Finite Group Databasebeta

← Group #12089949

Character table — Group #12089949

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size111122222222222244444444444444444444488888888888888888888888888888816161616161616161616202020202020202032323232404040404040808080
order1222444455101010101010444882020202020202020404040404040404048888888202020202020202020204040404040404040404040404440404040404040402244888820202020444488248
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1
χ411111111111111111111111111111111111111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11
χ51111111111111111111-1-111111111-1-1-1-1-1-1-1-1111-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-111-1-1-1-1-1-111-1-1-11-1-111-111
χ61111111111111111111-1-111111111-1-1-1-1-1-1-1-1111-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-1-1-111111111-1-11-111-1-11-1-1
χ71111111111111111111-1-111111111-1-1-1-1-1-1-1-11-1-111-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1111111-1-11111-1-111-1111-1-1-11-1
χ81111111111111111111-1-111111111-1-1-1-1-1-1-1-11-1-111-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-111-1-1-1-1-1-1111-1-1-1111-11
χ91111111111111111-1-11111111111111111111-111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-111-1-1-1
χ101111111111111111-1-11111111111111111111-111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111
χ111111111111111111-1-11111111111111111111-1-1-1-1-11-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11
χ121111111111111111-1-11111111111111111111-1-1-1-1-11-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1
χ131111111111111111-1-11-1-111111111-1-1-1-1-1-1-1-1-111-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-111111-1-1-1-111-1-1-1-1-1-1-1-111-1111111-1-1
χ141111111111111111-1-11-1-111111111-1-1-1-1-1-1-1-1-111-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-111111-1-1-1-1-1-1111111-1-1111-1-1-1-1-1-111
χ151111111111111111-1-11-1-111111111-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1111111-1-1111111-1-1-11-1-1-1-11-11
χ161111111111111111-1-11-1-111111111-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-1-1-1-11111-1-111-1-1-1-111-1-11-11111-11-1
χ1722222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−5222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1+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+52−1−52−1−52−1−52−1−5222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5200000000−1+52−1−52−1+52−1−52000000000
χ1822222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−5222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−522-2-2-2-2222−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-2-21−521−521+521+521−521−521+521+52000000001−521+521−521+52000000000
χ1922222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52222-2-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−521−521−521−521−521+521+521+521+52222-2-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521−521−521−521+521+521+521+522-2−1+52−1+52−1−52−1−521−521−521+521+5200000000−1+52−1−521−521+52000000000
χ2022222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52222-2-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−521−521−521−521−521+521+521+521+522-2-222-2-2-2−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521−521−521−521+521+521+521+52-221−521−521+521+52−1+52−1+52−1−52−1−52000000001−521+52−1+52−1−52000000000
χ2122222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-2222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-222222-2-21−521−521+521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+52-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52000000001−521+521−521+52000000000
χ2222222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-2222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-2-2-2-2-22-2-21−521−521+521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+52221−521−521+521+521−521−521+521+5200000000−1+52−1−52−1+52−1−52000000000
χ2322222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-22-2-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−521−521−521−521−521+521+521+521+52-222-2-2-2221−521−521+521+52−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-22−1+52−1+52−1−52−1−521−521−521+521+52000000001−521+52−1+52−1−52000000000
χ2422222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-22-2-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−521−521−521−521−521+521+521+521+52-2-2-222-2221−521−521+521+52−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−522-21−521−521+521+52−1+52−1+52−1−52−1−5200000000−1+52−1−521−521+52000000000
χ2522222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+5222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1−52−1−52−1+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+5222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5200000000−1−52−1+52−1−52−1+52000000000
χ2622222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+5222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+522-2-2-2-2222−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52-2-21+521+521−521−521+521+521−521−52000000001+521−521+521−52000000000
χ2722222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52222-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+521+521+521+521+521−521−521−521−52222-2-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521+521+521−521−521−521−522-2−1−52−1−52−1+52−1+521+521+521−521−5200000000−1−52−1+521+521−52000000000
χ2822222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52222-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+521+521+521+521+521−521−521−521−522-2-222-2-2-2−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521+521+521−521−521−521−52-221+521+521−521−52−1−52−1−52−1+52−1+52000000001+521−52−1−52−1+52000000000
χ2922222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-2222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52-222222-2-21+521+521−521−52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−52-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52000000001+521−521+521−52000000000
χ3022222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-2222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52-2-2-2-2-22-2-21+521+521−521−52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−52221+521+521−521−521+521+521−521−5200000000−1−52−1+52−1−52−1+52000000000
χ3122222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-22-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+521+521+521+521+521−521−521−521−52-222-2-2-2221+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+52-22−1−52−1−52−1+52−1+521+521+521−521−52000000001+521−52−1−52−1+52000000000
χ3222222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-22-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+521+521+521+521+521−521−521−521−52-2-2-222-2221+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+522-21+521+521−521−52−1−52−1−52−1+52−1+5200000000−1−52−1+521+521−52000000000
χ3322222-2-222222222200-222-2-22222-2-22222222200000-2000000-2-20000-2-2-2-2000000000000000000222200000000-2-20000000
χ3422222-2-222222222200-222-2-22222-2-22222222200000-2000000-2-20000-2-2-2-2000000000000000000-2-2-2-200000000220000000
χ3522222-2-222222222200-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2000002000000-2-20000222200000000000000000022-2-2000000002-20000000
χ3622222-2-222222222200-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2000002000000-2-200002222000000000000000000-2-22200000000-220000000
χ372222-222-22222222222-20022-2-2-2-22200000000-20000000-2-2-2-2-2-222220000000000000000000000000022-2-20000002-200000
χ382222-222-22222222222-20022-2-2-2-22200000000-20000000-2-2-2-2-2-2222200000000000000000000000000-2-222000000-2200000
χ392222-222-222222222-2-2-20022-2-2-2-22200000000200000002222-2-2-2-2-2-20000000000000000000000000022-2-2000000-2200000
χ402222-222-222222222-2-2-20022-2-2-2-22200000000200000002222-2-2-2-2-2-200000000000000000000000000-2-2220000002-200000
χ4122-2-2-200222-2-222-2-20002i−2i00-2-222002i2i−2i−2i2i2i−2i−2i0i2−i22−2000000000000000000000000000i2−i2i2−i22−22−22-22i−2i2−22−200000000i2−i2000
χ4222-2-2-200222-2-222-2-20002i−2i00-2-222002i2i−2i−2i2i2i−2i−2i0i2−i22−2000000000000000000000000000i2−i2i2−i22−22−2-22−2i2i−22−2200000000−i2i2000
χ4322-2-2-200222-2-222-2-20002i−2i00-2-222002i2i−2i−2i2i2i−2i−2i0−i2i2−22000000000000000000000000000−i2i2−i2i2−22−222-22i−2i−22−2200000000−i2i2000
χ4422-2-2-200222-2-222-2-20002i−2i00-2-222002i2i−2i−2i2i2i−2i−2i0−i2i2−22000000000000000000000000000−i2i2−i2i2−22−22-22−2i2i2−22−200000000i2−i2000
χ4522-2-2-200222-2-222-2-2000−2i2i00-2-22200−2i−2i2i2i−2i−2i2i2i0i2−i2−22000000000000000000000000000i2−i2i2−i2−22−222-2−2i2i−22−2200000000i2−i2000
χ4622-2-2-200222-2-222-2-2000−2i2i00-2-22200−2i−2i2i2i−2i−2i2i2i0i2−i2−22000000000000000000000000000i2−i2i2−i2−22−22-222i−2i2−22−200000000−i2i2000
χ4722-2-2-200222-2-222-2-2000−2i2i00-2-22200−2i−2i2i2i−2i−2i2i2i0−i2i22−2000000000000000000000000000−i2i2−i2i22−22−22-2−2i2i2−22−200000000−i2i2000
χ4822-2-2-200222-2-222-2-2000−2i2i00-2-22200−2i−2i2i2i−2i−2i2i2i0−i2i22−2000000000000000000000000000−i2i2−i2i22−22−2-222i−2i−22−2200000000i2−i2000
χ4944444-4-44−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−500-4441−51+5−1+5−1−5−1+5−1−51−51+5−1+5−1+5−1+5−1+5−1−5−1−5−1−5−1−500000-40000001−51+500001−51−51+51+5000000000000000000000000000000000000000
χ5044444-4-44−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−500-4-4-41−51+5−1+5−1−5−1+5−1−51−51+51−51−51−51−51+51+51+51+50000040000001−51+50000−1+5−1+5−1−5−1−5000000000000000000000000000000000000000
χ5144444-4-44−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+500-4441+51−5−1−5−1+5−1−5−1+51+51−5−1−5−1−5−1−5−1−5−1+5−1+5−1+5−1+500000-40000001+51−500001+51+51−51−5000000000000000000000000000000000000000
χ5244444-4-44−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+500-4-4-41+51−5−1−5−1+5−1−5−1+51+51−51+51+51+51+51−51−51−51−50000040000001+51−50000−1−5−1−5−1+5−1+5000000000000000000000000000000000000000
χ534444-444-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−544-400−1+5−1−51−51+51−51+5−1+5−1−500000000-400000001−51−51+51+51−51+5−1+5−1+5−1−5−1−50000000000000000000000000000000000000000000
χ544444-444-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−5-4-4-400−1+5−1−51−51+51−51+5−1+5−1−50000000040000000−1+5−1+5−1−5−1−51−51+51−51−51+51+50000000000000000000000000000000000000000000
χ554444-444-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+544-400−1−5−1+51+51−51+51−5−1−5−1+500000000-400000001+51+51−51−51+51−5−1−5−1−5−1+5−1+50000000000000000000000000000000000000000000
χ564444-444-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+5-4-4-400−1−5−1+51+51−51+51−5−1−5−1+50000000040000000−1−5−1−5−1+5−1+51+51−51+51+51−51−50000000000000000000000000000000000000000000
χ574444-4-4-4-44444444400400-4-4-4-4-4-4-4-4000000000000000000004400000000000000000000000000000000000000000000000
χ584444-4-4-4-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−5004001−51+51−51+51−51+51−51+500000000000000000000−1+5−1−500000000−2ζ22+2ζ38−2ζ22+2ζ382ζ22−2ζ382ζ22−2ζ382ζ6−2ζ142ζ6−2ζ14−2ζ6+2ζ14−2ζ6+2ζ140000000000000000000000000000000
χ594444-4-4-4-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−5004001−51+51−51+51−51+51−51+500000000000000000000−1+5−1−5000000002ζ22−2ζ382ζ22−2ζ38−2ζ22+2ζ38−2ζ22+2ζ38−2ζ6+2ζ14−2ζ6+2ζ142ζ6−2ζ142ζ6−2ζ140000000000000000000000000000000
χ604444-4-4-4-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+5004001+51−51+51−51+51−51+51−500000000000000000000−1−5−1+5000000002ζ6−2ζ142ζ6−2ζ14−2ζ6+2ζ14−2ζ6+2ζ142ζ22−2ζ382ζ22−2ζ38−2ζ22+2ζ38−2ζ22+2ζ380000000000000000000000000000000
χ614444-4-4-4-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+5004001+51−51+51−51+51−51+51−500000000000000000000−1−5−1+500000000−2ζ6+2ζ14−2ζ6+2ζ142ζ6−2ζ142ζ6−2ζ14−2ζ22+2ζ38−2ζ22+2ζ382ζ22−2ζ382ζ22−2ζ380000000000000000000000000000000
χ6244-4-4400-444-4-444-4-4000000044-4-400000000000000000000000000000000000000000000000000000022−22−22220000000000000
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Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.