Finite Group Databasebeta

← Group #12157359

Character table — Group #12157359

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110
size1111111122222222222222222222444444444444888888888888888888888888888888881616161616161616161616161616161616162020202020202020404040404040404040404040
order1222222244445510101010101010101010101010102244202020202020202044448888101010102020202040404040404040404040404040404040442020202020202020202020202020202044444444444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111111-1-11-1-111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-11111
χ51111111111111111111111111111111111111111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1-11-1-1-1-11111
χ61111111111111111111111111111111111111111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-11111-1-1-1-1
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111111
χ91111111111111111111111111111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111-1-1-111-1-111
χ101111111111111111111111111111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1111-1-111-1-1
χ111111111111111111111111111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11-1-1-1111111-1-1
χ121111111111111111111111111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111111-1-1-1-1-1-1-1-11111-1-1111111-1111-1-1-1-1-1-111
χ131111111111111111111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-111111-1-1-111-1-1-1-111
χ141111111111111111111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1111-1-11111-1-1
χ151111111111111111111111111111-1-1-1-111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-111111111-1-1-1-111-1-11111111-1-1-1-1-111-1-1
χ161111111111111111111111111111-1-1-1-111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-111111-1-111
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+52−1−522222−1+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+52−1−52−1−52−1−52−1−5222−1+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+52−1−52−1−5200000000000000000000
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+52−1−522222−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1−522222-2-2-2-2−1+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+52-2-2−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+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+52−1−522222−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1−52-2-2-2-22222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-2-21−521−521+521+521−521−521+521+521−521−521+521+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+52−1−522222−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1−52-2-2-2-2-2-2-2-2−1+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+52221−521−521+521+52−1+52−1+52−1−52−1−521−521−521+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+52−1−52-2-2-2-2−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1−5222-2-222-2-21−521−521+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+522-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+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+52−1−52-2-2-2-2−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1−5222-2-2-2-2221−521−521+521+521−521−521+521+521−521−521−521−521+521+521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-22−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−5200000000000000000000
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+52−1−52-2-2-2-2−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1−52-2-22222-2-21−521−521+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+52-221−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5200000000000000000000
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+52−1−52-2-2-2-2−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1−52-2-222-2-2221−521−521+521+521−521−521+521+521−521−521−521−521+521+521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−522-21−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+5200000000000000000000
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+522222−1−52−1−52−1−52−1+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+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+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+522222−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1+522222-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−52-2-2−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+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+522222−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1+52-2-2-2-22222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1−52−1−52−1+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+521−521−521+521+521−521−521+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+522222−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1+52-2-2-2-2-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−52221+521+521−521−52−1−52−1−52−1+52−1+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+52-2-2-2-2−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1+5222-2-222-2-21+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+521−521−521−521−522-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−5200000000000000000000
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+52-2-2-2-2−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1+5222-2-2-2-2221+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+52-22−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+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+52-2-2-2-2−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1+52-2-22222-2-21+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+521−521−521−521−52-221+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+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+52-2-2-2-2−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1+52-2-222-2-2221+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+522-21+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−5200000000000000000000
χ3322222222-2-2-2-2222222222222222222-2-2-2-2-2-2-2-2-2-2000000002222-2-2-2-2000000000000000000000000000000000022220000-200-200000000
χ3422222222-2-2-2-2222222222222222222-2-2-2-2-2-2-2-2-2-2000000002222-2-2-2-20000000000000000000000000000000000-2-2-2-20000200200000000
χ3522222222-2-2-2-22222222222222222-2-222-2-2-2-2-2-2-2-200000000-2-2-2-22222000000000000000000000000000000000022-2-20000-200200000000
χ3622222222-2-2-2-22222222222222222-2-222-2-2-2-2-2-2-2-200000000-2-2-2-222220000000000000000000000000000000000-2-2220000200-200000000
χ37222-2-2-2-2222-2-22222-222-22-2-22-2-2-2-22-22-222-222-2-2-2000000002-22-22-22-20000000000000000000000000000000000000022-2-20000002-20000
χ38222-2-2-2-2222-2-22222-222-22-2-22-2-2-2-22-22-222-222-2-2-2000000002-22-22-22-200000000000000000000000000000000000000-2-222000000-220000
χ39222-2-2-2-2222-2-22222-222-22-2-22-2-2-2-2-22-2222-222-2-2-200000000-22-22-22-220000000000000000000000000000000000000022-2-2000000-220000
χ40222-2-2-2-2222-2-22222-222-22-2-22-2-2-2-2-22-2222-222-2-2-200000000-22-22-22-2200000000000000000000000000000000000000-2-2220000002-20000
χ41222-2-2-2-22-2-2222222-222-22-2-22-2-2-2-22-2-22-2-22-2-22222i−2i2i−2i00002-22-2-22-220000000000000000002i−2i2i−2i00002i−2i2i−2i000000000000000000000000
χ42222-2-2-2-22-2-2222222-222-22-2-22-2-2-2-22-2-22-2-22-2-2222−2i2i−2i2i00002-22-2-22-22000000000000000000−2i2i−2i2i0000−2i2i−2i2i000000000000000000000000
χ43222-2-2-2-22-2-2222222-222-22-2-22-2-2-2-2-222-2-2-22-2-22222i−2i−2i2i0000-22-222-22-20000000000000000002i−2i2i−2i0000−2i2i−2i2i000000000000000000000000
χ44222-2-2-2-22-2-2222222-222-22-2-22-2-2-2-2-222-2-2-22-2-2222−2i2i2i−2i0000-22-222-22-2000000000000000000−2i2i−2i2i00002i−2i2i−2i000000000000000000000000
χ45222-2-2-2-22-2-222−1+52−1−52−1+52−1+521−52−1−52−1−521+52−1+521−521−52−1−521+521+521−521+522-2-221−521−52−1+521+521+52−1−52−1+52−1−522i−2i2i−2i0000−1+521−52−1−521+521−52−1+521+52−1−52ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ28−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ36ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ28−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ3600−ζ22−ζ38ζ22+ζ38−ζ6−ζ14ζ6+ζ14−ζ22+ζ38ζ22−ζ38ζ6−ζ14−ζ6+ζ14−ζ22−ζ38ζ22+ζ38−ζ6−ζ14ζ6+ζ14−ζ22+ζ38ζ22−ζ38ζ6−ζ14−ζ6+ζ1400000000000000000000
χ46222-2-2-2-22-2-222−1+52−1−52−1+52−1+521−52−1−52−1−521+52−1+521−521−52−1−521+521+521−521+522-2-221−521−52−1+521+521+52−1−52−1+52−1−522i−2i2i−2i0000−1+521−52−1−521+521−52−1+521+52−1−52−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ28ζ4−ζ36ζ4−ζ36−ζ4+ζ36−ζ4+ζ36−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ28ζ4−ζ36ζ4−ζ36−ζ4+ζ36−ζ4+ζ3600−ζ22−ζ38ζ22+ζ38−ζ6−ζ14ζ6+ζ14ζ22−ζ38−ζ22+ζ38−ζ6+ζ14ζ6−ζ14−ζ22−ζ38ζ22+ζ38−ζ6−ζ14ζ6+ζ14ζ22−ζ38−ζ22+ζ38−ζ6+ζ14ζ6−ζ1400000000000000000000
χ47222-2-2-2-22-2-222−1+52−1−52−1+52−1+521−52−1−52−1−521+52−1+521−521−52−1−521+521+521−521+522-2-221−521−52−1+521+521+52−1−52−1+52−1−52−2i2i−2i2i0000−1+521−52−1−521+521−52−1+521+52−1−52ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ28−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ36ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ28−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ3600ζ22+ζ38−ζ22−ζ38ζ6+ζ14−ζ6−ζ14ζ22−ζ38−ζ22+ζ38−ζ6+ζ14ζ6−ζ14ζ22+ζ38−ζ22−ζ38ζ6+ζ14−ζ6−ζ14ζ22−ζ38−ζ22+ζ38−ζ6+ζ14ζ6−ζ1400000000000000000000
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χ984-44-4-444-4-44-44−1−5−1+51+51+5−1−51−51−5−1+5−1−51+51+5−1+51−51−5−1−5−1+500001+5−1−51+51−5−1+51−5−1−5−1+500000000000000002ζ4−2ζ36−2ζ4+2ζ36−2ζ4+2ζ362ζ4−2ζ362ζ12−2ζ28−2ζ12+2ζ28−2ζ12+2ζ282ζ12−2ζ280000000000000000000000000000000000000000000000
χ994-4-44-4-444000044-44-4-44-4-44-4-44-4440000000000000000000000000000000000000000000000000000000000000000000000000000000022−22
χ1004-4-44-4-444000044-44-4-44-4-44-4-44-44400000000000000000000000000000000000000000000000000000000000000000000000000000000−2222
χ1014-4-4-444-44000044-444-444-4-44-4-44-4-40000000000000000000000000000000000000000000000000000000000000000000000000000002i2−2i200
χ1024-4-4-444-44000044-444-444-4-44-4-44-4-4000000000000000000000000000000000000000000000000000000000000000000000000000000−2i22i200
χ10388-88-88-8-80000−2+25−2−25−2+252−25−2+25−2−252+25−2−252−25−2+252−252+25−2−252+252−252+250000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10488-88-88-8-80000−2−25−2+25−2−252+25−2−25−2+252−25−2+252+25−2−252+252−25−2+252−252+252−250000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10588-8-88-88-80000−2+25−2−25−2+252−252−25−2−252+252+252−252−25−2+252+252+25−2−25−2+25−2−250000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10688-8-88-88-80000−2−25−2+25−2−252+252+25−2+252−252−252+252+25−2−252−252−25−2+25−2−25−2+250000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-8-8880000−2+25−2−252−25−2+252−252+25−2−252+252−25−2+252−252+25−2−252+25−2+25−2−250000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1088-8-88-8-8880000−2−25−2+252+25−2−252+252−25−2+252−252+25−2−252+252−25−2+252−25−2−25−2+250000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1098-8-8-888-880000−2+25−2−252−25−2+25−2+252+25−2−25−2−252−252−25−2+252+252+25−2−252−252+250000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1108-8-8-888-880000−2−25−2+252+25−2−25−2−252−25−2+25−2+252+252+25−2−252−252−25−2+252+252−250000000000000000000000000000000000000000000000000000000000000000000000000000000000

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