Finite Group Databasebeta

← Group #10703010

Character table — Group #10703010

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size111111111111111122222222222222222222222244444444444444444444444444444444888888888888888888888888121212121212121212121212121212122424242424242424
order1222222244444444222234444666666612121212121212124444444466661212121212121212121212121212121212121212224466668888121212122424242424242424888888888888888844448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ911111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i11-1-11111ii−i−i-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-111-1-1ii−i−i
χ1011111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i11-1-11111ii−i−i-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111-1-111−i−iii
χ1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i-1-111-1-1-1-1−i−iii1111−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-111−i−iii
χ1211111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i-1-111-1-1-1-1−i−iii1111−i−i−i−iiiii−i−i−i−iiiii-1-1-1-1111111-1-1ii−i−i
χ1311111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii11-1-11111−i−iii-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111-1-111ii−i−i
χ1411111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii11-1-11111−i−iii-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-111-1-1−i−iii
χ1511111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-1-1-1ii−i−i1111iiii−i−i−i−iiiii−i−i−i−i-1-1-1-1111111-1-1−i−iii
χ1611111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-1-1-1ii−i−i1111iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-111ii−i−i
χ1722222222222222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ1822222222222222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111-2-2-2-2111111111111000000000000000000000000
χ1922222222222222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111112222-1-1-1-1-2-2-2-2-1-1-1-111111111000000000000000000000000
χ2022222222222222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-2111122221111-1-1-1-1-1-1-1-1000000000000000000000000
χ212222222222222222-2-2-2-22-2-2-2-222222222222222200000000-2-2-2-2-2-2-2-2000000000000000000000000000000000000000022-2-222-2-20000000000000000
χ222222222222222222-2-2-2-22-2-2-2-222222222222222200000000-2-2-2-2-2-2-2-20000000000000000000000000000000000000000-2-222-2-2220000000000000000
χ2322222222-2-2-2-2-2-2-2-222222-2-2-2-22222222-2-2-2-2-2-2-2-2000000002222-2-2-2-200000000000000000000000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ2422222222-2-2-2-2-2-2-2-222222-2-2-2-22222222-2-2-2-2-2-2-2-2000000002222-2-2-2-20000000000000000000000000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ2522222222-2-2-2-2-2-2-2-2-2-2-2-2-12222-1-1-1-1-1-1-1111111112i2i2i2i−2i−2i−2i−2i1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii22-2-2-1-1-1-12i2i−2i−2i1111−i−i−i−iiiii000000000000000000000000
χ2622222222-2-2-2-2-2-2-2-2-2-2-2-2-12222-1-1-1-1-1-1-1111111112i2i2i2i−2i−2i−2i−2i1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-2-2221111−2i−2i2i2i-1-1-1-1iiii−i−i−i−i000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2-12222-1-1-1-1-1-1-111111111−2i−2i−2i−2i2i2i2i2i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i22-2-2-1-1-1-1−2i−2i2i2i1111iiii−i−i−i−i000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2-12222-1-1-1-1-1-1-111111111−2i−2i−2i−2i2i2i2i2i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-2-22211112i2i−2i−2i-1-1-1-1−i−i−i−iiiii000000000000000000000000
χ29222-2-22-2-222-2-222-2-222-2-222-2-2222-2-2-2-222222-2-2-2-20000000022-2-222-2-20000000000000000000000002i−2i2i−2i00002i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ30222-2-22-2-222-2-222-2-222-2-222-2-2222-2-2-2-222222-2-2-2-20000000022-2-222-2-2000000000000000000000000−2i2i−2i2i0000−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ31222-2-22-2-222-2-222-2-222-2-2-12-2-22-1-11111-1-1-1-1-1111100000000-1-111-1-1113333−3−3−3−33333−3−3−3−30000−i3−i3i3i32i−2i2i−2i−i3−i3i3i3−i−iii−i−iii000000000000000000000000
χ32222-2-22-2-222-2-222-2-222-2-2-12-2-22-1-11111-1-1-1-1-1111100000000-1-111-1-1113333−3−3−3−33333−3−3−3−30000i3i3−i3−i3−2i2i−2i2ii3i3−i3−i3ii−i−iii−i−i000000000000000000000000
χ33222-2-22-2-222-2-222-2-222-2-2-12-2-22-1-11111-1-1-1-1-1111100000000-1-111-1-111−3−3−3−33333−3−3−3−333330000−i3−i3i3i3−2i2i−2i2i−i3−i3i3i3ii−i−iii−i−i000000000000000000000000
χ34222-2-22-2-222-2-222-2-222-2-2-12-2-22-1-11111-1-1-1-1-1111100000000-1-111-1-111−3−3−3−33333−3−3−3−333330000i3i3−i3−i32i−2i2i−2ii3i3−i3−i3−i−iii−i−iii000000000000000000000000
χ35222-2-22-2-222-2-222-2-2-2-2222-222-222-2-2-2-222222-2-2-2-200000000-2-222-2-222000000000000000000000000000000000000000000000000000000002i−2i2i−2i0000
χ36222-2-22-2-222-2-222-2-2-2-2222-222-222-2-2-2-222222-2-2-2-200000000-2-222-2-22200000000000000000000000000000000000000000000000000000000−2i2i−2i2i0000
χ37222-2-22-2-2-2-222-2-22222-2-22-222-222-2-2-2-22-2-2-2-222220000000022-2-2-2-222000000000000000000000000000000000000000000000000000000002i−2i−2i2i0000
χ38222-2-22-2-2-2-222-2-22222-2-22-222-222-2-2-2-22-2-2-2-222220000000022-2-2-2-22200000000000000000000000000000000000000000000000000000000−2i2i2i−2i0000
χ39222-2-22-2-2-2-222-2-222-2-22222-2-2222-2-2-2-22-2-2-2-2222200000000-2-22222-2-20000000000000000000000002-2-22000022-2-2-2-222000000000000000000000000
χ40222-2-22-2-2-2-222-2-222-2-22222-2-2222-2-2-2-22-2-2-2-2222200000000-2-22222-2-2000000000000000000000000-222-20000-2-22222-2-2000000000000000000000000
χ41222-2-22-2-2-2-222-2-222-2-222-12-2-22-1-11111-11111-1-1-1-10000000011-1-1-1-111−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i30000−i3−i3i3i32-2-22i3i3−i3−i3-1-11111-1-1000000000000000000000000
χ42222-2-22-2-2-2-222-2-222-2-222-12-2-22-1-11111-11111-1-1-1-10000000011-1-1-1-111−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i30000i3i3−i3−i3-222-2−i3−i3i3i311-1-1-1-111000000000000000000000000
χ43222-2-22-2-2-2-222-2-222-2-222-12-2-22-1-11111-11111-1-1-1-10000000011-1-1-1-111i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i30000−i3−i3i3i3-222-2i3i3−i3−i311-1-1-1-111000000000000000000000000
χ44222-2-22-2-2-2-222-2-222-2-222-12-2-22-1-11111-11111-1-1-1-10000000011-1-1-1-111i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i30000i3i3−i3−i32-2-22−i3−i3i3i3-1-11111-1-1000000000000000000000000
χ4522-22-2-22-22i−2i2i−2i2i−2i2i−2i0000200002-222-2-2-22i2i−2i−2i2i−2i2i−2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i000000001+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i00000000000000000000000000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ23−i2−i2i2i222−2−200000000
χ4622-22-2-22-22i−2i2i−2i2i−2i2i−2i0000200002-222-2-2-22i2i−2i−2i2i−2i2i−2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i000000001+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ23i2i2−i2−i2−2−22200000000
χ4722-22-2-22-22i−2i2i−2i2i−2i2i−2i0000200002-222-2-2-22i2i−2i−2i2i−2i2i−2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i00000000000000000000000000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ23i2i2−i2−i2−2−22200000000
χ4822-22-2-22-22i−2i2i−2i2i−2i2i−2i0000200002-222-2-2-22i2i−2i−2i2i−2i2i−2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ23−i2−i2i2i222−2−200000000
χ4922-22-2-22-2−2i2i−2i2i−2i2i−2i2i0000200002-222-2-2-2−2i−2i2i2i−2i2i−2i2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i000000001−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ13i2i2−i2−i222−2−200000000
χ5022-22-2-22-2−2i2i−2i2i−2i2i−2i2i0000200002-222-2-2-2−2i−2i2i2i−2i2i−2i2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i000000001−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i00000000000000000000000000−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ13−i2−i2i2i2−2−22200000000
χ5122-22-2-22-2−2i2i−2i2i−2i2i−2i2i0000200002-222-2-2-2−2i−2i2i2i−2i2i−2i2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ13−i2−i2i2i2−2−22200000000
χ5222-22-2-22-2−2i2i−2i2i−2i2i−2i2i0000200002-222-2-2-2−2i−2i2i2i−2i2i−2i2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i00000000000000000000000000−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ13i2i2−i2−i222−2−200000000
χ532-222-2-2-222i−2i−2i2i−2i2i2i−2i000020000-222-22-2-22i−2i2i−2i2i−2i−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000001−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i000000000000000000000000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ23002−22−2−i2i2−i2i200000000
χ542-222-2-2-222i−2i−2i2i−2i2i2i−2i000020000-222-22-2-22i−2i2i−2i2i−2i−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000001−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i0000000000000000000000002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ2300−22−22i2−i2i2−i200000000
χ552-222-2-2-222i−2i−2i2i−2i2i2i−2i000020000-222-22-2-22i−2i2i−2i2i−2i−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i000000000000000000000000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ2300−22−22i2−i2i2−i200000000
χ562-222-2-2-222i−2i−2i2i−2i2i2i−2i000020000-222-22-2-22i−2i2i−2i2i−2i−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i0000000000000000000000002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ23002−22−2−i2i2−i2i200000000
χ572-222-2-2-22−2i2i2i−2i2i−2i−2i2i000020000-222-22-2-2−2i2i−2i2i−2i2i2i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000001+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i0000000000000000000000002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ13002−22−2i2−i2i2−i200000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.