Finite Group Databasebeta

← Group #12015724

Character table — Group #12015724

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size1111222222222222222222444444444444444444444444444444888888888888888888881010101010101010161616161616161616161616161616161616161620202020202020202020202080808080
order12222244445588881010101010108810101010161616161616161620202020202020204040404040404040404040408080808080808080808080808080808044448888448820202020202020204040404040404040448816161616161616164488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1
χ91111-1-1-111-1111111111111-1-1-1-1-1-11111-1-1-1-111-1-111-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111i−ii−iiiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111-1-1-1-1i−ii−i
χ101111-1-1-111-1111111111111-1-1-1-1-1-11111-1-1-1-111-1-111-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111−ii−ii−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111-1-1-1-1−ii−ii
χ111111-1-1-111-1111111111111-1-1-1-1-1-11111-1-1-1-111-1-111-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1i−ii−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11111−ii−ii
χ121111-1-1-111-1111111111111-1-1-1-1-1-11111-1-1-1-111-1-111-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−ii−ii−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11111i−ii−i
χ131111-1-1-111-1111111111111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111i−i−iiiiii−i−i−i−i−i−i−i−iiiii-1-1-1-1-1-1-1-11111i−i−ii
χ141111-1-1-111-1111111111111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111−iii−i−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-1-1-1-1-11111−iii−i
χ151111-1-1-111-1111111111111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1i−i−iiiiii−i−i−i−i−i−i−i−iiiii11111111-1-1-1-1−iii−i
χ161111-1-1-111-1111111111111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−iii−i−i−i−i−iiiiiiiii−i−i−i−i11111111-1-1-1-1i−i−ii
χ17222222222222-2-2-2-2222222-2-222220000000022222222-2-2-2-2-2-2-2-2-2-2-2-200000000000000002222-2-2-2-20000000000000000000022-2-2000000000000
χ18222222222222-2-2-2-2222222-2-222220000000022222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000-2-2-2-2222200000000000000000000-2-222000000000000
χ192222222222−1+52−1−522222−1+52−1+52−1−52−1−52−1+52−1−5222−1+52−1−52−1+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+52−1−52−1−52−1−52−1−52000000002222−1+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+52−1−52−1−520000000000000000
χ202222222222−1+52−1−522222−1+52−1+52−1−52−1−52−1+52−1−5222−1+52−1−52−1+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+52−1−52−1−52−1−52−1−5200000000-2-2-2-21−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+520000000000000000
χ212222222222−1+52−1−522222−1+52−1+52−1−52−1−52−1+52−1−5222−1+52−1−52−1+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+52−1−52−1−521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+520000000022-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+520000000000000000
χ222222222222−1+52−1−522222−1+52−1+52−1−52−1−52−1+52−1−5222−1+52−1−52−1+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+52−1−52−1−521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+5200000000-2-2221−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−520000000000000000
χ232222222222−1−52−1+522222−1−52−1−52−1+52−1+52−1−52−1+5222−1−52−1+52−1−52−1+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+52000000002222−1−52−1−52−1+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+520000000000000000
χ242222222222−1−52−1+522222−1−52−1−52−1+52−1+52−1−52−1+5222−1−52−1+52−1−52−1+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+5200000000-2-2-2-21+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−520000000000000000
χ252222222222−1−52−1+522222−1−52−1−52−1+52−1+52−1−52−1+5222−1−52−1+52−1−52−1+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+521+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−520000000022-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−520000000000000000
χ262222222222−1−52−1+522222−1−52−1−52−1+52−1+52−1−52−1+5222−1−52−1+52−1−52−1+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+521+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−5200000000-2-2221+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+520000000000000000
χ27222222-2-2-2-2220000222222002222i2i2−i2−i2i2i2−i2−i2-2-2-2-2-2-2-2-2000000000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i222-2-20000000000000000000000002-200i2i2−i2−i2i2i2−i2−i20000
χ28222222-2-2-2-2220000222222002222i2i2−i2−i2i2i2−i2−i2-2-2-2-2-2-2-2-2000000000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2-2-222000000000000000000000000-2200−i2−i2i2i2−i2−i2i2i20000
χ29222222-2-2-2-2220000222222002222−i2−i2i2i2−i2−i2i2i2-2-2-2-2-2-2-2-2000000000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i222-2-20000000000000000000000002-200−i2−i2i2i2−i2−i2i2i20000
χ30222222-2-2-2-2220000222222002222−i2−i2i2i2−i2−i2i2i2-2-2-2-2-2-2-2-2000000000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2-2-222000000000000000000000000-2200i2i2−i2−i2i2i2−i2−i20000
χ312222-2-22-2-2222000022222200-2-2-2-2i2i2−i2−i2−i2−i2i2i2-2-222-2-222000000000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i222-2-2000000000000000000000000-2200i2i2−i2−i2−i2−i2i2i20000
χ322222-2-22-2-2222000022222200-2-2-2-2i2i2−i2−i2−i2−i2i2i2-2-222-2-222000000000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2-2-2220000000000000000000000002-200−i2−i2i2i2i2i2−i2−i20000
χ332222-2-22-2-2222000022222200-2-2-2-2−i2−i2i2i2i2i2−i2−i2-2-222-2-222000000000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i222-2-2000000000000000000000000-2200−i2−i2i2i2i2i2−i2−i20000
χ342222-2-22-2-2222000022222200-2-2-2-2−i2−i2i2i2i2i2−i2−i2-2-222-2-222000000000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2-2-2220000000000000000000000002-200i2i2−i2−i2−i2−i2i2i20000
χ352222-2-2-222-222-2-2-2-222222222-2-2-2-20000000022-2-222-2-2-2-2-2-2-2-2-2-2222200000000000000002222-2-2-2-200000000000000000000-2-222000000000000
χ362222-2-2-222-222-2-2-2-222222222-2-2-2-20000000022-2-222-2-2-2-2-2-2-2-2-2-222220000000000000000-2-2-2-222220000000000000000000022-2-2000000000000
χ372222-2-2-222-2−1+52−1−522222−1+52−1+52−1−52−1−52−1+52−1−52-2-21−521+521−521+522222-2-2-2-2−1+52−1−521−521+52−1+52−1−521−521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−521−521−521−521−521+521+521+521+52000000002i−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+ζ140000000000000000
χ382222-2-2-222-2−1+52−1−522222−1+52−1+52−1−52−1−52−1+52−1−52-2-21−521+521−521+522222-2-2-2-2−1+52−1−521−521+52−1+52−1−521−521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−521−521−521−521−521+521+521+521+5200000000−2i2i−2i2iζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ140000000000000000
χ392222-2-2-222-2−1+52−1−522222−1+52−1+52−1−52−1−52−1+52−1−52-2-21−521+521−521+52-2-2-2-22222−1+52−1−521−521+52−1+52−1−521−521+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+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52000000002i−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−ζ140000000000000000
χ402222-2-2-222-2−1+52−1−522222−1+52−1+52−1−52−1−52−1+52−1−52-2-21−521+521−521+52-2-2-2-22222−1+52−1−521−521+52−1+52−1−521−521+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+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5200000000−2i2i2i−2iζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ140000000000000000
χ412222-2-2-222-2−1−52−1+522222−1−52−1−52−1+52−1+52−1−52−1+52-2-21+521−521+521−522222-2-2-2-2−1−52−1+521+521−52−1−52−1+521+521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+521+521+521+521+521−521−521−521−52000000002i−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+ζ380000000000000000
χ422222-2-2-222-2−1−52−1+522222−1−52−1−52−1+52−1+52−1−52−1+52-2-21+521−521+521−522222-2-2-2-2−1−52−1+521+521−52−1−52−1+521+521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+521+521+521+521+521−521−521−521−5200000000−2i2i−2i2iζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ380000000000000000
χ432222-2-2-222-2−1−52−1+522222−1−52−1−52−1+52−1+52−1−52−1+52-2-21+521−521+521−52-2-2-2-22222−1−52−1+521+521−52−1−52−1+521+521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521+521+521−521−521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52000000002i−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−ζ380000000000000000
χ442222-2-2-222-2−1−52−1+522222−1−52−1−52−1+52−1+52−1−52−1+52-2-21+521−521+521−52-2-2-2-22222−1−52−1+521+521−52−1−52−1+521+521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521+521+521−521−521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5200000000−2i2i2i−2iζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ380000000000000000
χ4522-2-22-222-2-22222-2-2-2-2-2-2222-222-2-22-22-22-22-2-2-22222-2-2-2-2-2-222222-22-22-22-22-22-22-22-22-22-200000000000000000000000000000000000000000000
χ4622-2-22-222-2-22222-2-2-2-2-2-2222-222-2-2-22-22-22-22-2-22222-2-2-2-2-2-222222-22-2-22-22-22-22-22-22-22-2200000000000000000000000000000000000000000000
χ4722-2-22-222-2-222-2-222-2-2-2-222-2222-2-200000000-2-22222-2-22222-2-2-2-2-22-220000000000000000000000000000000000000000000000002-22-22-22-20000
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Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.