Finite Group Databasebeta

← Group #12019139

Character table — Group #12019139

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11112222222222222222224444444444444444444444888888888888888888888888161616161616161616161616161616161616161620202020202020204040404080808080
order1244222444558888101020202020881010101010102020202020204040404040404040161616164040404080808080808080808080808080808080248810101010202020204040404040404040161616161616161644884444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1
χ611111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ711111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-111
χ811111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1
χ9222222222222-2-2-2-2222222-2-2222222222222-2-2-2-2-2-2-2-20000-2-2-2-20000000000000000000000000000000000000000000022-2-20000
χ10222222222222-2-2-2-2222222-2-2222222222222-2-2-2-2-2-2-2-20000-2-2-2-200000000000000000000000000000000000000000000-2-2220000
χ112222222222−1+52−1−522222−1+52−1−52−1+52−1+52−1−52−1−5222−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1−52−1+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+52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−522222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−520000000000000000
χ122222222222−1+52−1−522222−1+52−1−52−1+52−1+52−1−52−1−5222−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1−52−1+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+52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52-2-2-2-21−521−521+521+521−521−521+521+521−521−521−521−521+521+521+521+520000000000000000
χ132222222222−1+52−1−522222−1+52−1−52−1+52−1+52−1−52−1−5222−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-2-2-2−1+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+520000000000000000
χ142222222222−1+52−1−522222−1+52−1−52−1+52−1+52−1−52−1−5222−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-2-2-2−1+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+52−1−52−1−52−1−52−1−520000000000000000
χ152222222222−1−52−1+522222−1−52−1+52−1−52−1−52−1+52−1+5222−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1+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+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+520000000000000000
χ162222222222−1−52−1+522222−1−52−1+52−1−52−1−52−1+52−1+5222−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1+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+52−1+52−1+52−1+52−1+52-2-2-2-21+521+521−521−521+521+521−521−521+521+521+521+521−521−521−521−520000000000000000
χ172222222222−1−52−1+522222−1−52−1+52−1−52−1−52−1+52−1+5222−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-2-2-2−1−52−1−52−1+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+521−521−521−521−520000000000000000
χ182222222222−1−52−1+522222−1−52−1+52−1−52−1−52−1+52−1+5222−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-2-2-2−1−52−1−52−1+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+520000000000000000
χ1922222-2-2-22-2222222222222-2-22-2-22-2-2-2-222-2-2222222220000-2-2-2-20000000000000000000000000000000000000000000000002i−2i00
χ2022222-2-2-22-2222222222222-2-22-2-22-2-2-2-222-2-2222222220000-2-2-2-2000000000000000000000000000000000000000000000000−2i2i00
χ2122222-2-2-22-222-2-2-2-2222222222-2-22-2-2-2-222-2-2-2-2-2-2-2-2-2-2000022220000000000000000002i−2i000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ2222222-2-2-22-222-2-2-2-2222222222-2-22-2-2-2-222-2-2-2-2-2-2-2-2-2-200002222000000000000000000−2i2i00000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ2322222-2-2-22-2−1+52−1−52-2-2-2-2−1+52−1−52−1+52−1+52−1−52−1−5222−1+521−521−52−1−521+521+521−521+52−1+52−1−521−521+521−521−521+521+521−521−521+521+520000−1+52−1+52−1−52−1−52−ζ44+ζ76−ζ44+ζ76−ζ44+ζ76−ζ44+ζ76ζ44−ζ76ζ44−ζ76ζ44−ζ76ζ44−ζ76ζ12−ζ28ζ12−ζ28ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ28−ζ12+ζ28−ζ12+ζ28002i−2iζ24−ζ56−ζ24+ζ56−ζ8+ζ72ζ8−ζ72ζ24−ζ56−ζ24+ζ56−ζ8+ζ72ζ8−ζ72−ζ44−ζ76−ζ44−ζ76ζ44+ζ76ζ44+ζ76−ζ12−ζ28−ζ12−ζ28ζ12+ζ28ζ12+ζ280000000000000000
χ2422222-2-2-22-2−1+52−1−52-2-2-2-2−1+52−1−52−1+52−1+52−1−52−1−5222−1+521−521−52−1−521+521+521−521+52−1+52−1−521−521+521−521−521+521+521−521−521+521+520000−1+52−1+52−1−52−1−52−ζ44+ζ76−ζ44+ζ76−ζ44+ζ76−ζ44+ζ76ζ44−ζ76ζ44−ζ76ζ44−ζ76ζ44−ζ76ζ12−ζ28ζ12−ζ28ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ28−ζ12+ζ28−ζ12+ζ2800−2i2i−ζ24+ζ56ζ24−ζ56ζ8−ζ72−ζ8+ζ72−ζ24+ζ56ζ24−ζ56ζ8−ζ72−ζ8+ζ72ζ44+ζ76ζ44+ζ76−ζ44−ζ76−ζ44−ζ76ζ12+ζ28ζ12+ζ28−ζ12−ζ28−ζ12−ζ280000000000000000
χ2522222-2-2-22-2−1+52−1−52-2-2-2-2−1+52−1−52−1+52−1+52−1−52−1−5222−1+521−521−52−1−521+521+521−521+52−1+52−1−521−521+521−521−521+521+521−521−521+521+520000−1+52−1+52−1−52−1−52ζ44−ζ76ζ44−ζ76ζ44−ζ76ζ44−ζ76−ζ44+ζ76−ζ44+ζ76−ζ44+ζ76−ζ44+ζ76−ζ12+ζ28−ζ12+ζ28−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ28ζ12−ζ28ζ12−ζ28002i−2i−ζ24+ζ56ζ24−ζ56ζ8−ζ72−ζ8+ζ72−ζ24+ζ56ζ24−ζ56ζ8−ζ72−ζ8+ζ72−ζ44−ζ76−ζ44−ζ76ζ44+ζ76ζ44+ζ76−ζ12−ζ28−ζ12−ζ28ζ12+ζ28ζ12+ζ280000000000000000
χ2622222-2-2-22-2−1+52−1−52-2-2-2-2−1+52−1−52−1+52−1+52−1−52−1−5222−1+521−521−52−1−521+521+521−521+52−1+52−1−521−521+521−521−521+521+521−521−521+521+520000−1+52−1+52−1−52−1−52ζ44−ζ76ζ44−ζ76ζ44−ζ76ζ44−ζ76−ζ44+ζ76−ζ44+ζ76−ζ44+ζ76−ζ44+ζ76−ζ12+ζ28−ζ12+ζ28−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ28ζ12−ζ28ζ12−ζ2800−2i2iζ24−ζ56−ζ24+ζ56−ζ8+ζ72ζ8−ζ72ζ24−ζ56−ζ24+ζ56−ζ8+ζ72ζ8−ζ72ζ44+ζ76ζ44+ζ76−ζ44−ζ76−ζ44−ζ76ζ12+ζ28ζ12+ζ28−ζ12−ζ28−ζ12−ζ280000000000000000
χ2722222-2-2-22-2−1−52−1+52-2-2-2-2−1−52−1+52−1−52−1−52−1+52−1+5222−1−521+521+52−1+521−521−521+521−52−1−52−1+521+521−521+521+521−521−521+521+521−521−520000−1−52−1−52−1+52−1+52ζ12−ζ28ζ12−ζ28ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ28−ζ12+ζ28−ζ12+ζ28ζ44−ζ76ζ44−ζ76ζ44−ζ76ζ44−ζ76−ζ44+ζ76−ζ44+ζ76−ζ44+ζ76−ζ44+ζ76002i−2iζ8−ζ72−ζ8+ζ72ζ24−ζ56−ζ24+ζ56ζ8−ζ72−ζ8+ζ72ζ24−ζ56−ζ24+ζ56−ζ12−ζ28−ζ12−ζ28ζ12+ζ28ζ12+ζ28−ζ44−ζ76−ζ44−ζ76ζ44+ζ76ζ44+ζ760000000000000000
χ2822222-2-2-22-2−1−52−1+52-2-2-2-2−1−52−1+52−1−52−1−52−1+52−1+5222−1−521+521+52−1+521−521−521+521−52−1−52−1+521+521−521+521+521−521−521+521+521−521−520000−1−52−1−52−1+52−1+52ζ12−ζ28ζ12−ζ28ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ28−ζ12+ζ28−ζ12+ζ28ζ44−ζ76ζ44−ζ76ζ44−ζ76ζ44−ζ76−ζ44+ζ76−ζ44+ζ76−ζ44+ζ76−ζ44+ζ7600−2i2i−ζ8+ζ72ζ8−ζ72−ζ24+ζ56ζ24−ζ56−ζ8+ζ72ζ8−ζ72−ζ24+ζ56ζ24−ζ56ζ12+ζ28ζ12+ζ28−ζ12−ζ28−ζ12−ζ28ζ44+ζ76ζ44+ζ76−ζ44−ζ76−ζ44−ζ760000000000000000
χ2922222-2-2-22-2−1−52−1+52-2-2-2-2−1−52−1+52−1−52−1−52−1+52−1+5222−1−521+521+52−1+521−521−521+521−52−1−52−1+521+521−521+521+521−521−521+521+521−521−520000−1−52−1−52−1+52−1+52−ζ12+ζ28−ζ12+ζ28−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ28ζ12−ζ28ζ12−ζ28−ζ44+ζ76−ζ44+ζ76−ζ44+ζ76−ζ44+ζ76ζ44−ζ76ζ44−ζ76ζ44−ζ76ζ44−ζ76002i−2i−ζ8+ζ72ζ8−ζ72−ζ24+ζ56ζ24−ζ56−ζ8+ζ72ζ8−ζ72−ζ24+ζ56ζ24−ζ56−ζ12−ζ28−ζ12−ζ28ζ12+ζ28ζ12+ζ28−ζ44−ζ76−ζ44−ζ76ζ44+ζ76ζ44+ζ760000000000000000
χ3022222-2-2-22-2−1−52−1+52-2-2-2-2−1−52−1+52−1−52−1−52−1+52−1+5222−1−521+521+52−1+521−521−521+521−52−1−52−1+521+521−521+521+521−521−521+521+521−521−520000−1−52−1−52−1+52−1+52−ζ12+ζ28−ζ12+ζ28−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ28ζ12−ζ28ζ12−ζ28−ζ44+ζ76−ζ44+ζ76−ζ44+ζ76−ζ44+ζ76ζ44−ζ76ζ44−ζ76ζ44−ζ76ζ44−ζ7600−2i2iζ8−ζ72−ζ8+ζ72ζ24−ζ56−ζ24+ζ56ζ8−ζ72−ζ8+ζ72ζ24−ζ56−ζ24+ζ56ζ12+ζ28ζ12+ζ28−ζ12−ζ28−ζ12−ζ28ζ44+ζ76ζ44+ζ76−ζ44−ζ76−ζ44−ζ760000000000000000
χ312222-22-22-2-222000022222200-22-2-22-222-2-2-2-200000000i2i2−i2−i20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000000000000000002222−2−2−2−22i−2i000000
χ322222-22-22-2-222000022222200-22-2-22-222-2-2-2-200000000i2i2−i2−i20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200000000000000000000−2−2−2−22222−2i2i000000
χ332222-22-22-2-222000022222200-22-2-22-222-2-2-2-200000000−i2−i2i2i20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000000000000000002222−2−2−2−2−2i2i000000
χ342222-22-22-2-222000022222200-22-2-22-222-2-2-2-200000000−i2−i2i2i20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200000000000000000000−2−2−2−222222i−2i000000
χ3522-2-22-2-22-2222000022-2-2-2-2002-2-22-2-222-2-222000000002−22−200002−22−22−22−22−22−22−22−200000000000000000000i2i2−i2−i2i2i2−i2−i2002i−2i0000
χ3622-2-22-2-22-2222000022-2-2-2-2002-2-22-2-222-2-222000000002−22−200002−22−22−22−22−22−22−22−200000000000000000000−i2−i2i2i2−i2−i2i2i200−2i2i0000
χ3722-2-22-2-22-2222000022-2-2-2-2002-2-22-2-222-2-22200000000−22−220000−22−22−22−22−22−22−22−2200000000000000000000i2i2−i2−i2i2i2−i2−i200−2i2i0000
χ3822-2-22-2-22-2222000022-2-2-2-2002-2-22-2-222-2-22200000000−22−220000−22−22−22−22−22−22−22−2200000000000000000000−i2−i2i2i2−i2−i2i2i2002i−2i0000
χ3922-2-2-22-2-2222222-2-222-2-2-2-22-2-22-2-22-2-2-222222222-2-2-2-200002-22-2000000000000000000000000000000000000000000000000002i−2i
χ4022-2-2-22-2-2222222-2-222-2-2-2-22-2-22-2-22-2-2-222222222-2-2-2-200002-22-200000000000000000000000000000000000000000000000000−2i2i
χ4122-2-2-22-2-22222-2-22222-2-2-2-2-22-22-2-22-2-2-22222-2-2-2-222220000-22-2200000000000000002-2002222-2-2-2-2000000000000000000000000
χ4222-2-2-22-2-22222-2-22222-2-2-2-2-22-22-2-22-2-2-22222-2-2-2-222220000-22-220000000000000000-2200-2-2-2-22222000000000000000000000000
χ4322-2-2-22-2-222−1+52−1−52-2-222−1+52−1−521−521−521+521+52-221−52−1+521−521+52−1−521+521−521+52−1+52−1−52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−5200001−52−1+521+52−1−52ζ24−ζ56−ζ24+ζ56−ζ24+ζ56ζ24−ζ56−ζ24+ζ56ζ24−ζ56ζ24−ζ56−ζ24+ζ56ζ8−ζ72−ζ8+ζ72−ζ8+ζ72ζ8−ζ72−ζ8+ζ72ζ8−ζ72ζ8−ζ72−ζ8+ζ722-200−1+52−1+52−1−52−1−521−521−521+521+52ζ24−ζ56−ζ24+ζ56ζ24−ζ56−ζ24+ζ56−ζ8+ζ72ζ8−ζ72−ζ8+ζ72ζ8−ζ720000000000000000
χ4422-2-2-22-2-222−1+52−1−52-2-222−1+52−1−521−521−521+521+52-221−52−1+521−521+52−1−521+521−521+52−1+52−1−52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−5200001−52−1+521+52−1−52ζ24−ζ56−ζ24+ζ56−ζ24+ζ56ζ24−ζ56−ζ24+ζ56ζ24−ζ56ζ24−ζ56−ζ24+ζ56ζ8−ζ72−ζ8+ζ72−ζ8+ζ72ζ8−ζ72−ζ8+ζ72ζ8−ζ72ζ8−ζ72−ζ8+ζ72-22001−521−521+521+52−1+52−1+52−1−52−1−52−ζ24+ζ56ζ24−ζ56−ζ24+ζ56ζ24−ζ56ζ8−ζ72−ζ8+ζ72ζ8−ζ72−ζ8+ζ720000000000000000
χ4522-2-2-22-2-222−1+52−1−52-2-222−1+52−1−521−521−521+521+52-221−52−1+521−521+52−1−521+521−521+52−1+52−1−52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−5200001−52−1+521+52−1−52−ζ24+ζ56ζ24−ζ56ζ24−ζ56−ζ24+ζ56ζ24−ζ56−ζ24+ζ56−ζ24+ζ56ζ24−ζ56−ζ8+ζ72ζ8−ζ72ζ8−ζ72−ζ8+ζ72ζ8−ζ72−ζ8+ζ72−ζ8+ζ72ζ8−ζ722-200−1+52−1+52−1−52−1−521−521−521+521+52−ζ24+ζ56ζ24−ζ56−ζ24+ζ56ζ24−ζ56ζ8−ζ72−ζ8+ζ72ζ8−ζ72−ζ8+ζ720000000000000000
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χ1048-8−8i8i000000−2−25−2+25−4i24i242−422+252−254ζ12+4ζ28−4ζ12−4ζ284ζ44+4ζ76−4ζ44−4ζ7600000000000000−2ζ42−2ζ58−2ζ62−2ζ782ζ42+2ζ58+2ζ62+2ζ78−2ζ14−2ζ26−2ζ46−2ζ742ζ14+2ζ26+2ζ46+2ζ742ζ42+2ζ58−2ζ62−2ζ78−2ζ42−2ζ58+2ζ62+2ζ78−2ζ14+2ζ26−2ζ46+2ζ742ζ14−2ζ26+2ζ46−2ζ74000000000000000000000000000000000000000000000000000000000000

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