Finite Group Databasebeta

← Group #13030076

Character table — Group #13030076

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size111122222222444444444555588888888888888810101010101010101010101010101010161616161616161616202020202020202020202020202020202020202020404040404040404040
order12224444444444444510101044444442020202020202020202020202244444488888888202020202020202020224448888888888888888224888888
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
χ5111111111111111-1-111111111-1-1-111-1-1-1-111111111111111111111111-1-111-1-1-1-111-1-11-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1
χ6111111111111111-1-111111111-1-1-111-1-1-1-111111111111111-1-1-1-1-1-1-1-11-1-111-1-1-1-111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ7111111111111111-1-11111-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1iiii−i−i−i−i1-1-111-1-1-1-1-1-111-1−i−iiiiiiiii−i−i−i−i−i−i111−i−i−iiii
χ8111111111111111-1-11111-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1−i−i−i−iiiii1-1-111-1-1-1-1-1-111-1ii−i−i−i−i−i−i−i−iiiiiii111iii−i−i−i
χ9111111-1-1-1-111-1-111111111111-1-11111111-1-1-1-11111-1-1-1-11111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-111-1-1-1-1-1-111-1-11-1-1
χ10111111-1-1-1-111-1-111111111111-1-11111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1111-1-1-1-1-1-11111-1-11111-1-11-111-111
χ11111111-1-1-1-111-1-11111111-1-1-1-1-1-11111111-1-1-1-111-1-11111-1-1iiii−i−i−i−i111-1-1-1-1-1-111-1-1-1ii−i−iii−i−i−i−i−i−iiiii11-1i−i−i−iii
χ12111111-1-1-1-111-1-11111111-1-1-1-1-1-11111111-1-1-1-111-1-11111-1-1−i−i−i−iiiii111-1-1-1-1-1-111-1-1-1−i−iii−i−iiiiiii−i−i−i−i11-1−iiii−i−i
χ13111111-1-1-1-111-1-11-1-11111111111-111-1-1-1-1-1-1-1-11111-1-1-1-111111111111-1-1-1-11111-1-1-1-11-1-1-1-111-1-1-1-111-1-1-1-111-1-111-111
χ14111111-1-1-1-111-1-11-1-11111111111-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-111111-1-11111-1-1111111-11-1-11-1-1
χ15111111-1-1-1-111-1-11-1-11111-1-1-1-111-111-1-1-1-1-1-1-1-111-1-11111-1-1iiii−i−i−i−i1-1-1-1-111111111-1−i−iiiii−i−i−i−i−i−iiiii-1-11−iiii−i−i
χ16111111-1-1-1-111-1-11-1-11111-1-1-1-111-111-1-1-1-1-1-1-1-111-1-11111-1-1−i−i−i−iiiii1-1-1-1-111111111-1ii−i−i−i−iiiiiii−i−i−i−i-1-11i−i−i−iii
χ171111-1-111-1-1111-1-111111111111-1-111111111-1-1-1-1-1-111-1-11111111111-1-1-11-111-1-11-111-11111-1-111-1-1-1-111-1-11-1-1-11-1-11-1
χ181111-1-111-1-1111-1-111111111111-1-111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-11-111-1-11-111-1-1-1-1-111-1-11111-1-1111-1-11-111-11
χ191111-1-111-1-1111-1-1111111-1-1-1-11-1-111111111-1-1-1-111-1-111-1-1iiii−i−i−i−i-1-1-11-111-1-1-11-1-11ii−i−i−i−iii−i−iii−i−iii-111−ii−ii−ii
χ201111-1-111-1-1111-1-1111111-1-1-1-11-1-111111111-1-1-1-111-1-111-1-1−i−i−i−iiiii-1-1-11-111-1-1-11-1-11−i−iiiii−i−iii−i−iii−i−i-111i−ii−ii−i
χ211111-1-111-1-1111-1-1-1-111111111-11111-1-1-1-111-1-1-1-1-1-111-1-11111111111-1111-1-1-1111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1111-111-11
χ221111-1-111-1-1111-1-1-1-111111111-11111-1-1-1-111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1111-1-1-1111-1-1-1-1111111-1-11111-1-111-111-11-1-11-1
χ231111-1-111-1-1111-1-1-1-11111-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-111-1-1iiii−i−i−i−i-1111-1-1-111-11111−i−iii−i−iii−i−iii−i−iii1-1-1i−ii−ii−i
χ241111-1-111-1-1111-1-1-1-11111-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-111-1-1−i−i−i−iiiii-1111-1-1-111-11111ii−i−iii−i−iii−i−iii−i−i1-1-1−ii−ii−ii
χ251111-1-1-1-11111-11-11111111111-11-1111111-1-111-1-1-1-1-1-1111111111111-1-1-1-11-1-111-1111-11111-1-1-1-111-1-1-1-111-11-1-1-11-1-11
χ261111-1-1-1-11111-11-11111111111-11-1111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1111-1-1-1-1-11111-1-11111-1-1-11-111-111-1
χ271111-1-1-1-11111-11-1111111-1-1-1-1-11-1111111-1-111-1-11111-1-1-1-1iiii−i−i−i−i-1-1-1-11-1-1111-1-1-11ii−i−i−i−i−i−iiiiiii−i−i1-11−i−iiii−i
χ281111-1-1-1-11111-11-1111111-1-1-1-1-11-1111111-1-111-1-11111-1-1-1-1−i−i−i−iiiii-1-1-1-11-1-1111-1-1-11−i−iiiiiii−i−i−i−i−i−iii1-11ii−i−i−ii
χ291111-1-1-1-11111-11-1-1-1111111111-1111-1-1-1-1-1-111-1-1-1-1-1-1111111111111-111-1111-1-1-11-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111-1111-111-1
χ301111-1-1-1-11111-11-1-1-1111111111-1111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1111-1-1-11-1-1-111111111-1-11111-1-11-11-1-11-1-11
χ311111-1-1-1-11111-11-1-1-11111-1-1-1-11-1111-1-1-1-1-1-111-1-11111-1-1-1-1iiii−i−i−i−i-111-1111-1-11-1111−i−iii−i−i−i−iiiiiii−i−i-11-1ii−i−i−ii
χ321111-1-1-1-11111-11-1-1-11111-1-1-1-11-1111-1-1-1-1-1-111-1-11111-1-1-1-1−i−i−i−iiiii-111-1111-1-11-1111ii−i−iiiii−i−i−i−i−i−iii-11-1−i−iiii−i
χ332222222222-2-2-2-2-20022222222000-2-20000222222222222-2-200000000-200-2-20000-2-200-20000000000000000000000000
χ342222222222-2-2-2-2-2002222-2-2-2-2000-2-20000222222-2-2-2-2-2-22200000000-200-2-20000220020000000000000000000000000
χ35222222-2-2-2-2-2-222-20022222222000-2-20000-2-2-2-22222-2-2-2-2-2-200000000-2002200002200-20000000000000000000000000
χ36222222-2-2-2-2-2-222-2002222-2-2-2-2000-2-20000-2-2-2-222-2-222222200000000-200220000-2-20020000000000000000000000000
χ372222-2-222-2-2-2-2-2220022222222000-2-2000022-2-2-2-2-2-222-2-2-2-200000000200-220000-220020000000000000000000000000
χ382222-2-222-2-2-2-2-222002222-2-2-2-2000-2-2000022-2-2-2-222-2-2222200000000200-2200002-200-20000000000000000000000000
χ392222-2-2-2-222-2-22-220022222222000-2-20000-2-222-2-2-2-2-2-222-2-2000000002002-200002-20020000000000000000000000000
χ402222-2-2-2-222-2-22-22002222-2-2-2-2000-2-20000-2-222-2-22222-2-222000000002002-20000-2200-20000000000000000000000000
χ4122-2-22-22i−2i2i−2i00000002-2-2222-2-20000000002i−2i2i−2i2-22-22i−2i2i−2i00i2i2−i2−i2i2i2−i2−i2000000000000000000i2−i22−22−2i2−i22−22−2000000000
χ4222-2-22-22i−2i2i−2i00000002-2-2222-2-20000000002i−2i2i−2i2-22-22i−2i2i−2i00−i2−i2i2i2−i2−i2i2i2000000000000000000−i2i2−22−22−i2i2−22−22000000000
χ4322-2-22-22i−2i2i−2i00000002-2-22-2-2220000000002i−2i2i−2i2-2-22−2i2i−2i2i0022−2−2−2−2220000000000000000002−2−i2i2−i2i2−22i2−i2i2−i2000000000
χ4422-2-22-22i−2i2i−2i00000002-2-22-2-2220000000002i−2i2i−2i2-2-22−2i2i−2i2i00−2−22222−2−2000000000000000000−22i2−i2i2−i22−2−i2i2−i2i2000000000
χ4522-2-22-2−2i2i−2i2i00000002-2-2222-2-2000000000−2i2i−2i2i2-22-2−2i2i−2i2i00i2i2−i2−i2i2i2−i2−i2000000000000000000i2−i2−22−22i2−i2−22−22000000000
χ4622-2-22-2−2i2i−2i2i00000002-2-2222-2-2000000000−2i2i−2i2i2-22-2−2i2i−2i2i00−i2−i2i2i2−i2−i2i2i2000000000000000000−i2i22−22−2−i2i22−22−2000000000
χ4722-2-22-2−2i2i−2i2i00000002-2-22-2-222000000000−2i2i−2i2i2-2-222i−2i2i−2i0022−2−2−2−2220000000000000000002−2i2−i2i2−i2−22−i2i2−i2i2000000000
χ4822-2-22-2−2i2i−2i2i00000002-2-22-2-222000000000−2i2i−2i2i2-2-222i−2i2i−2i00−2−22222−2−2000000000000000000−22−i2i2−i2i22−2i2−i2i2−i2000000000
χ4922-2-2-222i−2i−2i2i00000002-2-2222-2-20000000002i−2i−2i2i-22-222i−2i−2i2i00i2i2−i2−i2i2i2−i2−i2000000000000000000−i2i22−2−22−i2i22−2−22000000000
χ5022-2-2-222i−2i−2i2i00000002-2-2222-2-20000000002i−2i−2i2i-22-222i−2i−2i2i00−i2−i2i2i2−i2−i2i2i2000000000000000000i2−i2−222−2i2−i2−222−2000000000
χ5122-2-2-222i−2i−2i2i00000002-2-22-2-2220000000002i−2i−2i2i-222-2−2i2i2i−2i0022−2−2−2−222000000000000000000−22−i2i2i2−i22−2i2−i2−i2i2000000000
χ5222-2-2-222i−2i−2i2i00000002-2-22-2-2220000000002i−2i−2i2i-222-2−2i2i2i−2i00−2−22222−2−20000000000000000002−2i2−i2−i2i2−22−i2i2i2−i2000000000
χ5322-2-2-22−2i2i2i−2i00000002-2-2222-2-2000000000−2i2i2i−2i-22-22−2i2i2i−2i00i2i2−i2−i2i2i2−i2−i2000000000000000000−i2i2−222−2−i2i2−222−2000000000
χ5422-2-2-22−2i2i2i−2i00000002-2-2222-2-2000000000−2i2i2i−2i-22-22−2i2i2i−2i00−i2−i2i2i2−i2−i2i2i2000000000000000000i2−i22−2−22i2−i22−2−22000000000
χ5522-2-2-22−2i2i2i−2i00000002-2-22-2-222000000000−2i2i2i−2i-222-22i−2i−2i2i0022−2−2−2−222000000000000000000−22i2−i2−i2i22−2−i2i2i2−i2000000000
χ5622-2-2-22−2i2i2i−2i00000002-2-22-2-222000000000−2i2i2i−2i-222-22i−2i−2i2i00−2−22222−2−20000000000000000002−2−i2i2i2−i2−22i2−i2−i2i2000000000
χ572-2-220000002-20002-222-2-22i−2i2i−2i0002-222-2-20000000000002i−2i−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000000002i−2i0−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000000000000000000
χ582-2-220000002-20002-222-2-22i−2i2i−2i0002-222-2-20000000000002i−2i2ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000000002i−2i02ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000000000000000000
χ592-2-220000002-20002-222-2-2−2i2i−2i2i0002-222-2-2000000000000−2i2i−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700000000000−2i2i0−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000000000000000000
χ602-2-220000002-20002-222-2-2−2i2i−2i2i0002-222-2-2000000000000−2i2i2ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700000000000−2i2i02ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000000000000000
χ612-2-220000002-2000-2222-2-22i−2i2i−2i0002-2-2-2220000000000002i−2i−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900000000000−2i2i02ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000000000000000000
χ622-2-220000002-2000-2222-2-22i−2i2i−2i0002-2-2-2220000000000002i−2i2ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900000000000−2i2i0−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000000000000000000
χ632-2-220000002-2000-2222-2-2−2i2i−2i2i0002-2-2-222000000000000−2i2i−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000000002i−2i02ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000000000000000
χ642-2-220000002-2000-2222-2-2−2i2i−2i2i0002-2-2-222000000000000−2i2i2ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000002i−2i0−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000000000000000000
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
χ66444444444444444-4-4-1-1-1-10000-4-4-4-1-11111-1-1-1-1-1-10000000000000000-111-1-11111000000000000000000000000000000
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χ794444-4-4-4-444-4-44-4400-1-1-1-10000000115−55−511-1-1110000000000000000-1−55-11−555−5000000000000000000000000000000
χ804444-4-4-4-444-4-44-4400-1-1-1-1000000011−55−5511-1-1110000000000000000-15−5-115−5−55000000000000000000000000000000
χ814-44-400000000000004-44-44i−4i−4i4i000000000000000000000002−2i−2+2i−2+2i2−2i2+2i−2−2i−2−2i2+2i000000000000000000000000000000000000000
χ824-44-400000000000004-44-44i−4i−4i4i00000000000000000000000−2+2i2−2i2−2i−2+2i−2−2i2+2i2+2i−2−2i000000000000000000000000000000000000000
χ834-44-400000000000004-44-4−4i4i4i−4i000000000000000000000002+2i−2−2i−2−2i2+2i2−2i−2+2i−2+2i2−2i000000000000000000000000000000000000000
χ844-44-400000000000004-44-4−4i4i4i−4i00000000000000000000000−2−2i2+2i2+2i−2−2i−2+2i2−2i2−2i−2+2i000000000000000000000000000000000000000
χ854-4-44000000-440000044-4-44i−4i4i−4i000-440000000000000000−4i4i00000000000000000000000000000000000000000000000
χ864-4-44000000-440000044-4-4−4i4i−4i4i000-4400000000000000004i−4i00000000000000000000000000000000000000000000000
χ8788-8-88-88i−8i8i−8i0000000-222-20000000000000−2i2i−2i2i-220000000000000000000000000000000000000000000000000000000
χ8888-8-88-8−8i8i−8i8i0000000-222-200000000000002i−2i2i−2i-220000000000000000000000000000000000000000000000000000000
χ8988-8-8-888i−8i−8i8i0000000-222-20000000000000−2i2i2i−2i2-20000000000000000000000000000000000000000000000000000000
χ9088-8-8-88−8i8i8i−8i0000000-222-200000000000002i−2i−2i2i2-20000000000000000000000000000000000000000000000000000000
χ918-8-880000008-80008-8-2-2220000000-22-2-2220000000000000000000000000000000000000000000000000000000000000
χ928-8-880000008-8000-88-2-2220000000-2222-2-20000000000000000000000000000000000000000000000000000000000000
χ938-8-88000000-8800000-2-22200000002-225−25−25250000000000000000000000000000000000000000000000000000000000000
χ948-8-88000000-8800000-2-22200000002-2−252525−250000000000000000000000000000000000000000000000000000000000000
χ9516-1616-160000000000000-44-4400000000000000000000000000000000000000000000000000000000000000000000000000

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