Finite Group Databasebeta

← Group #12157367

Character table — Group #12157367

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122
size11111111222222222222222222224444444444444444444444888888888888888888888888888888888888888888888161616161616161616202020202020404040404040404040404080
order1222222244445510101010101010101010101010104444442020202020202020202020202020202044444888820202020202020202020202020202020202020204040404040404040404040404040404042020202020202020224444444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-11-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-11-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111
χ511111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-11111-1-111-1-1-1
χ611111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111-1-1-1-111-1-1111
χ711111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-11111-1-1-111-1-1-1-1-1-1111
χ811111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1111-1-1111111-1-1-1
χ91111111111111111111111111111-1-1-1-1111111111111111111-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-111-1-1-1-1-1-11
χ101111111111111111111111111111-1-1-1-1111111111111111111-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-111-1-1111111-1
χ111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-11111-1
χ121111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11
χ131111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-111111111-1-1-1-1-11111-1-111-1
χ141111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-11111-1-1-1-111111-1-1-1-111-1-11
χ151111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-11111-1-11
χ161111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11111111-1-1-1-111-1
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+52−1−52−1−52−1−52−1−52−1+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+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−522−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52000000000000000000
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+52−1−52−1−52−1−52−1−52−1+52−1+52−1−52−1−5222-2-22-2-2-2-2−1+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+52−1−52−1−52−1−52−1−521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+52-21−521−521+521+521−521−521+521+52000000000000000000
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+52−1−522222-2-2−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+52−1+52−1+52−1−52−1−52-2-222-2-2-2221−521−521+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+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−521−521−521−521−521+521+521+521+52-21−521−521+521+52−1+52−1+52−1−52−1−52000000000000000000
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+52−1−522222-2-2−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+52−1+52−1+52−1−52−1−52-2-2-2-2-222-2-21−521−521+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+521−521−521−521−521+521+521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−522−1+52−1+52−1−52−1−521−521−521+521+52000000000000000000
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+52−1−52-2-2-2-222−1+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+52−1−52−1−52-2-2222-2-2-2-2−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+522−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52000000000000000000
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+52−1−52-2-2-2-222−1+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+52−1−52−1−52-2-2-2-222222−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-21−521−521+521+521−521−521+521+52000000000000000000
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+52−1−52−1−521−521−521−521−521+521+521+521+52−1+52−1+52−1−52−1−522222-222-2-21−521−521+521+521−521−521−521−521+521+521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−521−521−521−521−521+521+521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-21−521−521+521+52−1+52−1+52−1−52−1−52000000000000000000
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+52−1−52−1−521−521−521−521−521+521+521+521+52−1+52−1+52−1−52−1−5222-2-2-2-2-2221−521−521+521+521−521−521−521−521+521+521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−521−521−521−521−521+521+521+521+522−1+52−1+52−1−52−1−521−521−521+521+52000000000000000000
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+52−1−52−1−52−1−52−1−52−1+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+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+522−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52000000000000000000
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+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1+52−1+5222-2-22-2-2-2-2−1−52−1−52−1+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+521+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−52-21+521+521−521−521+521+521−521−52000000000000000000
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+522222-2-2−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−52−1−52−1−52−1+52−1+52-2-222-2-2-2221+521+521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+521+521+521+521+521−521−521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+521+521+521+521+521−521−521−521−52-21+521+521−521−52−1−52−1−52−1+52−1+52000000000000000000
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+522222-2-2−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−52−1−52−1−52−1+52−1+52-2-2-2-2-222-2-21+521+521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+521+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+522−1−52−1−52−1+52−1+521+521+521−521−52000000000000000000
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+52-2-2-2-222−1−52−1−52−1+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+52-2-2222-2-2-2-2−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−522−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52000000000000000000
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+52-2-2-2-222−1−52−1−52−1+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+52-2-2-2-222222−1−52−1−52−1+52−1+521+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+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52-21+521+521−521−521+521+521−521−52000000000000000000
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+521+521+521+521+521−521−521−521−52−1−52−1−52−1+52−1+522222-222-2-21+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+521+521+521+521+521−521−521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52-21+521+521−521−52−1−52−1−52−1+52−1+52000000000000000000
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+521+521+521+521+521−521−521−521−52−1−52−1−52−1+52−1+5222-2-2-2-2-2221+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+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+521+521+521+521+521−521−521−521−522−1−52−1−52−1+52−1+521+521+521−521−52000000000000000000
χ3322222222-2-2-2-22222222222222222000022-2-2-2-222222222-2-2-2-20000-20000-2-2-2-20000000000000000000000000000000000000000022-2-2-2-2200000000000
χ3422222222-2-2-2-22222222222222222000022-2-2-2-222222222-2-2-2-20000-20000-2-2-2-200000000000000000000000000000000000000000-2-22222-200000000000
χ3522222222-2-2-2-222222222222222220000-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200002000022220000000000000000000000000000000000000000022-2-222-200000000000
χ3622222222-2-2-2-222222222222222220000-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000020000222200000000000000000000000000000000000000000-2-222-2-2200000000000
χ37222-2-22-2-222-2-222222-22-22-2-22-2-2-2-222-2-200222200000000-2-2-2-2000000000000022-2-222-2-20000000000000000000000000000000002-22-20002-2000000000
χ38222-2-22-2-222-2-222222-22-22-2-22-2-2-2-222-2-200222200000000-2-2-2-2000000000000022-2-222-2-2000000000000000000000000000000000-22-22000-22000000000
χ39222-2-22-2-222-2-222222-22-22-2-22-2-2-2-2-2-22200222200000000-2-2-2-20000000000000-2-222-2-2220000000000000000000000000000000002-22-2000-22000000000
χ40222-2-22-2-222-2-222222-22-22-2-22-2-2-2-2-2-22200222200000000-2-2-2-20000000000000-2-222-2-222000000000000000000000000000000000-22-220002-2000000000
χ41222-2-22-2-2-2-22222222-22-22-2-22-2-2-2-2000000-2-2-2-20000000022222i−2i00000000000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000000002-2-2200000002i−2i00000
χ42222-2-22-2-2-2-22222222-22-22-2-22-2-2-2-2000000-2-2-2-20000000022222i−2i00000000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000000000000-222-20000000−2i2i00000
χ43222-2-22-2-2-2-22222222-22-22-2-22-2-2-2-2000000-2-2-2-2000000002222−2i2i0000000000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000000002-2-220000000−2i2i00000
χ44222-2-22-2-2-2-22222222-22-22-2-22-2-2-2-2000000-2-2-2-2000000002222−2i2i0000000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000000000000-222-200000002i−2i00000
χ452-2222-2-2-22-2-2222-2-22-22-2-222-222-2-22i−2i2i−2i002-22-2000000002-22-2002i−2i0002-200002i−2i2i−2i2i−2i2i−2i0000000022-2-222-2-200000000000002i−2i2i−2i000000000000000000
χ462-2222-2-2-22-2-2222-2-22-22-2-222-222-2-22i−2i2i−2i002-22-2000000002-22-200−2i2i000-2200002i−2i2i−2i2i−2i2i−2i00000000-2-222-2-2220000000000000−2i2i−2i2i000000000000000000
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χ12088-88-8-88-80000−2−25−2+252+252−252+252+252−252−25−2−25−2−252+25−2+25−2+252−25−2−25−2+250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1218-8-88-88-880000−2+25−2−25−2+25−2−252−25−2+252+25−2−252−25−2+252−252+25−2−252+252−252+250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1228-8-88-88-880000−2−25−2+25−2−25−2+252+25−2−252−25−2+252+25−2−252+252−25−2+252−252+252−250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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