Finite Group Databasebeta

← Group #13030071

Character table — Group #13030071

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size111122222222444444444555588888888888888810101010101010101010101010101010161616161616161616202020202020202020202020202020202020202020404040404040404040
order12224444444444444510101044444442020202020202020202020202222224488888888202020202020202020444448888888888888888444888888
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
χ5111111111111111-1-111111111-1-1-111111111-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1
χ6111111111111111-1-111111111-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ7111111111111111-1-11111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i111-1-1-1-1-1-111-1-1-1−i−iiiiiiiii−i−i−i−i−i−i111−i−i−iiii
χ8111111111111111-1-11111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii111-1-1-1-1-1-111-1-1-1ii−i−i−i−i−i−i−i−iiiiiii111iii−i−i−i
χ9111111-1-1-1-1111-1-111111111111-1-11111-1-1-1-1111111-1-1-1-111111111111-1-111-1-1-1-1111-1-1111111-1-1-1-111-1-1-1-11-1-11-1-11-1-1
χ10111111-1-1-1-1111-1-111111111111-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11-1-111-1-1-1-1111-1-1-1-1-1-1-1-11111-1-111111-1-1-111-111
χ11111111-1-1-1-1111-1-1111111-1-1-1-11-1-11111-1-1-1-11111-1-11111-1-1iiii−i−i−i−i1-1-111-1-1-1-1-1-1-111ii−i−iii−i−i−i−i−i−iiiii-111i−i−i−iii
χ12111111-1-1-1-1111-1-1111111-1-1-1-11-1-11111-1-1-1-11111-1-11111-1-1−i−i−i−iiiii1-1-111-1-1-1-1-1-1-111−i−iii−i−iiiiiii−i−i−i−i-111−iiii−i−i
χ13111111-1-1-1-1111-1-1-1-111111111-1111111-1-1-1-1-1-1-1-111-1-1-1-111111111111-1-1-1-11111-1-11-1-1-1-1-1-111-1-1-1-111-1-1-1-1-111-111-111
χ14111111-1-1-1-1111-1-1-1-111111111-1111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-11111-1-11-1-11111-1-11111-1-11111-1111-1-11-1-1
χ15111111-1-1-1-1111-1-1-1-11111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1iiii−i−i−i−i1-1-1-1-1111111-111−i−iiiii−i−i−i−i−i−iiiii1-1-1−iiii−i−i
χ16111111-1-1-1-1111-1-1-1-11111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1−i−i−i−iiiii1-1-1-1-1111111-111ii−i−i−i−iiiiiii−i−i−i−i1-1-1i−i−i−iii
χ171111-1-111-1-111-11-11111111111-11-111-1-111-1-11111-1-111-1-11111111111-11-1-1-111-1-111-11-11111-1-111-1-1-1-111-1-1-11-1-11-1-11-1
χ181111-1-111-1-111-11-11111111111-11-111-1-111-1-11111-1-111-1-111-1-1-1-1-1-1-1-1-11-1-1-111-1-111-11-1-1-1-1-111-1-11111-1-111-11-11-111-11
χ191111-1-111-1-111-11-1111111-1-1-1-1-11-111-1-111-1-1111111-1-111-1-1iiii−i−i−i−i-11-1-1-111-1-1-1-11-11ii−i−i−i−iii−i−iii−i−iii1-11−ii−ii−ii
χ201111-1-111-1-111-11-1111111-1-1-1-1-11-111-1-111-1-1111111-1-111-1-1−i−i−i−iiiii-11-1-1-111-1-1-1-11-11−i−iiiii−i−iii−i−iii−i−i1-11i−ii−ii−i
χ211111-1-111-1-111-11-1-1-1111111111-1111-1-111-1-1-1-1-1-1-1-111-1-11111111111-11-111-1-111-1-1-11-1-1-1-1-1-1-111-1-1-1-111-1-11-111-111-11
χ221111-1-111-1-111-11-1-1-1111111111-1111-1-111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-11-111-1-111-1-1-11-1111111-1-11111-1-1111-11-11-1-11-1
χ231111-1-111-1-111-11-1-1-11111-1-1-1-11-1111-1-111-1-1-1-1-1-111-1-111-1-1iiii−i−i−i−i-11-111-1-111111-11−i−iii−i−iii−i−iii−i−iii-11-1i−ii−ii−i
χ241111-1-111-1-111-11-1-1-11111-1-1-1-11-1111-1-111-1-1-1-1-1-111-1-111-1-1−i−i−i−iiiii-11-111-1-111111-11ii−i−iii−i−iii−i−iii−i−i-11-1−ii−ii−ii
χ251111-1-1-1-11111-1-111111111111-1-1111-1-1-1-1111111-1-1-1-1111111111111-1-11-1-1-1-11111-1-111111-1-1-1-111-1-1-1-111-1-11-1-11-1-11
χ261111-1-1-1-11111-1-111111111111-1-1111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-11-1-1-1-11111-1-11111-1-1-1-1111-111-1
χ271111-1-1-1-11111-1-11111111-1-1-1-1-1-1111-1-1-1-11111111111-1-1-1-1iiii−i−i−i−i-1-11-1-1-1-111-1-111-1ii−i−i−i−i−i−iiiiiii−i−i11-1−i−iiii−i
χ281111-1-1-1-11111-1-11111111-1-1-1-1-1-1111-1-1-1-11111111111-1-1-1-1−i−i−i−iiiii-1-11-1-1-1-111-1-111-1−i−iiiiiii−i−i−i−i−i−iii11-1ii−i−i−ii
χ291111-1-1-1-11111-1-11-1-11111111111-111-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-111111-1-1-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-11111-111-111-1
χ301111-1-1-1-11111-1-11-1-11111111111-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1111111111-1-11111-1-111-1-1-11-1-11
χ311111-1-1-1-11111-1-11-1-11111-1-1-1-111-111-1-1-1-111-1-1-1-11111-1-1-1-1iiii−i−i−i−i-1-111111-1-11111-1−i−iii−i−i−i−iiiiiii−i−i-1-11ii−i−i−ii
χ321111-1-1-1-11111-1-11-1-11111-1-1-1-111-111-1-1-1-111-1-1-1-11111-1-1-1-1−i−i−i−iiiii-1-111111-1-11111-1ii−i−iiiii−i−i−i−i−i−iii-1-11−i−iiii−i
χ332222222222-2-2-2-2-20022222222000-2-22222220000222222-2-200000000-2-2-200000000-2-2-20000000000000000000000000
χ342222222222-2-2-2-2-2002222-2-2-2-2000-2-22222220000-2-2-2-2-2-22200000000-2-2-2000000002220000000000000000000000000
χ35222222-2-2-2-2-2-2-2220022222222000-2-222-2-2-2-2000022-2-2-2-2-2-200000000-22200000000-2220000000000000000000000000
χ36222222-2-2-2-2-2-2-222002222-2-2-2-2000-2-222-2-2-2-20000-2-222222200000000-222000000002-2-20000000000000000000000000
χ372222-2-222-2-2-2-22-220022222222000-2-2-2-222-2-20000-2-222-2-2-2-2000000002-22000000002-220000000000000000000000000
χ382222-2-222-2-2-2-22-22002222-2-2-2-2000-2-2-2-222-2-2000022-2-22222000000002-2200000000-22-20000000000000000000000000
χ392222-2-2-2-222-2-222-20022222222000-2-2-2-2-2-2220000-2-2-2-222-2-20000000022-20000000022-20000000000000000000000000
χ402222-2-2-2-222-2-222-2002222-2-2-2-2000-2-2-2-2-2-22200002222-2-2220000000022-200000000-2-220000000000000000000000000
χ4122-2-22-22-22-2000000022-2-222-2-2000002-22-22-200002-22-22-20022−2−222−2−20000000000000000002−22−22−22−22−22−2000000000
χ4222-2-22-22-22-2000000022-2-222-2-2000002-22-22-200002-22-22-200−2−222−2−222000000000000000000−22−22−22−22−22−22000000000
χ4322-2-22-22-22-2000000022-2-2-2-222000002-22-22-20000-22-22-2200i2i2−i2−i2−i2−i2i2i2000000000000000000i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2000000000
χ4422-2-22-22-22-2000000022-2-2-2-222000002-22-22-20000-22-22-2200−i2−i2i2i2i2i2−i2−i2000000000000000000−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2000000000
χ4522-2-22-2-22-22000000022-2-222-2-2000002-2-22-2200002-2-22-220022−2−222−2−20000000000000000002−2−22−222−2−22−22000000000
χ4622-2-22-2-22-22000000022-2-222-2-2000002-2-22-2200002-2-22-2200−2−222−2−222000000000000000000−222−22−2−222−22−2000000000
χ4722-2-22-2-22-22000000022-2-2-2-222000002-2-22-220000-222-22-200i2i2−i2−i2−i2−i2i2i2000000000000000000i2−i2−i2i2−i2i2−i2i2i2−i2i2−i2000000000
χ4822-2-22-2-22-22000000022-2-2-2-222000002-2-22-220000-222-22-200−i2−i2i2i2i2i2−i2−i2000000000000000000−i2i2i2−i2i2−i2i2−i2−i2i2−i2i2000000000
χ4922-2-2-222-2-22000000022-2-222-2-200000-222-2-220000-222-2-220022−2−222−2−2000000000000000000−222−2−22−222−2−22000000000
χ5022-2-2-222-2-22000000022-2-222-2-200000-222-2-220000-222-2-2200−2−222−2−2220000000000000000002−2−222−22−2−222−2000000000
χ5122-2-2-222-2-22000000022-2-2-2-22200000-222-2-2200002-2-222-200i2i2−i2−i2−i2−i2i2i2000000000000000000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2000000000
χ5222-2-2-222-2-22000000022-2-2-2-22200000-222-2-2200002-2-222-200−i2−i2i2i2i2i2−i2−i2000000000000000000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2000000000
χ5322-2-2-22-222-2000000022-2-222-2-200000-22-222-20000-22-222-20022−2−222−2−2000000000000000000−22−222−2−22−222−2000000000
χ5422-2-2-22-222-2000000022-2-222-2-200000-22-222-20000-22-222-200−2−222−2−2220000000000000000002−22−2−222−22−2−22000000000
χ5522-2-2-22-222-2000000022-2-2-2-22200000-22-222-200002-22-2-2200i2i2−i2−i2−i2−i2i2i2000000000000000000−i2i2−i2i2i2−i2i2−i2i2−i2−i2i2000000000
χ5622-2-2-22-222-2000000022-2-2-2-22200000-22-222-200002-22-2-2200−i2−i2i2i2i2i2−i2−i2000000000000000000i2−i2i2−i2−i2i2−i2i2−i2i2i2−i2000000000
χ572-2-220000002-20002-22-22-22i−2i2i−2i0002-200000022-2-20000002i−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+2ζ390000000002i−2i000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000000000000000000
χ582-2-220000002-20002-22-22-22i−2i2i−2i0002-200000022-2-20000002i−2i2ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000000002i−2i0002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000000000000000000
χ592-2-220000002-20002-22-22-2−2i2i−2i2i0002-200000022-2-2000000−2i2i−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+2ζ37000000000−2i2i000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000000000000000000
χ602-2-220000002-20002-22-22-2−2i2i−2i2i0002-200000022-2-2000000−2i2i2ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000−2i2i0002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000000000000000
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χ622-2-220000002-2000-222-22-22i−2i2i−2i0002-2000000-2-2220000002i−2i2ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000000−2i2i000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000000000000000000
χ632-2-220000002-2000-222-22-2−2i2i−2i2i0002-2000000-2-222000000−2i2i−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+2ζ370000000002i−2i0002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000000000000000
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χ834-44-400000000000004-4-44−4i4i4i−4i000000000000000000000002−2i−2+2i−2+2i2−2i−2−2i2+2i2+2i−2−2i000000000000000000000000000000000000000
χ844-44-400000000000004-4-44−4i4i4i−4i00000000000000000000000−2+2i2−2i2−2i−2+2i2+2i−2−2i−2−2i2+2i000000000000000000000000000000000000000
χ854-4-44000000-44000004-44-44i−4i4i−4i000-440000000000000000−4i4i00000000000000000000000000000000000000000000000
χ864-4-44000000-44000004-44-4−4i4i−4i4i000-4400000000000000004i−4i00000000000000000000000000000000000000000000000
χ8788-8-88-88-88-80000000-2-222000000000-22-22-2200000000000000000000000000000000000000000000000000000000000
χ8888-8-88-8-88-880000000-2-222000000000-222-22-200000000000000000000000000000000000000000000000000000000000
χ8988-8-8-888-8-880000000-2-2220000000002-2-222-200000000000000000000000000000000000000000000000000000000000
χ9088-8-8-88-888-80000000-2-2220000000002-22-2-2200000000000000000000000000000000000000000000000000000000000
χ918-8-880000008-80008-8-22-220000000-22000000-2-2220000000000000000000000000000000000000000000000000000000
χ928-8-880000008-8000-88-22-220000000-2200000022-2-20000000000000000000000000000000000000000000000000000000
χ938-8-88000000-8800000-22-2200000002-200000025−25−25250000000000000000000000000000000000000000000000000000000
χ948-8-88000000-8800000-22-2200000002-2000000−252525−250000000000000000000000000000000000000000000000000000000
χ9516-1616-160000000000000-444-400000000000000000000000000000000000000000000000000000000000000000000000000

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