Finite Group Databasebeta

← Group #10703016

Character table — Group #10703016

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size111111111111111122222222222222222222222244444444444444444444444444444444888888888888888888888888121212121212121212121212121212122424242424242424
order12222222444444442222344446666666121212121212121244444444666612121212121212121212121212121212121212124444888812121212121212122424242424242424888888888888888822448888
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
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111
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−i11-1-1ii−i−i1111-1-1-1-1iiii−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−i11-1-1ii−i−i1111-1-1-1-1iiii−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−i−iii-1-1-1-11111−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−i−iii-1-1-1-11111−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−iiiiiiiii11-1-1−i−iii1111-1-1-1-1−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−iiiiiiiii11-1-1−i−iii1111-1-1-1-1−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-1-111ii−i−i-1-1-1-11111iiii−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-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-111ii−i−i
χ1722222222222222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ1822222222222222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111000000000000000000000000
χ1922222222222222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111112222-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000000000000000
χ2022222222222222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-1000000000000000000000000
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−iiiiiiiii22-2-22i2i−2i−2i-1-1-1-11111−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-2-222−2i−2i2i2i1111-1-1-1-1iiii−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−i22-2-2−2i−2i2i2i-1-1-1-11111iiii−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-2-2222i2i−2i−2i1111-1-1-1-1−i−i−i−iiiii000000000000000000000000
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χ32222-2-22-2-22i−2i2i−2i2i2i−2i−2i00002000022-2-22-2-22i2i2i−2i−2i−2i2i−2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000−1−i−1−i−1−i−1−i1+i1+i1+i1+i−1+i−1+i−1+i−1+i1−i1−i1−i1−i00000000000000000000000000−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ1322−2−2−i2−i2i2i200000000
χ33222-2-22-2-2−2i2i−2i2i−2i−2i2i2i00002000022-2-22-2-2−2i−2i−2i2i2i2i−2i2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i000000001−i1−i1−i1−i−1+i−1+i−1+i−1+i1+i1+i1+i1+i−1−i−1−i−1−i−1−i00000000000000000000000000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ2322−2−2i2i2−i2−i200000000
χ34222-2-22-2-2−2i2i−2i2i−2i−2i2i2i00002000022-2-22-2-2−2i−2i−2i2i2i2i−2i2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i000000001−i1−i1−i1−i−1+i−1+i−1+i−1+i1+i1+i1+i1+i−1−i−1−i−1−i−1−i000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ23−2−222−i2−i2i2i200000000
χ35222-2-22-2-2−2i2i−2i2i−2i−2i2i2i00002000022-2-22-2-2−2i−2i−2i2i2i2i−2i2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000−1+i−1+i−1+i−1+i1−i1−i1−i1−i−1−i−1−i−1−i−1−i1+i1+i1+i1+i00000000000000000000000000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ23−2−222−i2−i2i2i200000000
χ36222-2-22-2-2−2i2i−2i2i−2i−2i2i2i00002000022-2-22-2-2−2i−2i−2i2i2i2i−2i2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000−1+i−1+i−1+i−1+i1−i1−i1−i1−i−1−i−1−i−1−i−1−i1+i1+i1+i1+i000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ2322−2−2i2i2−i2−i200000000
χ3722-22-2-22-22i−2i2i−2i−2i−2i2i2i0000200002-22-2-22-22i−2i−2i2i2i−2i2i−2i1−i−1+i1−i−1+i1+i−1−i1+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−i0000000000000000000000002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ1300−i2i2−i2i22−22−200000000
χ3822-22-2-22-22i−2i2i−2i−2i−2i2i2i0000200002-22-2-22-22i−2i−2i2i2i−2i2i−2i1−i−1+i1−i−1+i1+i−1−i1+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−i000000000000000000000000−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ1300i2−i2i2−i2−22−2200000000
χ3922-22-2-22-22i−2i2i−2i−2i−2i2i2i0000200002-22-2-22-22i−2i−2i2i2i−2i2i−2i−1+i1−i−1+i1−i−1−i1+i−1−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+i0000000000000000000000002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ1300i2−i2i2−i2−22−2200000000
χ4022-22-2-22-22i−2i2i−2i−2i−2i2i2i0000200002-22-2-22-22i−2i−2i2i2i−2i2i−2i−1+i1−i−1+i1−i−1−i1+i−1−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+i000000000000000000000000−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ1300−i2i2−i2i22−22−200000000
χ4122-22-2-22-2−2i2i−2i2i2i2i−2i−2i0000200002-22-2-22-2−2i2i2i−2i−2i2i−2i2i1+i−1−i1+i−1−i1−i−1+i1−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+i000000000000000000000000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ2300i2−i2i2−i22−22−200000000
χ4222-22-2-22-2−2i2i−2i2i2i2i−2i−2i0000200002-22-2-22-2−2i2i2i−2i−2i2i−2i2i1+i−1−i1+i−1−i1−i−1+i1−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+i0000000000000000000000002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ2300−i2i2−i2i2−22−2200000000
χ4322-22-2-22-2−2i2i−2i2i2i2i−2i−2i0000200002-22-2-22-2−2i2i2i−2i−2i2i−2i2i−1−i1+i−1−i1+i−1+i1−i−1+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−i000000000000000000000000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ2300−i2i2−i2i2−22−2200000000
χ4422-22-2-22-2−2i2i−2i2i2i2i−2i−2i0000200002-22-2-22-2−2i2i2i−2i−2i2i−2i2i−1−i1+i−1−i1+i−1+i1−i−1+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−i0000000000000000000000002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ2300i2−i2i2−i22−22−200000000
χ4522-2-22-2-222222-2-2-2-222-2-222-2-222-2-22-2-222-2-2-2-22222i−2i−2i2i−2i2i2i−2i22-2-222-2-22i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ4622-2-22-2-222222-2-2-2-222-2-222-2-222-2-22-2-222-2-2-2-2222−2i2i2i−2i2i−2i−2i2i22-2-222-2-2−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ4722-2-22-2-222222-2-2-2-222-2-2-12-2-22-111-111-1-11111-1-1-12i−2i−2i2i−2i2i2i−2i-1-111-1-111−i−iiiii−i−iii−i−i−i−iii0000000033−3−333−3−3−i3−i3i3i3−i3−i3i3i3000000000000000000000000
χ4822-2-22-2-222222-2-2-2-222-2-2-12-2-22-111-111-1-11111-1-1-12i−2i−2i2i−2i2i2i−2i-1-111-1-111−i−iiiii−i−iii−i−i−i−iii00000000−3−333−3−333i3i3−i3−i3i3i3−i3−i3000000000000000000000000
χ4922-2-22-2-222222-2-2-2-222-2-2-12-2-22-111-111-1-11111-1-1-1−2i2i2i−2i2i−2i−2i2i-1-111-1-111ii−i−i−i−iii−i−iiiii−i−i0000000033−3−333−3−3i3i3−i3−i3i3i3−i3−i3000000000000000000000000
χ5022-2-22-2-222222-2-2-2-222-2-2-12-2-22-111-111-1-11111-1-1-1−2i2i2i−2i2i−2i−2i2i-1-111-1-111ii−i−i−i−iii−i−iiiii−i−i00000000−3−333−3−333−i3−i3i3i3−i3−i3i3i3000000000000000000000000
χ5122-2-22-2-222222-2-2-2-2-2-2222-222-22-2-22-2-222-2-2-2-222200000000-2-222-2-2220000000000000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000
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χ5322-2-22-2-22-2-2-2-2222222-2-22-222-22-2-22-2-22-22222-2-2-20000000022-2-2-2-2220000000000000000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000
χ5422-2-22-2-22-2-2-2-2222222-2-22-222-22-2-22-2-22-22222-2-2-20000000022-2-2-2-222000000000000000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000
χ5522-2-22-2-22-2-2-2-22222-2-22222-2-222-2-22-2-22-22222-2-2-22-2-222-2-22-2-22222-2-222-2-2-2-22222-2-2-2-222000000000000000000000000000000000000000000000000
χ5622-2-22-2-22-2-2-2-22222-2-22222-2-222-2-22-2-22-22222-2-2-2-222-2-222-2-2-22222-2-2-2-22222-2-2-2-22222-2-2000000000000000000000000000000000000000000000000
χ5722-2-22-2-22-2-2-2-22222-2-222-12-2-22-111-111-11-1-1-1-11112-2-222-2-2211-1-1-1-111-1-11111-1-1-1-11111-1-10000000033−3−3−3−333−3−33333−3−3000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.