Finite Group Databasebeta

← Group #12253872

Character table — Group #12253872

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size1122222222244444444444444488888888881010101016161616161616161616202020202020808011222222222444444444444444888888888810101010161616161616161616162020202020208080
order122445588101081010161616162020202040404040404080808080808080801616161648202020204040404024881616282224410108810108101016161616202020204040404040408080808080808080161616164820202020404040402488161628
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-11111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1
χ3111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ511111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111111-11111-1-1-1-1-1-1-1-1111-111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111111-11111-1-1-1-1-1-1-1-1111-1
χ611111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-11-1-1-1-11111-1-1-1-111-1111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-11-1-1-1-11111-1-1-1-111-11
χ711111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-11111-1-1-1111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-11111-1-1-11
χ811111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111111-1-11-111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111111-1-11-1
χ92222222-2-222-22200002222-2-2-2-2-2-2000000000000000000000022-2-200002222222-2-222-22200002222-2-2-2-2-2-2000000000000000000000022-2-20000
χ102222222-2-222-22200002222-2-2-2-2-2-20000000000000000000000-2-22200002222222-2-222-22200002222-2-2-2-2-2-20000000000000000000000-2-2220000
χ1122222−1+52−1−5222−1+52−1−522−1+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+52−1−52−1−52−1−52−1−52000022−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−520000000022222−1+52−1−5222−1+52−1−522−1+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+52−1−52−1−52−1−52−1−52000022−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5200000000
χ1222222−1+52−1−5222−1+52−1−522−1+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+52−1−52−1−52−1−52−1−520000-2-21−521−521+521+521−521−521+521+520000000022222−1+52−1−5222−1+52−1−522−1+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+52−1−52−1−52−1−52−1−520000-2-21−521−521+521+521−521−521+521+5200000000
χ1322222−1+52−1−5222−1+52−1−522−1+52−1−52-2-2-2-2−1+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+5200002-2−1+52−1+52−1−52−1−521−521−521+521+520000000022222−1+52−1−5222−1+52−1−522−1+52−1−52-2-2-2-2−1+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+5200002-2−1+52−1+52−1−52−1−521−521−521+521+5200000000
χ1422222−1+52−1−5222−1+52−1−522−1+52−1−52-2-2-2-2−1+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+520000-221−521−521+521+52−1+52−1+52−1−52−1−520000000022222−1+52−1−5222−1+52−1−522−1+52−1−52-2-2-2-2−1+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+520000-221−521−521+521+52−1+52−1+52−1−52−1−5200000000
χ1522222−1−52−1+5222−1−52−1+522−1−52−1+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+52−1+52−1+52000022−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+520000000022222−1−52−1+5222−1−52−1+522−1−52−1+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+52−1+52−1+52000022−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5200000000
χ1622222−1−52−1+5222−1−52−1+522−1−52−1+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+52−1+52−1+520000-2-21+521+521−521−521+521+521−521−520000000022222−1−52−1+5222−1−52−1+522−1−52−1+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+52−1+52−1+520000-2-21+521+521−521−521+521+521−521−5200000000
χ1722222−1−52−1+5222−1−52−1+522−1−52−1+52-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+521+521+521+521+521−521−521−521−5200002-2−1−52−1−52−1+52−1+521+521+521−521−520000000022222−1−52−1+5222−1−52−1+522−1−52−1+52-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+521+521+521+521+521−521−521−521−5200002-2−1−52−1−52−1+52−1+521+521+521−521−5200000000
χ1822222−1−52−1+5222−1−52−1+522−1−52−1+52-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+521+521+521+521+521−521−521−521−520000-221+521+521−521−52−1−52−1−52−1+52−1+520000000022222−1−52−1+5222−1−52−1+522−1−52−1+52-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+521+521+521+521+521−521−521−521−520000-221+521+521−521−52−1−52−1−52−1+52−1+5200000000
χ19222-2-2220022022i2i2−i2−i2-2-2-2-2000000i2i2−i2−i2i2i2−i2−i222−2−20000000000002i−2i2−200222-2-2220022022i2i2−i2−i2-2-2-2-2000000i2i2−i2−i2i2i2−i2−i222−2−20000000000002i−2i2−200
χ20222-2-2220022022i2i2−i2−i2-2-2-2-2000000i2i2−i2−i2i2i2−i2−i2−2−222000000000000−2i2i−2200222-2-2220022022i2i2−i2−i2-2-2-2-2000000i2i2−i2−i2i2i2−i2−i2−2−222000000000000−2i2i−2200
χ21222-2-2220022022−i2−i2i2i2-2-2-2-2000000−i2−i2i2i2−i2−i2i2i222−2−2000000000000−2i2i2−200222-2-2220022022−i2−i2i2i2-2-2-2-2000000−i2−i2i2i2−i2−i2i2i222−2−2000000000000−2i2i2−200
χ22222-2-2220022022−i2−i2i2i2-2-2-2-2000000−i2−i2i2i2−i2−i2i2i2−2−2220000000000002i−2i−2200222-2-2220022022−i2−i2i2i2-2-2-2-2000000−i2−i2i2i2−i2−i2i2i2−2−2220000000000002i−2i−2200
χ2322-22-2222222-2-2-2000022-2-22222-2-200000000222200000000000000-2-20022-22-2222222-2-2-2000022-2-22222-2-200000000222200000000000000-2-200
χ2422-22-2222222-2-2-2000022-2-22222-2-200000000-2-2-2-200000000000000220022-22-2222222-2-2-2000022-2-22222-2-200000000-2-2-2-2000000000000002200
χ2522-22-222-2-2222-2-22i−2i2i−2i22-2-2-2-2-2-2222i−2i2i−2i2i−2i2i−2i000000000000000000000022-22-222-2-2222-2-22i−2i2i−2i22-2-2-2-2-2-2222i−2i2i−2i2i−2i2i−2i0000000000000000000000
χ2622-22-222-2-2222-2-2−2i2i−2i2i22-2-2-2-2-2-222−2i2i−2i2i−2i2i−2i2i000000000000000000000022-22-222-2-2222-2-2−2i2i−2i2i22-2-2-2-2-2-222−2i2i−2i2i−2i2i−2i2i0000000000000000000000
χ2722-22-2−1+52−1−52-2-2−1+52−1−5221−521+522i−2i2i−2i−1+52−1−521−521+521−521−521+521+52−1+52−1−52−ζ44−ζ76ζ44+ζ76−ζ44−ζ76ζ44+ζ76−ζ12−ζ28ζ12+ζ28−ζ12−ζ28ζ12+ζ28000000ζ24−ζ56−ζ24+ζ56−ζ8+ζ72ζ8−ζ72−ζ44+ζ76ζ44−ζ76ζ12−ζ28−ζ12+ζ280000000022-22-2−1+52−1−52-2-2−1+52−1−5221−521+522i−2i2i−2i−1+52−1−521−521+521−521−521+521+52−1+52−1−52−ζ44−ζ76ζ44+ζ76−ζ44−ζ76ζ44+ζ76−ζ12−ζ28ζ12+ζ28−ζ12−ζ28ζ12+ζ28000000ζ24−ζ56−ζ24+ζ56−ζ8+ζ72ζ8−ζ72−ζ44+ζ76ζ44−ζ76ζ12−ζ28−ζ12+ζ2800000000
χ2822-22-2−1+52−1−52-2-2−1+52−1−5221−521+522i−2i2i−2i−1+52−1−521−521+521−521−521+521+52−1+52−1−52−ζ44−ζ76ζ44+ζ76−ζ44−ζ76ζ44+ζ76−ζ12−ζ28ζ12+ζ28−ζ12−ζ28ζ12+ζ28000000−ζ24+ζ56ζ24−ζ56ζ8−ζ72−ζ8+ζ72ζ44−ζ76−ζ44+ζ76−ζ12+ζ28ζ12−ζ280000000022-22-2−1+52−1−52-2-2−1+52−1−5221−521+522i−2i2i−2i−1+52−1−521−521+521−521−521+521+52−1+52−1−52−ζ44−ζ76ζ44+ζ76−ζ44−ζ76ζ44+ζ76−ζ12−ζ28ζ12+ζ28−ζ12−ζ28ζ12+ζ28000000−ζ24+ζ56ζ24−ζ56ζ8−ζ72−ζ8+ζ72ζ44−ζ76−ζ44+ζ76−ζ12+ζ28ζ12−ζ2800000000
χ2922-22-2−1+52−1−52-2-2−1+52−1−5221−521+52−2i2i−2i2i−1+52−1−521−521+521−521−521+521+52−1+52−1−52ζ44+ζ76−ζ44−ζ76ζ44+ζ76−ζ44−ζ76ζ12+ζ28−ζ12−ζ28ζ12+ζ28−ζ12−ζ28000000ζ24−ζ56−ζ24+ζ56−ζ8+ζ72ζ8−ζ72ζ44−ζ76−ζ44+ζ76−ζ12+ζ28ζ12−ζ280000000022-22-2−1+52−1−52-2-2−1+52−1−5221−521+52−2i2i−2i2i−1+52−1−521−521+521−521−521+521+52−1+52−1−52ζ44+ζ76−ζ44−ζ76ζ44+ζ76−ζ44−ζ76ζ12+ζ28−ζ12−ζ28ζ12+ζ28−ζ12−ζ28000000ζ24−ζ56−ζ24+ζ56−ζ8+ζ72ζ8−ζ72ζ44−ζ76−ζ44+ζ76−ζ12+ζ28ζ12−ζ2800000000
χ3022-22-2−1+52−1−52-2-2−1+52−1−5221−521+52−2i2i−2i2i−1+52−1−521−521+521−521−521+521+52−1+52−1−52ζ44+ζ76−ζ44−ζ76ζ44+ζ76−ζ44−ζ76ζ12+ζ28−ζ12−ζ28ζ12+ζ28−ζ12−ζ28000000−ζ24+ζ56ζ24−ζ56ζ8−ζ72−ζ8+ζ72−ζ44+ζ76ζ44−ζ76ζ12−ζ28−ζ12+ζ280000000022-22-2−1+52−1−52-2-2−1+52−1−5221−521+52−2i2i−2i2i−1+52−1−521−521+521−521−521+521+52−1+52−1−52ζ44+ζ76−ζ44−ζ76ζ44+ζ76−ζ44−ζ76ζ12+ζ28−ζ12−ζ28ζ12+ζ28−ζ12−ζ28000000−ζ24+ζ56ζ24−ζ56ζ8−ζ72−ζ8+ζ72−ζ44+ζ76ζ44−ζ76ζ12−ζ28−ζ12+ζ2800000000
χ3122-22-2−1−52−1+52-2-2−1−52−1+5221+521−522i−2i2i−2i−1−52−1+521+521−521+521+521−521−52−1−52−1+52−ζ12−ζ28ζ12+ζ28−ζ12−ζ28ζ12+ζ28−ζ44−ζ76ζ44+ζ76−ζ44−ζ76ζ44+ζ76000000−ζ8+ζ72ζ8−ζ72−ζ24+ζ56ζ24−ζ56−ζ12+ζ28ζ12−ζ28−ζ44+ζ76ζ44−ζ760000000022-22-2−1−52−1+52-2-2−1−52−1+5221+521−522i−2i2i−2i−1−52−1+521+521−521+521+521−521−52−1−52−1+52−ζ12−ζ28ζ12+ζ28−ζ12−ζ28ζ12+ζ28−ζ44−ζ76ζ44+ζ76−ζ44−ζ76ζ44+ζ76000000−ζ8+ζ72ζ8−ζ72−ζ24+ζ56ζ24−ζ56−ζ12+ζ28ζ12−ζ28−ζ44+ζ76ζ44−ζ7600000000
χ3222-22-2−1−52−1+52-2-2−1−52−1+5221+521−522i−2i2i−2i−1−52−1+521+521−521+521+521−521−52−1−52−1+52−ζ12−ζ28ζ12+ζ28−ζ12−ζ28ζ12+ζ28−ζ44−ζ76ζ44+ζ76−ζ44−ζ76ζ44+ζ76000000ζ8−ζ72−ζ8+ζ72ζ24−ζ56−ζ24+ζ56ζ12−ζ28−ζ12+ζ28ζ44−ζ76−ζ44+ζ760000000022-22-2−1−52−1+52-2-2−1−52−1+5221+521−522i−2i2i−2i−1−52−1+521+521−521+521+521−521−52−1−52−1+52−ζ12−ζ28ζ12+ζ28−ζ12−ζ28ζ12+ζ28−ζ44−ζ76ζ44+ζ76−ζ44−ζ76ζ44+ζ76000000ζ8−ζ72−ζ8+ζ72ζ24−ζ56−ζ24+ζ56ζ12−ζ28−ζ12+ζ28ζ44−ζ76−ζ44+ζ7600000000
χ3322-22-2−1−52−1+52-2-2−1−52−1+5221+521−52−2i2i−2i2i−1−52−1+521+521−521+521+521−521−52−1−52−1+52ζ12+ζ28−ζ12−ζ28ζ12+ζ28−ζ12−ζ28ζ44+ζ76−ζ44−ζ76ζ44+ζ76−ζ44−ζ76000000−ζ8+ζ72ζ8−ζ72−ζ24+ζ56ζ24−ζ56ζ12−ζ28−ζ12+ζ28ζ44−ζ76−ζ44+ζ760000000022-22-2−1−52−1+52-2-2−1−52−1+5221+521−52−2i2i−2i2i−1−52−1+521+521−521+521+521−521−52−1−52−1+52ζ12+ζ28−ζ12−ζ28ζ12+ζ28−ζ12−ζ28ζ44+ζ76−ζ44−ζ76ζ44+ζ76−ζ44−ζ76000000−ζ8+ζ72ζ8−ζ72−ζ24+ζ56ζ24−ζ56ζ12−ζ28−ζ12+ζ28ζ44−ζ76−ζ44+ζ7600000000
χ3422-22-2−1−52−1+52-2-2−1−52−1+5221+521−52−2i2i−2i2i−1−52−1+521+521−521+521+521−521−52−1−52−1+52ζ12+ζ28−ζ12−ζ28ζ12+ζ28−ζ12−ζ28ζ44+ζ76−ζ44−ζ76ζ44+ζ76−ζ44−ζ76000000ζ8−ζ72−ζ8+ζ72ζ24−ζ56−ζ24+ζ56−ζ12+ζ28ζ12−ζ28−ζ44+ζ76ζ44−ζ760000000022-22-2−1−52−1+52-2-2−1−52−1+5221+521−52−2i2i−2i2i−1−52−1+521+521−521+521+521−521−52−1−52−1+52ζ12+ζ28−ζ12−ζ28ζ12+ζ28−ζ12−ζ28ζ44+ζ76−ζ44−ζ76ζ44+ζ76−ζ44−ζ76000000ζ8−ζ72−ζ8+ζ72ζ24−ζ56−ζ24+ζ56−ζ12+ζ28ζ12−ζ28−ζ44+ζ76ζ44−ζ7600000000
χ3522-2-222200220-2-22−2−22-2-2220000002−2−222−2−2222−2−200000000002-200−220022-2-222200220-2-22−2−22-2-2220000002−2−222−2−2222−2−200000000002-200−2200
χ3622-2-222200220-2-22−2−22-2-2220000002−2−222−2−22−2−2220000000000-22002−20022-2-222200220-2-22−2−22-2-2220000002−2−222−2−22−2−2220000000000-22002−200
χ3722-2-222200220-2-2−222−2-2-222000000−222−2−222−222−2−20000000000-2200−220022-2-222200220-2-2−222−2-2-222000000−222−2−222−222−2−20000000000-2200−2200
χ3822-2-222200220-2-2−222−2-2-222000000−222−2−222−2−2−22200000000002-2002−20022-2-222200220-2-2−222−2-2-222000000−222−2−222−2−2−22200000000002-2002−200
χ3944444−1+5−1−5-4-4−1+5−1−5-4−1+5−1−50000−1+5−1−5−1+5−1−51−51−51+51+51−51+500000000000000000000000000000044444−1+5−1−5-4-4−1+5−1−5-4−1+5−1−50000−1+5−1−5−1+5−1−51−51−51+51+51−51+5000000000000000000000000000000
χ4044444−1−5−1+5-4-4−1−5−1+5-4−1−5−1+50000−1−5−1+5−1−5−1+51+51+51−51−51+51−500000000000000000000000000000044444−1−5−1+5-4-4−1−5−1+5-4−1−5−1+50000−1−5−1+5−1−5−1+51+51+51−51−51+51−5000000000000000000000000000000
χ41444-4-4−1+5−1−500−1+5−1−50−1+5−1−52i22i2−2i2−2i21−51+51−51+5000000ζ14+ζ26+ζ46+ζ74ζ14+ζ26+ζ46+ζ74−ζ14−ζ26−ζ46−ζ74−ζ14−ζ26−ζ46−ζ74ζ42+ζ58+ζ62+ζ78ζ42+ζ58+ζ62+ζ78−ζ42−ζ58−ζ62−ζ78−ζ42−ζ58−ζ62−ζ780000000000000000000000444-4-4−1+5−1−500−1+5−1−50−1+5−1−52i22i2−2i2−2i21−51+51−51+5000000ζ14+ζ26+ζ46+ζ74ζ14+ζ26+ζ46+ζ74−ζ14−ζ26−ζ46−ζ74−ζ14−ζ26−ζ46−ζ74ζ42+ζ58+ζ62+ζ78ζ42+ζ58+ζ62+ζ78−ζ42−ζ58−ζ62−ζ78−ζ42−ζ58−ζ62−ζ780000000000000000000000
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χ1168-8000−2−25−2+25−42422+252−2500000000000−2ζ42−2ζ58+2ζ62+2ζ782ζ42+2ζ58−2ζ62−2ζ782ζ14−2ζ26+2ζ46−2ζ74−2ζ14+2ζ26−2ζ46+2ζ7400000000000000000000000000000000-880002+252−2542−42−2−25−2+25000000000002ζ42+2ζ58−2ζ62−2ζ78−2ζ42−2ζ58+2ζ62+2ζ78−2ζ14+2ζ26−2ζ46+2ζ742ζ14−2ζ26+2ζ46−2ζ7400000000000000000000000000000000

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