Finite Group Databasebeta

← Group #12015453

Character table — Group #12015453

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size1111222222222222222222444444444444444444444444444444888888888888888888881010101010101010161616161616161616161616161616161616161620202020202020202020202080808080
order124422244455888810102020202088101010101010161616161616161620202020202040404040404040404040404080808080808080808080808080808080161616161616161644882020202020202020404040404040404022448888161616164488
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
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ6111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-111
χ911111-1-1-11-1111111111111-1-111-1-1-1-11111-1-1-1-1-1-111-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111i−ii−iiiii−i−i−i−iiiii−i−i−i−i1-11-111-1-1-1-1-1-1i−ii−i
χ1011111-1-1-11-1111111111111-1-111-1-1-1-11111-1-1-1-1-1-111-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111−ii−ii−i−i−i−iiiii−i−i−i−iiiii1-11-111-1-1-1-1-1-1−ii−ii
χ1111111-1-1-11-1111111111111-1-111-1-1-1-11111-1-1-1-1-1-111-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1i−ii−iiiii−i−i−i−iiiii−i−i−i−i-11-11-1-1111111−ii−ii
χ1211111-1-1-11-1111111111111-1-111-1-1-1-11111-1-1-1-1-1-111-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−ii−ii−i−i−i−iiiii−i−i−i−iiiii-11-11-1-1111111i−ii−i
χ1311111-1-1-11-1111111111111-1-111-1-1-1-1-1-1-1-11111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111i−i−iiiiii−i−i−i−i−i−i−i−iiiii-11-11-1-111-1-1-1-1−iii−i
χ1411111-1-1-11-1111111111111-1-111-1-1-1-1-1-1-1-11111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111−iii−i−i−i−i−iiiiiiiii−i−i−i−i-11-11-1-111-1-1-1-1i−i−ii
χ1511111-1-1-11-1111111111111-1-111-1-1-1-1-1-1-1-11111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1i−i−iiiiii−i−i−i−i−i−i−i−iiiii1-11-111-1-11111i−i−ii
χ1611111-1-1-11-1111111111111-1-111-1-1-1-1-1-1-1-11111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−iii−i−i−i−i−iiiiiiiii−i−i−i−i1-11-111-1-11111−iii−i
χ17222222222222-2-2-2-2222222-2-222222200000000222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000002222-2-2-2-200000000
χ18222222222222-2-2-2-2222222-2-222222200000000222222-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000-2-2-2-2222200000000
χ192222222222−1+52−1−522222−1+52−1−52−1+52−1+52−1−52−1−5222−1+52−1−52−1+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+52−1−52−1−52−1−52−1−52000000002222−1+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+52−1−52−1+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+52−1−52−1−52−1−52−1−5200000000-2-2-2-21−521−521+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+52−1−52−1+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+52−1−52−1−521−521−521−521−521+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+52−1−52−1+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+52−1−52−1−521−521−521−521−521+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+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+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+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+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+52−1−52−1+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+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+52−1−52−1+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+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
χ2722222-2-2-22-222-2-2-2-22222222222-2-2-2-200000000-2-222-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000000000000000002-22-2-2-22200000000
χ2822222-2-2-22-222-2-2-2-22222222222-2-2-2-200000000-2-222-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000000000000000-22-2222-2-200000000
χ2922222-2-2-22-2−1+52−1−522222−1+52−1−52−1+52−1+52−1−52−1−52-2-2−1+52−1−521−521+521−521+522222-2-2-2-21−521+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−ζ44−ζ76−ζ44−ζ76−ζ12−ζ28−ζ12−ζ28ζ44+ζ76ζ44+ζ76ζ12+ζ28ζ12+ζ28−ζ44−ζ76−ζ44−ζ76−ζ12−ζ28−ζ12−ζ28ζ44+ζ76ζ44+ζ76ζ12+ζ28ζ12+ζ280000000000000000
χ3022222-2-2-22-2−1+52−1−522222−1+52−1−52−1+52−1+52−1−52−1−52-2-2−1+52−1−521−521+521−521+522222-2-2-2-21−521+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−2i2iζ44+ζ76ζ44+ζ76ζ12+ζ28ζ12+ζ28−ζ44−ζ76−ζ44−ζ76−ζ12−ζ28−ζ12−ζ28ζ44+ζ76ζ44+ζ76ζ12+ζ28ζ12+ζ28−ζ44−ζ76−ζ44−ζ76−ζ12−ζ28−ζ12−ζ280000000000000000
χ3122222-2-2-22-2−1+52−1−522222−1+52−1−52−1+52−1+52−1−52−1−52-2-2−1+52−1−521−521+521−521+52-2-2-2-222221−521+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−ζ44−ζ76−ζ44−ζ76−ζ12−ζ28−ζ12−ζ28ζ44+ζ76ζ44+ζ76ζ12+ζ28ζ12+ζ28ζ44+ζ76ζ44+ζ76ζ12+ζ28ζ12+ζ28−ζ44−ζ76−ζ44−ζ76−ζ12−ζ28−ζ12−ζ280000000000000000
χ3222222-2-2-22-2−1+52−1−522222−1+52−1−52−1+52−1+52−1−52−1−52-2-2−1+52−1−521−521+521−521+52-2-2-2-222221−521+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−2iζ44+ζ76ζ44+ζ76ζ12+ζ28ζ12+ζ28−ζ44−ζ76−ζ44−ζ76−ζ12−ζ28−ζ12−ζ28−ζ44−ζ76−ζ44−ζ76−ζ12−ζ28−ζ12−ζ28ζ44+ζ76ζ44+ζ76ζ12+ζ28ζ12+ζ280000000000000000
χ3322222-2-2-22-2−1−52−1+522222−1−52−1+52−1−52−1−52−1+52−1+52-2-2−1−52−1+521+521−521+521−522222-2-2-2-21+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−ζ12−ζ28−ζ12−ζ28−ζ44−ζ76−ζ44−ζ76ζ12+ζ28ζ12+ζ28ζ44+ζ76ζ44+ζ76−ζ12−ζ28−ζ12−ζ28−ζ44−ζ76−ζ44−ζ76ζ12+ζ28ζ12+ζ28ζ44+ζ76ζ44+ζ760000000000000000
χ3422222-2-2-22-2−1−52−1+522222−1−52−1+52−1−52−1−52−1+52−1+52-2-2−1−52−1+521+521−521+521−522222-2-2-2-21+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−2i2iζ12+ζ28ζ12+ζ28ζ44+ζ76ζ44+ζ76−ζ12−ζ28−ζ12−ζ28−ζ44−ζ76−ζ44−ζ76ζ12+ζ28ζ12+ζ28ζ44+ζ76ζ44+ζ76−ζ12−ζ28−ζ12−ζ28−ζ44−ζ76−ζ44−ζ760000000000000000
χ3522222-2-2-22-2−1−52−1+522222−1−52−1+52−1−52−1−52−1+52−1+52-2-2−1−52−1+521+521−521+521−52-2-2-2-222221+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−ζ12−ζ28−ζ12−ζ28−ζ44−ζ76−ζ44−ζ76ζ12+ζ28ζ12+ζ28ζ44+ζ76ζ44+ζ76ζ12+ζ28ζ12+ζ28ζ44+ζ76ζ44+ζ76−ζ12−ζ28−ζ12−ζ28−ζ44−ζ76−ζ44−ζ760000000000000000
χ3622222-2-2-22-2−1−52−1+522222−1−52−1+52−1−52−1−52−1+52−1+52-2-2−1−52−1+521+521−521+521−52-2-2-2-222221+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−2iζ12+ζ28ζ12+ζ28ζ44+ζ76ζ44+ζ76−ζ12−ζ28−ζ12−ζ28−ζ44−ζ76−ζ44−ζ76−ζ12−ζ28−ζ12−ζ28−ζ44−ζ76−ζ44−ζ76ζ12+ζ28ζ12+ζ28ζ44+ζ76ζ44+ζ760000000000000000
χ372222-22-2-2-2222000022222200-2-2-2-222i2i2−i2−i2i2i2−i2−i222-2-2-2-2000000000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i22222−2−2−2−20000000000000000000000002i−2i2i−2i22−2−20000
χ382222-22-2-2-2222000022222200-2-2-2-222i2i2−i2−i2i2i2−i2−i222-2-2-2-2000000000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2−2−2−2−22222000000000000000000000000−2i2i−2i2i−2−2220000
χ392222-22-2-2-2222000022222200-2-2-2-222−i2−i2i2i2−i2−i2i2i222-2-2-2-2000000000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i22222−2−2−2−2000000000000000000000000−2i2i−2i2i22−2−20000
χ402222-22-2-2-2222000022222200-2-2-2-222−i2−i2i2i2−i2−i2i2i222-2-2-2-2000000000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−2−2−2−222220000000000000000000000002i−2i2i−2i−2−2220000
χ412222-2-222-2-222000022222200-2-222-2-2i2i2−i2−i2−i2−i2i2i2-2-2-2-222000000000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i22222−2−2−2−20000000000000000000000002i−2i−2i2i−2−2220000
χ422222-2-222-2-222000022222200-2-222-2-2i2i2−i2−i2−i2−i2i2i2-2-2-2-222000000000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2−2−2−2−22222000000000000000000000000−2i2i2i−2i22−2−20000
χ432222-2-222-2-222000022222200-2-222-2-2−i2−i2i2i2i2i2−i2−i2-2-2-2-222000000000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i22222−2−2−2−2000000000000000000000000−2i2i2i−2i−2−2220000
χ442222-2-222-2-222000022222200-2-222-2-2−i2−i2i2i2i2i2−i2−i2-2-2-2-222000000000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−2−2−2−222220000000000000000000000002i−2i−2i2i22−2−20000
χ4522-2-2222-2-2-222000022-2-2-2-200222222i2−i2i2−i2i2−i2i2−i2-2-2-2-2-2-2000000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2000000000000000000002-2-220000i2−i2i2−i20000
χ4622-2-2222-2-2-222000022-2-2-2-200222222i2−i2i2−i2i2−i2i2−i2-2-2-2-2-2-2000000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2−i2−i2i2i2−i2−i2i2i200000000000000000000-222-20000−i2i2−i2i20000
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χ1148-8−8i8i000000−2+25−2−25−42424i2−4i22−252+254ζ44+4ζ76−4ζ44−4ζ764ζ12+4ζ28−4ζ12−4ζ2800000000000000000000002ζ14−2ζ26+2ζ46−2ζ74−2ζ14+2ζ26−2ζ46+2ζ74−2ζ42−2ζ58+2ζ62+2ζ782ζ42+2ζ58−2ζ62−2ζ782ζ14+2ζ26+2ζ46+2ζ74−2ζ14−2ζ26−2ζ46−2ζ742ζ42+2ζ58+2ζ62+2ζ78−2ζ42−2ζ58−2ζ62−2ζ780000000000000000000000000000000000000000000000000000000000000000
χ1158-8−8i8i000000−2−25−2+2542−42−4i24i22+252−254ζ12+4ζ28−4ζ12−4ζ284ζ44+4ζ76−4ζ44−4ζ7600000000000000000000002ζ42+2ζ58−2ζ62−2ζ78−2ζ42−2ζ58+2ζ62+2ζ78−2ζ14+2ζ26−2ζ46+2ζ742ζ14−2ζ26+2ζ46−2ζ74−2ζ42−2ζ58−2ζ62−2ζ782ζ42+2ζ58+2ζ62+2ζ78−2ζ14−2ζ26−2ζ46−2ζ742ζ14+2ζ26+2ζ46+2ζ740000000000000000000000000000000000000000000000000000000000000000
χ1168-8−8i8i000000−2−25−2+25−42424i2−4i22+252−254ζ12+4ζ28−4ζ12−4ζ284ζ44+4ζ76−4ζ44−4ζ760000000000000000000000−2ζ42−2ζ58+2ζ62+2ζ782ζ42+2ζ58−2ζ62−2ζ782ζ14−2ζ26+2ζ46−2ζ74−2ζ14+2ζ26−2ζ46+2ζ742ζ42+2ζ58+2ζ62+2ζ78−2ζ42−2ζ58−2ζ62−2ζ782ζ14+2ζ26+2ζ46+2ζ74−2ζ14−2ζ26−2ζ46−2ζ740000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 80 (ζ80 = 1); i = ζ20.