Finite Group Databasebeta

← Group #12090453

Character table — Group #12090453

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size1111222222222222444444444444444444444448888888888888888888888888881616161616161616161616202020202020323232324040404040404040408080
order1222444455101010101010444888820202020202020204040404040404040288881010101020202020202040404040404040404040404024840404040404040404444881010202022448888824
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11-1-1-111111-1-1
χ4111111111111111111111111111111111111111111-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1111-1-1-1-1-111
χ51111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-111111111-1-11-1-111-1-1-1-11-1
χ61111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-111-1-11111-11
χ71111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-111-1-111111-11-1-1-1-1-11
χ81111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-111-1-1-11-111111-1
χ91111111111111111-1-1111111111111111111111-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-111
χ101111111111111111-1-1111111111111111111111-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111111-1-11111-1-1-1-1-11111-1-111-1-1
χ111111111111111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11111-1-111111111-111-1-1-1-1
χ121111111111111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11-1-11111
χ131111111111111111-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111111111-11-11111-1-1-1-111-1-1-1-1-1-111111-1-1-1-1111-1
χ141111111111111111-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111111111-11-11111-1-1-1-1-1-11111-1-111-1-1-11111-1-1-11
χ151111111111111111-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111-11-1-1-1-111111111-1-111-1-11-1-11-1-1-111-11
χ161111111111111111-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111-11-1-1-1-11111-1-1-1-11111-1-1-111-1111-1-11-1
χ1722222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−522222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+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+52−1+52−1+52−1−52−1−52−1−52−1−52222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52000000−1+52−1−52−1+52−1−5200000000000
χ1822222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−522222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+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+52−1−52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-2-2-21−521−521+521+521−521−521+521+520000001−521+521−521+5200000000000
χ1922222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52222-2-2-2-2−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−521−521−521−521−521+521+521+521+522-2-222−1+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+522-2-2−1+52−1+52−1−52−1−521−521−521+521+52000000−1+52−1−521−521+5200000000000
χ2022222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52222-2-2-2-2−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−521−521−521−521−521+521+521+521+522-2-2-2-2−1+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+52-2221−521−521+521+52−1+52−1+52−1−52−1−520000001−521+52−1+52−1−5200000000000
χ2122222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-2-2-2221−521−521+521+521−521−521+521+52−1+52−1−52−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+52-2-22−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−520000001−521+521−521+5200000000000
χ2222222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-2-2-2-2-21−521−521+521+521−521−521+521+52−1+52−1−52−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+5222-21−521−521+521+521−521−521+521+52000000−1+52−1−52−1+52−1−5200000000000
χ2322222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-22-2-2-2-2−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−521−521−521−521−521+521+521+521+52-222221−521−521+521+521−521−521+521+52−1+52−1−521−521−521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-22-2−1+52−1+52−1−52−1−521−521−521+521+520000001−521+52−1+52−1−5200000000000
χ2422222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-22-2-2-2-2−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−521−521−521−521−521+521+521+521+52-222-2-21−521−521+521+521−521−521+521+52−1+52−1−521−521−521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−522-221−521−521+521+52−1+52−1+52−1−52−1−52000000−1+52−1−521−521+5200000000000
χ2522222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+522222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1−52−1−52−1+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+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52000000−1−52−1+52−1−52−1+5200000000000
χ2622222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+522222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52222-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52-2-2-21+521+521−521−521+521+521−521−520000001+521−521+521−5200000000000
χ2722222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52222-2-2-2-2−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+521+521+521+521+521−521−521−521−522-2-222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1+521+521+521−521−521+521+521+521+521−521−521−521−522-2-2−1−52−1−52−1+52−1+521+521+521−521−52000000−1−52−1+521+521−5200000000000
χ2822222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52222-2-2-2-2−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+521+521+521+521+521−521−521−521−522-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1+521+521+521−521−521+521+521+521+521−521−521−521−52-2221+521+521−521−52−1−52−1−52−1+52−1+520000001+521−52−1−52−1+5200000000000
χ2922222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52-2-2-2221+521+521−521−521+521+521−521−52−1−52−1+52−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−52-2-22−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+520000001+521−521+521−5200000000000
χ3022222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52-2-2-2-2-21+521+521−521−521+521+521−521−52−1−52−1+52−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−5222-21+521+521−521−521+521+521−521−52000000−1−52−1+52−1−52−1+5200000000000
χ3122222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-22-2-2-2-2−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+521+521+521+521+521−521−521−521−52-222221+521+521−521−521+521+521−521−52−1−52−1+521+521+521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52-22-2−1−52−1−52−1+52−1+521+521+521−521−520000001+521−52−1−52−1+5200000000000
χ3222222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-22-2-2-2-2−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+521+521+521+521+521−521−521−521−52-222-2-21+521+521−521−521+521+521−521−52−1−52−1+521+521+521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+522-221+521+521−521−52−1−52−1−52−1+52−1+52000000−1−52−1+521+521−5200000000000
χ3322222-2-222222222200-222-2-222-2-2-2-222222222220000000000000-2-2-2-2-2-20000000000000000000002200000002-2-20000000
χ3422222-2-222222222200-222-2-222-2-2-2-222222222220000000000000-2-2-2-2-2-2000000000000000000000-2-20000000-2220000000
χ3522222-2-222222222200-2-2-22222-2-2-2-222-2-2-2-2-2-2-2-20000000000000-2-22222000000000000000000000220000000-22-20000000
χ3622222-2-222222222200-2-2-22222-2-2-2-222-2-2-2-2-2-2-2-20000000000000-2-22222000000000000000000000-2-200000002-220000000
χ372222-222-22222222222-20000-2-22222-2-200000000-20000-2-2-2-22222-2-2000000000000000000000002200220000-2000-2000000
χ382222-222-22222222222-20000-2-22222-2-200000000-20000-2-2-2-22222-2-200000000000000000000000-2-200-2-2000020002000000
χ392222-222-222222222-2-2-20000-2-22222-2-200000000200002222-2-2-2-2-2-2000000000000000000000002200-2-20000-20002000000
χ402222-222-222222222-2-2-20000-2-22222-2-200000000200002222-2-2-2-2-2-200000000000000000000000-2-2002200002000-2000000
χ4122-2-202-202222-2-2-2-22i−2i0i2−i2i2−i2002-22-200i2i2−i2−i2i2i2−i2−i202−20000002i−2i2i−2i00i2−i2i2−i222−2−222−2−2000000000002i−2i002-20000000002−2i2−i200
χ4222-2-202-202222-2-2-2-22i−2i0i2−i2i2−i2002-22-200i2i2−i2−i2i2i2−i2−i202−20000002i−2i2i−2i00i2−i2i2−i222−2−222−2−200000000000−2i2i00-22000000000−22−i2i200
χ4322-2-202-202222-2-2-2-22i−2i0−i2i2−i2i2002-22-200−i2−i2i2i2−i2−i2i2i20−220000002i−2i2i−2i00−i2i2−i2i2−2−222−2−222000000000002i−2i002-2000000000−22−i2i200
χ4422-2-202-202222-2-2-2-22i−2i0−i2i2−i2i2002-22-200−i2−i2i2i2−i2−i2i2i20−220000002i−2i2i−2i00−i2i2−i2i2−2−222−2−22200000000000−2i2i00-220000000002−2i2−i200
χ4522-2-202-202222-2-2-2-2−2i2i0i2−i2i2−i2002-22-200i2i2−i2−i2i2i2−i2−i20−22000000−2i2i−2i2i00i2−i2i2−i2−2−222−2−222000000000002i−2i00-220000000002−2−i2i200
χ4622-2-202-202222-2-2-2-2−2i2i0i2−i2i2−i2002-22-200i2i2−i2−i2i2i2−i2−i20−22000000−2i2i−2i2i00i2−i2i2−i2−2−222−2−22200000000000−2i2i002-2000000000−22i2−i200
χ4722-2-202-202222-2-2-2-2−2i2i0−i2i2−i2i2002-22-200−i2−i2i2i2−i2−i2i2i202−2000000−2i2i−2i2i00−i2i2−i2i222−2−222−2−2000000000002i−2i00-22000000000−22i2−i200
χ4822-2-202-202222-2-2-2-2−2i2i0−i2i2−i2i2002-22-200−i2−i2i2i2−i2−i2i2i202−2000000−2i2i−2i2i00−i2i2−i2i222−2−222−2−200000000000−2i2i002-20000000002−2−i2i200
χ4944444-4-44−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−500-444-4-4−1+5−1−51−51−51+51+5−1+5−1−5−1+5−1+5−1+5−1+5−1−5−1−5−1−5−1−500000000000001−51+51−51−51+51+50000000000000000000000000000000000000000
χ5044444-4-44−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−500-4-4-444−1+5−1−51−51−51+51+5−1+5−1−51−51−51−51−51+51+51+51+500000000000001−51+5−1+5−1+5−1−5−1−50000000000000000000000000000000000000000
χ5144444-4-44−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+500-444-4-4−1−5−1+51+51+51−51−5−1−5−1+5−1−5−1−5−1−5−1−5−1+5−1+5−1+5−1+500000000000001+51−51+51+51−51−50000000000000000000000000000000000000000
χ5244444-4-44−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+500-4-4-444−1−5−1+51+51+51−51−5−1−5−1+51+51+51+51+51−51−51−51−500000000000001+51−5−1−5−1−5−1+5−1+50000000000000000000000000000000000000000
χ534444-444-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−544-400001−51+5−1+5−1+5−1−5−1−51−51+500000000-400001−51−51+51+5−1+5−1+5−1−5−1−51−51+500000000000000000000000000000000000000000000
χ544444-444-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−5-4-4-400001−51+5−1+5−1+5−1−5−1−51−51+50000000040000−1+5−1+5−1−5−1−51−51−51+51+51−51+500000000000000000000000000000000000000000000
χ554444-444-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+544-400001+51−5−1−5−1−5−1+5−1+51+51−500000000-400001+51+51−51−5−1−5−1−5−1+5−1+51+51−500000000000000000000000000000000000000000000
χ564444-444-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+5-4-4-400001+51−5−1−5−1−5−1+5−1+51+51−50000000040000−1−5−1−5−1+5−1+51+51+51−51−51+51−500000000000000000000000000000000000000000000
χ574444-4-4-4-4444444440040000-4-4-4-4-4-4-4-40000000000000000000004400000000000000000000000000000000000000000000
χ584444-4-4-4-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−500400001−51+51−51−51+51+51−51+5000000000000000000000−1+5−1−50000−2ζ22+2ζ382ζ22−2ζ38−2ζ22+2ζ382ζ22−2ζ382ζ6−2ζ14−2ζ6+2ζ142ζ6−2ζ14−2ζ6+2ζ1400000000000000000000000000000000
χ594444-4-4-4-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−500400001−51+51−51−51+51+51−51+5000000000000000000000−1+5−1−500002ζ22−2ζ38−2ζ22+2ζ382ζ22−2ζ38−2ζ22+2ζ38−2ζ6+2ζ142ζ6−2ζ14−2ζ6+2ζ142ζ6−2ζ1400000000000000000000000000000000
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χ978-8-88800-8−2+25−2−252−252+25−2+25−2−252−252+2500000002−252+250000−2+25−2−250000000000000000000000000000000000000000000000000000000000000000000
χ988-8-88800-8−2−25−2+252+252−25−2−25−2+252+252−2500000002+252−250000−2−25−2+250000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.