Finite Group Databasebeta

← Group #12078059

Character table — Group #12078059

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107
size1111222222222222222244444444444444444444444444488888888888888888888881616161616161616161616161616161616161616202020204040404040404040404040404040
order1222444444445510101010101024444442020202020202020202020202020202020202020241010101010102020202020202020202020202020448820202020202020204040404040404040444422244488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111-1-11-1-1111111111111111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111111-1-11-1-11111-1-1-1-1
χ6111111111111111111111-1-11-1-1111111111111111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-11111
χ7111111111111111111111-1-11-1-1111111111111111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111111-1-11-1-1-1-1-1-11111
χ8111111111111111111111-1-11-1-1111111111111111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1111111-1-1-1-1
χ911111-1-1-1-111111111111-111-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-11111111111-1-1-1-1-1-1-1-11-11-11111-1-1-1-11111-1-1-1-111-1-1-1111-1-111-1-111-1-1
χ1011111-1-1-1-111111111111-111-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-11111111111-1-1-1-1-1-1-1-11-11-11111-1-1-1-11111-1-1-1-1-1-1111-1-1-111-1-111-1-111
χ1111111-1-1-1-111111111111-111-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-11111111111-1-1-1-1-1-1-1-1-11-11-1-1-1-11111-1-1-1-1111111-1-1-1111-1-1-1-111-1-111
χ1211111-1-1-1-111111111111-111-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-11111111111-1-1-1-1-1-1-1-1-11-11-1-1-1-11111-1-1-1-11111-1-1111-1-1-11111-1-111-1-1
χ1311111-1-1-1-111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-1-1-1-1-1-1-1-1-111111111111-1-111111-1-1-1-1-1-1-1-1111111-1-1-1-1-111111-1-1-1-111
χ1411111-1-1-1-111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-1-1-1-1-1-1-1-1-111111111111-1-111111-1-1-1-1-1-1-1-11111-1-111111-1-1-1-1-11111-1-1
χ1511111-1-1-1-111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-1-1-1-1-1-1-1-1-11111111111-111-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1111-1-11111-1-1
χ1611111-1-1-1-111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-1-1-1-1-1-1-1-1-11111111111-111-1-1-1-1-111111111-1-1-1-1-1-111111-1-1-111-1-1-1-111
χ17222222222222−1+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+52−1−52−1−52−1−52−1−52−1+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+52−1−52−1−52−1−52−1−522222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+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+52−1−52−1−522222222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+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+52−1−52−1−52−1−52−1−52-2-2-2-21−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+52000000000000000000
χ19222222222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−522-2-22-2-22−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1−52−1−52-2-2−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1−521−521−521−521−521+521+521+521+5222-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52000000000000000000
χ20222222222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−522-2-22-2-22−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1−52−1−52-2-2−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1−521−521−521−521−521+521+521+521+52-2-2221−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52000000000000000000
χ21222222222222−1−52−1+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+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+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+522222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+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+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+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+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52-2-2-2-21+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−52000000000000000000
χ23222222222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+522-2-22-2-22−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1+52−1+52-2-2−1−52−1+521+521+521−521−521+521+521−521−52−1−52−1+521+521+521+521+521−521−521−521−5222-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52000000000000000000
χ24222222222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+522-2-22-2-22−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1+52−1+52-2-2−1−52−1+521+521+521−521−521+521+521−521−52−1−52−1+521+521+521+521+521−521−521−521−52-2-2221+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52000000000000000000
χ252222222-2-2-2-2222222222200-200-222222222-2-2-2-2-2-2-2-2-2-2-2-2002200000000-2-2000000000000000000000000000022-2-2200-20000000000
χ262222222-2-2-2-2222222222200-200-222222222-2-2-2-2-2-2-2-2-2-2-2-2002200000000-2-20000000000000000000000000000-2-222-20020000000000
χ2722222-2-222-2-2222222222-200200-22222-2-2-2-222222222-2-2-2-200-2-200000000-2-200000000000000000000000000002222-200-20000000000
χ2822222-2-222-2-2222222222-200200-22222-2-2-2-222222222-2-2-2-200-2-200000000-2-20000000000000000000000000000-2-2-2-220020000000000
χ2922222-2-2-2-2222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-222-2-2-22−1+52−1+52−1−52−1−521−521−521+521+521−521−521−521−521+521+521+521+52−1+52−1+52−1−52−1−522-21−521+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+522-22-2−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52000000000000000000
χ3022222-2-2-2-2222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-222-2-2-22−1+52−1+52−1−52−1−521−521−521+521+521−521−521−521−521+521+521+521+52−1+52−1+52−1−52−1−522-21−521+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+52-22-221−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−52000000000000000000
χ3122222-2-2-2-2222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-2-2-2-2222−1+52−1+52−1−52−1−521−521−521+521+521−521−521−521−521+521+521+521+52−1+52−1+52−1−52−1−52-221−521+521−521−521+521+521−521−521+521+52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−522-2-22−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52000000000000000000
χ3222222-2-2-2-2222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-2-2-2-2222−1+52−1+52−1−52−1−521−521−521+521+521−521−521−521−521+521+521+521+52−1+52−1+52−1−52−1−52-221−521+521−521−521+521+521−521−521+521+52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-222-21−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+52000000000000000000
χ3322222-2-2-2-2222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52-222-2-2-22−1−52−1−52−1+52−1+521+521+521−521−521+521+521+521+521−521−521−521−52−1−52−1−52−1+52−1+522-21+521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1+521+521+521+521+521−521−521−521−522-22-2−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52000000000000000000
χ3422222-2-2-2-2222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52-222-2-2-22−1−52−1−52−1+52−1+521+521+521−521−521+521+521+521+521−521−521−521−52−1−52−1−52−1+52−1+522-21+521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1+521+521+521+521+521−521−521−521−52-22-221+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+52000000000000000000
χ3522222-2-2-2-2222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52-2-2-2-2222−1−52−1−52−1+52−1+521+521+521−521−521+521+521+521+521−521−521−521−52−1−52−1−52−1+52−1+52-221+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+522-2-22−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52000000000000000000
χ3622222-2-2-2-2222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52-2-2-2-2222−1−52−1−52−1+52−1+521+521+521−521−521+521+521+521+521−521−521−521−52−1−52−1−52−1+52−1+52-221+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+52-222-21+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−52000000000000000000
χ372222-2222222-222222222-222-222-2-2-2-2-2222222-2-222-2-22222-2-2-2-2-2-2-2-22222-2-222-2-222-2-200000000000000000000000000000000000000
χ382222-2222222-222222222-2-2-2-2-2-2-2-2-2-2-2222222-2-222-2-2222222-2-22222-2-2-2-2-2-2-2-222-2-22200000000000000000000000000000000000000
χ392222-2222222-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-222-222-21−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+521−521−52−1−52−1−521+521+52−1+52−1+52−1−52−1−52-2-21−521+521−521−521+521+52−1+52−1+52−1−52−1−521−521+52−1+52−1+521−521−52−1−52−1−521+521+520000ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36000000000000000000
χ402222-2222222-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-222-222-21−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+521−521−52−1−52−1−521+521+52−1+52−1+52−1−52−1−52-2-21−521+521−521−521+521+52−1+52−1+52−1−52−1−521−521+52−1+52−1+521−521−52−1−52−1−521+521+520000−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36000000000000000000
χ412222-2222222-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-2-2-2-2-2-2-21−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+521−521−52−1−52−1−521+521+52−1+52−1+52−1−52−1−52221−521+52−1+52−1+52−1−52−1−521−521−521+521+521−521+521−521−52−1+52−1+521+521+52−1−52−1−520000ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36000000000000000000
χ422222-2222222-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-2-2-2-2-2-2-21−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+521−521−52−1−52−1−521+521+52−1+52−1+52−1−52−1−52221−521+52−1+52−1+52−1−52−1−521−521−521+521+521−521+521−521−52−1+52−1+521+521+52−1−52−1−520000−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36000000000000000000
χ432222-2222222-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52-222-222-21+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−521+521+52−1+52−1+521−521−52−1−52−1−52−1+52−1+52-2-21+521−521+521+521−521−52−1−52−1−52−1+52−1+521+521−52−1−52−1−521+521+52−1+52−1+521−521−520000−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28000000000000000000
χ442222-2222222-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52-222-222-21+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−521+521+52−1+52−1+521−521−52−1−52−1−52−1+52−1+52-2-21+521−521+521+521−521−52−1−52−1−52−1+52−1+521+521−52−1−52−1−521+521+52−1+52−1+521−521−520000ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28000000000000000000
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χ1038-8-880000000088-8-8-88-88000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1048-8-8800000000−2+25−2−252−252+252−25−2+252+25−2−2500000000000000000−4ζ22+4ζ384ζ22−4ζ38004ζ6−4ζ14−4ζ6+4ζ140000000000000000000000000000000000000000000000000000000000000000
χ1058-8-8800000000−2+25−2−252−252+252−25−2+252+25−2−25000000000000000004ζ22−4ζ38−4ζ22+4ζ3800−4ζ6+4ζ144ζ6−4ζ140000000000000000000000000000000000000000000000000000000000000000
χ1068-8-8800000000−2−25−2+252+252−252+25−2−252−25−2+25000000000000000004ζ6−4ζ14−4ζ6+4ζ14004ζ22−4ζ38−4ζ22+4ζ380000000000000000000000000000000000000000000000000000000000000000
χ1078-8-8800000000−2−25−2+252+252−252+25−2−252−25−2+2500000000000000000−4ζ6+4ζ144ζ6−4ζ1400−4ζ22+4ζ384ζ22−4ζ380000000000000000000000000000000000000000000000000000000000000000

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