−i−iiiii-1-1-1-1-1-111111-1-1-1−i−iiiiiii−i−i−i−i−i−iii-111ii−i−i−ii
χ291111-1-1-1-111111-1-1-1-11111111111-11111-1-1-1-1-1-1-1-111-1-1-1-111111111111111-1-1-1-11-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-111-11111-111-1
χ301111-1-1-1-111111-1-1-1-11111111111-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11-1-11-1-111111111-1-11111-1-1-111-1-11-1-11
χ311111-1-1-1-111111-1-1-1-11111-1-1-1-111-11111-1-1-1-1-1-1-1-1-1-11111-1-1iiii−i−i−i−i1111-1-1-1-1111-111−i−iii−i−i−i−iiiiiii−i−i1-1-1ii−i−i−ii
χ321111-1-1-1-111111-1-1-1-11111-1-1-1-111-11111-1-1-1-1-1-1-1-1-1-11111-1-1−i−i−i−iiiii1111-1-1-1-1111-111ii−i−iiiii−i−i−i−i−i−iii1-1-1−i−iiii−i
χ3322222222-2-222-200-2-222222222000-2-22222220000222222-2-2000000000000-2-200-2-2-2-2000000000000000000000000000
χ3422222222-2-222-200-2-22222-2-2-2-2000-2-22222220000-2-2-2-2-2-222000000000000-2-200-2222000000000000000000000000000
χ35222222-2-2-2-2-2-2200-2222222222000-2-2-2-222-2-20000-2-222-2-2-2-2000000000000-22002-222000000000000000000000000000
χ36222222-2-2-2-2-2-2200-222222-2-2-2-2000-2-2-2-222-2-2000022-2-22222000000000000-220022-2-2000000000000000000000000000
χ372222-2-222-2-2-2-22002-222222222000-2-2-2-2-2-2220000-2-2-2-222-2-20000000000002-20022-22000000000000000000000000000
χ382222-2-222-2-2-2-22002-22222-2-2-2-2000-2-2-2-2-2-22200002222-2-2220000000000002-2002-22-2000000000000000000000000000
χ392222-2-2-2-2-2-222-2002222222222000-2-222-2-2-2-2000022-2-2-2-2-2-20000000000002200-222-2000000000000000000000000000
χ402222-2-2-2-2-2-222-200222222-2-2-2-2000-2-222-2-2-2-20000-2-22222220000000000002200-2-2-22000000000000000000000000000
χ412-22-200002-20002i−2i0022-2-22i2i−2i−2i0002-20000002i2i−2i−2i0000002i−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+2ζ390000000000002-2−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000000000000000000
χ422-22-200002-20002i−2i0022-2-22i2i−2i−2i0002-20000002i2i−2i−2i0000002i−2i2ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000000000002-22ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000000000000000
χ432-22-200002-20002i−2i0022-2-2−2i−2i2i2i0002-20000002i2i−2i−2i000000−2i2i−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+2ζ37000000000000-222ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000000000000000000
χ442-22-200002-20002i−2i0022-2-2−2i−2i2i2i0002-20000002i2i−2i−2i000000−2i2i2ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000000-22−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000000000000000000
χ452-22-200002-2000−2i2i0022-2-22i2i−2i−2i0002-2000000−2i−2i2i2i0000002i−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+2ζ39000000000000-222ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000000000000000
χ462-22-200002-2000−2i2i0022-2-22i2i−2i−2i0002-2000000−2i−2i2i2i0000002i−2i2ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000000000-22−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000000000000000000
χ472-22-200002-2000−2i2i0022-2-2−2i−2i2i2i0002-2000000−2i−2i2i2i000000−2i2i−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+2ζ370000000000002-2−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000000000000000000
χ482-22-200002-2000−2i2i0022-2-2−2i−2i2i2i0002-2000000−2i−2i2i2i000000−2i2i2ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000000000002-22ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000000000000000000
χ492-2-222i−2i2i−2i002-2000002-22-22-22-2000002-22i−2i2i−2i00002-22i−2i2i−2i00i2−i2i2−i2i2−i2i2−i20000000000000000002−22−2i2−i22−22−2i2−i2000000000
χ502-2-222i−2i2i−2i002-2000002-22-22-22-2000002-22i−2i2i−2i00002-22i−2i2i−2i00−i2i2−i2i2−i2i2−i2i2000000000000000000−22−22−i2i2−22−22−i2i2000000000
χ512-2-222i−2i2i−2i002-2000002-22-2-22-22000002-22i−2i2i−2i0000-22−2i2i−2i2i002−22−2−22−22000000000000000000−i2i2−i2i22−2i2−i2i2−i2−22000000000
χ522-2-222i−2i2i−2i002-2000002-22-2-22-22000002-22i−2i2i−2i0000-22−2i2i−2i2i00−22−222−22−2000000000000000000i2−i2i2−i2−22−i2i2−i2i22−2000000000
χ532-2-222i−2i−2i2i00-22000002-22-22-22-200000-222i−2i−2i2i0000-222i−2i−2i2i00i2−i2i2−i2i2−i2i2−i20000000000000000002−2−22−i2i22−2−22−i2i2000000000
χ542-2-222i−2i−2i2i00-22000002-22-22-22-200000-222i−2i−2i2i0000-222i−2i−2i2i00−i2i2−i2i2−i2i2−i2i2000000000000000000−222−2i2−i2−222−2i2−i2000000000
χ552-2-222i−2i−2i2i00-22000002-22-2-22-2200000-222i−2i−2i2i00002-2−2i2i2i−2i002−22−2−22−22000000000000000000−i2i2i2−i2−22i2−i2−i2i22−2000000000
χ562-2-222i−2i−2i2i00-22000002-22-2-22-2200000-222i−2i−2i2i00002-2−2i2i2i−2i00−22−222−22−2000000000000000000i2−i2−i2i22−2−i2i2i2−i2−22000000000
χ572-2-22−2i2i2i−2i00-22000002-22-22-22-200000-22−2i2i2i−2i0000-22−2i2i2i−2i00i2−i2i2−i2i2−i2i2−i2000000000000000000−222−2−i2i2−222−2−i2i2000000000
χ582-2-22−2i2i2i−2i00-22000002-22-22-22-200000-22−2i2i2i−2i0000-22−2i2i2i−2i00−i2i2−i2i2−i2i2−i2i20000000000000000002−2−22i2−i22−2−22i2−i2000000000
χ592-2-22−2i2i2i−2i00-22000002-22-2-22-2200000-22−2i2i2i−2i00002-22i−2i−2i2i002−22−2−22−22000000000000000000i2−i2−i2i2−22−i2i2i2−i22−2000000000
χ602-2-22−2i2i2i−2i00-22000002-22-2-22-2200000-22−2i2i2i−2i00002-22i−2i−2i2i00−22−222−22−2000000000000000000−i2i2i2−i22−2i2−i2−i2i2−22000000000
χ612-2-22−2i2i−2i2i002-2000002-22-22-22-2000002-2−2i2i−2i2i00002-2−2i2i−2i2i00i2−i2i2−i2i2−i2i2−i2000000000000000000−22−22i2−i2−22−22i2−i2000000000
χ622-2-22−2i2i−2i2i002-2000002-22-22-22-2000002-2−2i2i−2i2i00002-2−2i2i−2i2i00−i2i2−i2i2−i2i2−i2i20000000000000000002−22−2−i2i22−22−2−i2i2000000000
χ632-2-22−2i2i−2i2i002-2000002-22-2-22-22000002-2−2i2i−2i2i0000-222i−2i2i−2i002−22−2−22−22000000000000000000i2−i2i2−i22−2−i2i2−i2i2−22000000000
χ642-2-22−2i2i−2i2i002-2000002-22-2-22-22000002-2−2i2i−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
χ664444444444444-4-444-1-1-1-10000-4-4-4-1-1-1-1-1-1-1-1111100000000000000001111-1-111-1000000000000000000000000000000
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χ784444-4-4-4-444444-4-4-4-4-1-1-1-1000044-4-1-1-1-1111111110000000000000000-1-1-1-11111-1000000000000000000000000000000
χ794444-4-4-4-4-4-444-40044-1-1-1-1000000011-1-111115−55−50000000000000000−55−55-1-15−51000000000000000000000000000000
χ804444-4-4-4-4-4-444-40044-1-1-1-1000000011-1-11111−55−5500000000000000005−55−5-1-1−551000000000000000000000000000000
χ8144-4-400000000000004-4-444i−4i−4i4i000000000000000000000002−2i−2+2i−2+2i2−2i2+2i−2−2i−2−2i2+2i000000000000000000000000000000000000000
χ8244-4-400000000000004-4-444i−4i−4i4i00000000000000000000000−2+2i2−2i2−2i−2+2i−2−2i2+2i2+2i−2−2i000000000000000000000000000000000000000
χ8344-4-400000000000004-4-44−4i4i4i−4i000000000000000000000002+2i−2−2i−2−2i2+2i2−2i−2+2i−2+2i2−2i000000000000000000000000000000000000000
χ8444-4-400000000000004-4-44−4i4i4i−4i00000000000000000000000−2−2i2+2i2+2i−2−2i−2+2i2−2i2−2i−2+2i000000000000000000000000000000000000000
χ854-44-40000-44000000044-4-44i4i−4i−4i000-440000000000000000−4i4i00000000000000000000000000000000000000000000000
χ864-44-40000-44000000044-4-4−4i−4i4i4i000-4400000000000000004i−4i00000000000000000000000000000000000000000000000
χ878-88-800008-80008i−8i00-2-2220000000-22000000−2i−2i2i2i0000000000000000000000000000000000000000000000000000000
χ888-88-800008-8000−8i8i00-2-2220000000-220000002i2i−2i−2i0000000000000000000000000000000000000000000000000000000
χ898-88-80000-880000000-2-22200000002-20000002i5−2i5−2i52i50000000000000000000000000000000000000000000000000000000
χ908-88-80000-880000000-2-22200000002-2000000−2i52i52i5−2i50000000000000000000000000000000000000000000000000000000
χ918-8-888i−8i8i−8i008-800000-22-22000000000-22−2i2i−2i2i00000000000000000000000000000000000000000000000000000000000
χ928-8-888i−8i−8i8i00-8800000-22-220000000002-2−2i2i2i−2i00000000000000000000000000000000000000000000000000000000000
χ938-8-88−8i8i8i−8i00-8800000-22-220000000002-22i−2i−2i2i00000000000000000000000000000000000000000000000000000000000
χ948-8-88−8i8i−8i8i008-800000-22-22000000000-222i−2i2i−2i00000000000000000000000000000000000000000000000000000000000
χ951616-16-160000000000000-444-400000000000000000000000000000000000000000000000000000000000000000000000000

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