Finite Group Databasebeta

← Group #10601421

Character table — Group #10601421

Order 640.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100
size111111112222222222222222222222222222444444444444444444444444888888888888888888881010101010101010101010101010101040404040
order1222222244445588888888101010101010101010101010101020202020202020204040404040404040404040404040404044442020202020202020202020202020202044444444888888882222
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1
χ611111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111
χ711111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111
χ811111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1
χ9111-11-1-1-11-11-1111111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1i−ii−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1-11-1
χ10111-11-1-1-11-11-1111111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1i−ii−iiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-11-11
χ11111-11-1-1-11-11-1111111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1−ii−ii−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-11-11
χ12111-11-1-1-11-11-1111111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1−ii−ii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1-11-1
χ13111-11-1-1-11-11-111-1-1-1-111111111-1-1-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111i−i−iiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii1-1-11
χ14111-11-1-1-11-11-111-1-1-1-111111111-1-1-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111i−i−iiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-111-1
χ15111-11-1-1-11-11-111-1-1-1-111111111-1-1-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111−iii−i−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-111-1
χ16111-11-1-1-11-11-111-1-1-1-111111111-1-1-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111−iii−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i1-1-11
χ17222222222222−1+52−1−5222222222−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−522222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5200000000000000000000
χ18222222222222−1+52−1−5222222222−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-2-2-2-21−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+5200000000000000000000
χ19222222222222−1+52−1−52-2-2-2-2-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+5222-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+5200000000000000000000
χ20222222222222−1+52−1−52-2-2-2-2-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+52-2-2221−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5200000000000000000000
χ21222222222222−1−52−1+5222222222−1−52−1−52−1+52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+522222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5200000000000000000000
χ22222222222222−1−52−1+5222222222−1−52−1−52−1+52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52-2-2-2-21+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−5200000000000000000000
χ23222222222222−1−52−1+52-2-2-2-2-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+521+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−5222-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−5200000000000000000000
χ24222222222222−1−52−1+52-2-2-2-2-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+521+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−52-2-2221+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5200000000000000000000
χ2522222222-2-2-2-2220000000022222222222222-2-2-2-2-2-2-2-200000000000000000000000000000000000022-2-222-2-2000000000000
χ2622222222-2-2-2-2220000000022222222222222-2-2-2-2-2-2-2-2000000000000000000000000000000000000-2-222-2-222000000000000
χ27222-22-2-2-22-22-2−1+52−1−522222-2-2-2-2−1+52−1+52−1−52−1−521−521−521−521+521+521+52−1+52−1−521−521+52−1+52−1−521−521−521+521+52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−521−521−521−521−521+521+521+521+522i−2i2i−2i−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ1400000000000000000000
χ28222-22-2-2-22-22-2−1+52−1−522222-2-2-2-2−1+52−1+52−1−52−1−521−521−521−521+521+521+52−1+52−1−521−521+52−1+52−1−521−521−521+521+52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−521−521−521−521−521+521+521+521+52−2i2i−2i2iζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ1400000000000000000000
χ29222-22-2-2-22-22-2−1+52−1−52-2-2-2-22222−1+52−1+52−1−52−1−521−521−521−521+521+521+52−1+52−1−521−521+52−1+52−1−521−521−521+521+52−1+52−1−521−521−521−521−521+521+521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−522i−2i−2i2i−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ1400000000000000000000
χ30222-22-2-2-22-22-2−1+52−1−52-2-2-2-22222−1+52−1+52−1−52−1−521−521−521−521+521+521+52−1+52−1−521−521+52−1+52−1−521−521−521+521+52−1+52−1−521−521−521−521−521+521+521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−2i2i2i−2iζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ1400000000000000000000
χ31222-22-2-2-22-22-2−1−52−1+522222-2-2-2-2−1−52−1−52−1+52−1+521+521+521+521−521−521−52−1−52−1+521+521−52−1−52−1+521+521+521−521−52−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+521+521+521+521+521−521−521−521−522i−2i2i−2i−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ3800000000000000000000
χ32222-22-2-2-22-22-2−1−52−1+522222-2-2-2-2−1−52−1−52−1+52−1+521+521+521+521−521−521−52−1−52−1+521+521−52−1−52−1+521+521+521−521−52−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+521+521+521+521+521−521−521−521−52−2i2i−2i2iζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ3800000000000000000000
χ33222-22-2-2-22-22-2−1−52−1+52-2-2-2-22222−1−52−1−52−1+52−1+521+521+521+521−521−521−52−1−52−1+521+521−52−1−52−1+521+521+521−521−52−1−52−1+521+521+521+521+521−521−521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+522i−2i−2i2i−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ3800000000000000000000
χ34222-22-2-2-22-22-2−1−52−1+52-2-2-2-22222−1−52−1−52−1+52−1+521+521+521+521−521−521−52−1−52−1+521+521−52−1−52−1+521+521+521−521−52−1−52−1+521+521+521+521+521−521−521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−2i2i2i−2iζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ3800000000000000000000
χ35222-22-2-2-2-22-2222000000002222-2-2-2-2-2-222-2-2-2-22222-2-20000000000000000000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ36222-22-2-2-2-22-2222000000002222-2-2-2-2-2-222-2-2-2-22222-2-2000000000000000000000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ3722-22-2-22-200002222−2−222−2−22-22-222-222-2-2-2-2-20000000022−2−222−2−222−2−222−2−200000000000000000000002i−2i002i−2ii2i2−i2−i2i2i2−i2−i20000
χ3822-22-2-22-200002222−2−222−2−22-22-222-222-2-2-2-2-20000000022−2−222−2−222−2−222−2−20000000000000000000000−2i2i00−2i2i−i2−i2i2i2−i2−i2i2i20000
χ3922-22-2-22-2000022−2−222−2−2222-22-222-222-2-2-2-2-200000000−2−222−2−222−2−222−2−22200000000000000000000002i−2i002i−2i−i2−i2i2i2−i2−i2i2i20000
χ4022-22-2-22-2000022−2−222−2−2222-22-222-222-2-2-2-2-200000000−2−222−2−222−2−222−2−2220000000000000000000000−2i2i00−2i2ii2i2−i2−i2i2i2−i2−i20000
χ4122-2-2-22-2200002222−2−2−2−2222-22-2-2-22-2-22-2-2220000000022−2−222−2−2−2−222−2−22200000000000000000000002-200-2222−2−2−2−2220000
χ4222-2-2-22-2200002222−2−2−2−2222-22-2-2-22-2-22-2-2220000000022−2−222−2−2−2−222−2−2220000000000000000000000-22002-2−2−22222−2−20000
χ4322-2-2-22-22000022−2−22222−2−22-22-2-2-22-2-22-2-22200000000−2−222−2−22222−2−222−2−200000000000000000000002-200-22−2−22222−2−20000
χ4422-2-2-22-22000022−2−22222−2−22-22-2-2-22-2-22-2-22200000000−2−222−2−22222−2−222−2−20000000000000000000000-22002-222−2−2−2−2220000
χ452-222-2-2-220000222−22−22−22−2-22-222-222-22-2-2-2-2000000002−22−22−22−22−22−22−22−2000000000000000000002i−2i002i−2i00i2−i2i2−i2i2−i2i2−i20000
χ462-222-2-2-220000222−22−22−22−2-22-222-222-22-2-2-2-2000000002−22−22−22−22−22−22−22−200000000000000000000−2i2i00−2i2i00−i2i2−i2i2−i2i2−i2i20000
χ472-222-2-2-22000022−22−22−22−22-22-222-222-22-2-2-2-200000000−22−22−22−22−22−22−22−22000000000000000000002i−2i002i−2i00−i2i2−i2i2−i2i2−i2i20000
χ482-222-2-2-22000022−22−22−22−22-22-222-222-22-2-2-2-200000000−22−22−22−22−22−22−22−2200000000000000000000−2i2i00−2i2i00i2−i2i2−i2i2−i2i2−i20000
χ492-22-2-222-20000222−22−2−22−22-22-22-22-2-22-2-2-222000000002−22−22−22−2−22−22−22−22000000000000000000002-200-22002−22−2−22−220000
χ502-22-2-222-20000222−22−2−22−22-22-22-22-2-22-2-2-222000000002−22−22−22−2−22−22−22−2200000000000000000000-22002-200−22−222−22−20000
χ512-22-2-222-2000022−22−222−22−2-22-22-22-2-22-2-2-22200000000−22−22−22−222−22−22−22−2000000000000000000002-200-2200−22−222−22−20000
χ522-22-2-222-2000022−22−222−22−2-22-22-22-2-22-2-2-22200000000−22−22−22−222−22−22−22−200000000000000000000-22002-2002−22−2−22−220000
χ532-2-2222-2-22-2-222200000000-2-2-2-22-2-22-2-22222222-22-2-2-2000000000000000000000000000000000000000000002-2-222-2-220000
χ542-2-2222-2-22-2-222200000000-2-2-2-22-2-22-2-22222222-22-2-2-200000000000000000000000000000000000000000000-222-2-222-20000
χ552-2-2222-2-2-222-2222-2-222-2-22-2-2-2-22-2-22-2-22222-2-2-22-22222-2-222-2-222-2-222-2-220000000000000000000000000000000000000000
χ562-2-2222-2-2-222-222-222-2-222-2-2-2-2-22-2-22-2-22222-2-2-22-2222-222-2-222-2-222-2-222-20000000000000000000000000000000000000000
χ572-2-2222-2-2-222-2−1+52−1−522-2-222-2-221−521−521+521+52−1+521−521−52−1−521+521+52−1+52−1−52−1+52−1−521−521+521−52−1+521+52−1−52−1+52−1−52−1+521−521−52−1+52−1−521+521+52−1−52−1+521−521−52−1+52−1−521+521+52−1−520000ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ3600000000000000000000
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χ954-44-4-444-40000−1−5−1+522−2222−22−2222−22221+5−1−51−5−1+51+5−1−51+51−5−1+51−51+51−5−1−5−1+500000000ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ370000000000000000000000000000000000000000
χ964-44-4-444-40000−1−5−1+5−2222−222222−2222−221+5−1−51−5−1+51+5−1−51+51−5−1+51−51+51−5−1−5−1+500000000−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ370000000000000000000000000000000000000000
χ974-4-4444-4-44-4-44−1+5−1−5000000001−51−51+51+5−1+51−51−5−1−51+51+5−1+5−1−5−1+5−1−5−1+5−1−5−1+51−5−1−51+51−51+500000000000000000000000000000000000000000000000000000000
χ984-4-4444-4-44-4-44−1−5−1+5000000001+51+51−51−5−1−51+51+5−1+51−51−5−1−5−1+5−1−5−1+5−1−5−1+5−1−51+5−1+51−51+51−500000000000000000000000000000000000000000000000000000000
χ994-4-4-44-44444-4-4−1+5−1−5000000001−51−51+51+51−5−1+5−1+51+5−1−5−1−5−1+5−1−51−51+5−1+5−1−51−5−1+51+5−1−51−51+500000000000000000000000000000000000000000000000000000000
χ1004-4-4-44-44444-4-4−1−5−1+5000000001+51+51−51−51+5−1−5−1−51−5−1+5−1+5−1−5−1+51+51−5−1−5−1+51+5−1−51−5−1+51+51−500000000000000000000000000000000000000000000000000000000

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