Finite Group Databasebeta

← Group #12159370

Character table — Group #12159370

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size1111111122222222222222222222444444444444448888888888888888888888888888888881010101016161616161616161616161616161616162020202020202020202020204040404040404080
order1222222244445510101010101010101010101010104488882020202020202020444444488202020202020202040404040404040404040404040404040444442020202020202020202020202020202022224444888822444884
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111-1-1-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11-1-111-1
χ41111111111111111111111111111111111111111111-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-111-1-11
χ5111111111111111111111111111111-1-1-1-11111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1111-1-1-1
χ6111111111111111111111111111111-1-1-1-11111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1111
χ7111111111111111111111111111111-1-1-1-1111111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111-1-1-1-11
χ8111111111111111111111111111111-1-1-1-1111111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-11111-1
χ91111111111111111111111111111-1-1111111111111-111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-11111-1-1-1-11111111111-1-1111111-1-1-1-1-1-1
χ101111111111111111111111111111-1-1111111111111-111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1111111
χ111111111111111111111111111111-1-1111111111111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-111-1-11
χ121111111111111111111111111111-1-1111111111111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1111-1-111-1
χ131111111111111111111111111111-1-1-1-1-1-111111111-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1111
χ141111111111111111111111111111-1-1-1-1-1-111111111-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1
χ151111111111111111111111111111-1-1-1-1-1-111111111-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-111-11111-1
χ161111111111111111111111111111-1-1-1-1-1-111111111-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1111111-1-11-1-1-1-11
χ17222222222222−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−52222222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52222222222−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5200002−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5200000000000000000000
χ18222222222222−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−52222222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−522-2-2-2-2-2-222−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−520000-21−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+5200000000000000000000
χ19222222222222−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−5222-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5222222-2-2-2-2−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+520000-21−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+5200000000000000000000
χ20222222222222−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−5222-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−522-2-2-2-222-2-2−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+5200002−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−5200000000000000000000
χ21222222222222−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−52-2-22222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-222-2-222-2-21−521−521−521−521+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+520000-21−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−5200000000000000000000
χ22222222222222−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−52-2-22222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-2-222-2-2-2-21−521−521−521−521+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+5200002−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+5200000000000000000000
χ23222222222222−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−52-2-2-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-222-2-2-2-2221−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5200002−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+5200000000000000000000
χ24222222222222−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−52-2-2-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-2-22222221−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−520000-21−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5200000000000000000000
χ25222222222222−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+52222222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52222222222−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5200002−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5200000000000000000000
χ26222222222222−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+52222222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+522-2-2-2-2-2-222−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+520000-21+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−5200000000000000000000
χ27222222222222−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+5222-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5222222-2-2-2-2−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+521+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−520000-21+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−5200000000000000000000
χ28222222222222−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+5222-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+522-2-2-2-222-2-2−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+521+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−5200002−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+5200000000000000000000
χ29222222222222−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+52-2-22222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-222-2-222-2-21+521+521+521+521−521−521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+521+521+521+521+521−521−521−521−520000-21+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+5200000000000000000000
χ30222222222222−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+52-2-22222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-2-222-2-2-2-21+521+521+521+521−521−521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+521+521+521+521+521−521−521−521−5200002−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−5200000000000000000000
χ31222222222222−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+52-2-2-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-222-2-2-2-2221+521+521+521+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+5200002−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−5200000000000000000000
χ32222222222222−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+52-2-2-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-2-22222221+521+521+521+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+520000-21+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5200000000000000000000
χ3322222222-2-2-2-22222222222222222220000-2-2-2-2-2-2-2-2-20000000022-2-222-2-200000000000000002222000000000000000000000-2-222000000-200000
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χ3522222222-2-2-2-22222222222222222-2-20000-2-2-2-2-2-2-2-2200000000-2-222-2-22200000000000000002222000000000000000000000-2-2-2-2000000200000
χ3622222222-2-2-2-22222222222222222-2-20000-2-2-2-2-2-2-2-2200000000-2-222-2-2220000000000000000-2-2-2-20000000000000000000002222000000-200000
χ3722-222-2-2-2-22-222222-222-2-2-2-2-222-2-2000000-2-2-2-22222000002i−2i00000000000000000000000000000000000000000002i−2i2i−2i22-2-200002i2i−2i−2i00000000
χ3822-222-2-2-2-22-222222-222-2-2-2-2-222-2-2000000-2-2-2-22222000002i−2i00000000000000000000000000000000000000000002i−2i2i−2i-2-2220000−2i−2i2i2i00000000
χ3922-222-2-2-2-22-222222-222-2-2-2-2-222-2-2000000-2-2-2-2222200000−2i2i0000000000000000000000000000000000000000000−2i2i−2i2i22-2-20000−2i−2i2i2i00000000
χ4022-222-2-2-2-22-222222-222-2-2-2-2-222-2-2000000-2-2-2-2222200000−2i2i0000000000000000000000000000000000000000000−2i2i−2i2i-2-22200002i2i−2i−2i00000000
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χ482-222-2-22-2-222-222-2-2-2-2-2-2222222-2-2000000-22-22-22-22000−2i2i0000000000000000000000000000−2i−2i2i2i000000000−2i2i−2i2i000000002i−2i0000000002-2000
χ492-2-22-22-22-2-22222-2-22-2-22-2-2-2-222220022-2-2-22-222-22-20000000000000000022-2-222-2-2000000000000000000000000000002-2-22000000002-2000000
χ502-2-22-22-22-2-22222-2-22-2-22-2-2-2-222220022-2-2-22-222-22-20000000000000000022-2-222-2-200000000000000000000000000000-222-200000000-22000000
χ512-2-22-22-22-2-22222-2-22-2-22-2-2-2-2222200-2-222-22-222-22-200000000000000000-2-222-2-222000000000000000000000000000002-2-2200000000-22000000
χ522-2-22-22-22-2-22222-2-22-2-22-2-2-2-2222200-2-222-22-222-22-200000000000000000-2-222-2-22200000000000000000000000000000-222-2000000002-2000000
χ532-2-2-2222-20000222-222-222-22-2-2-2-2-22-22−22−20000000000000002−22-2002-2002−22−22−22−222−2−222−2−22i−2i2i−2i000000000000000000000002i−2ii2−i2i2−i200000i2−i20
χ542-2-2-2222-20000222-222-222-22-2-2-2-2-22-22−22−20000000000000002−22-2002-2002−22−22−22−222−2−222−2−2−2i2i−2i2i00000000000000000000000−2i2i−i2i2−i2i200000−i2i20
χ552-2-2-2222-20000222-222-222-22-2-2-2-2-22-2−22−22000000000000000−222-2002-200−22−22−22−22−2−222−2−2222i−2i2i−2i000000000000000000000002i−2i−i2i2−i2i200000−i2i20
χ562-2-2-2222-20000222-222-222-22-2-2-2-2-22-2−22−22000000000000000−222-2002-200−22−22−22−22−2−222−2−222−2i2i−2i2i00000000000000000000000−2i2ii2−i2i2−i200000i2−i20
χ572-2-2-2222-20000222-222-222-22-2-2-2-2-2-222−22−2000000000000000−22-2200-22002−22−22−22−2−2−222−2−2222i−2i2i−2i00000000000000000000000−2i2ii2−i2i2−i200000−i2i20
χ582-2-2-2222-20000222-222-222-22-2-2-2-2-2-222−22−2000000000000000−22-2200-22002−22−22−22−2−2−222−2−222−2i2i−2i2i000000000000000000000002i−2i−i2i2−i2i200000i2−i20
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χ1114-4-4-4444-40000−1−5−1+5−1−51+5−1−5−1+51−5−1+5−1−51+5−1+51−51+51−51+51−5-4422−2222−22000000000000000−22221+5−1−5001−5−1+500ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37−ζ21−ζ29+ζ31+ζ39−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39ζ21+ζ29−ζ31−ζ39ζ7−ζ13+ζ23−ζ37ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37−ζ7+ζ13−ζ23+ζ3700000000000000000000000000000000000000000
χ1124-4-4-4444-40000−1−5−1+5−1−51+5−1−5−1+51−5−1+5−1−51+5−1+51−51+51−51+51−5-44−2222−222200000000000000022−221+5−1−5001−5−1+500−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37ζ21+ζ29−ζ31−ζ39ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39−ζ21−ζ29+ζ31+ζ39−ζ7+ζ13−ζ23+ζ37−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37ζ7−ζ13+ζ23−ζ3700000000000000000000000000000000000000000
χ11388-8-8-8-8880000−2+25−2−252−25−2+252−252+25−2−252+25−2+252−25−2−252+252−252+25−2+25−2−250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ11488-8-8-8-8880000−2−25−2+252+25−2−252+252−25−2+252−25−2−252+25−2+252−252+252−25−2−25−2+250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1158-88-88-8-880000−2+25−2−25−2+252−252−25−2−252+252+252−25−2+252+25−2−252−252+25−2+25−2−250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1168-88-88-8-880000−2−25−2+25−2−252+252+25−2+252−252−252+25−2−252−25−2+252+252−25−2−25−2+250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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