Finite Group Databasebeta

← Group #10690545

Character table — Group #10690545

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size111111111111111122222222222222222222222244444444444444444444444444444444888888888888888888888888121212121212121212121212121212122424242424242424
order122222224444444434444444466666661212121212121212888888881212121212121212242424242424242424242424242424244444888812121212121212122424242424242424224444448888888844448888
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
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-1iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i11-1-111-1-1iiii−i−i−i−i11-1-1ii−i−i
χ1011111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-1iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i-1-111-1-111−i−i−i−iiiii-1-111−i−iii
χ1111111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-1iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111−i−iii-1-1-1-11111−i−i−i−iiiii11-1-111-1-1iiii−i−i−i−i-1-111−i−iii
χ1211111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-1iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111−i−iii-1-1-1-11111−i−i−i−iiiii-1-111-1-111−i−i−i−iiiii11-1-1ii−i−i
χ1311111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii11-1-111-1-1−i−i−i−iiiii11-1-1−i−iii
χ1411111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii-1-111-1-111iiii−i−i−i−i-1-111ii−i−i
χ1511111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i11-1-111-1-1−i−i−i−iiiii-1-111ii−i−i
χ1611111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i-1-111-1-111iiii−i−i−i−i11-1-1−i−iii
χ1722222222222222222-2-2-2-2-2-2-2-222222222222222200000000-2-2-2-2-2-2-2-200000000000000000000000000000000000000002222-2-2-2-20000000000000000
χ1822222222222222222-2-2-2-2-2-2-2-222222222222222200000000-2-2-2-2-2-2-2-20000000000000000000000000000000000000000-2-2-2-222220000000000000000
χ192222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ202222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111000000000000000000000000
χ212222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111112222-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000000000000000
χ222222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-1000000000000000000000000
χ2322222222-2-2-2-2-2-2-2-22-2-2-2-222222222222-2-2-2-2-2-2-2-200000000-2-2-2-22222000000000000000000000000000000000000000022-2-2-2-2220000000000000000
χ2422222222-2-2-2-2-2-2-2-22-2-2-2-222222222222-2-2-2-2-2-2-2-200000000-2-2-2-222220000000000000000000000000000000000000000-2-22222-2-20000000000000000
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χ2622222222-2-2-2-2-2-2-2-2-12222-2-2-2-2-1-1-1-1-1-1-1111111112i2i2i2i−2i−2i−2i−2i-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii-2-222−2i−2i2i2i1111-1-1-1-1iiii−i−i−i−i000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-12222-2-2-2-2-1-1-1-1-1-1-111111111−2i−2i−2i−2i2i2i2i2i-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i22-2-2−2i−2i2i2i-1-1-1-11111iiii−i−i−i−i000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-12222-2-2-2-2-1-1-1-1-1-1-111111111−2i−2i−2i−2i2i2i2i2i-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i-2-2222i2i−2i−2i1111-1-1-1-1−i−i−i−iiiii000000000000000000000000
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χ3222-2-222-2-22i2i−2i−2i2i−2i2i−2i20000000022-2-2-22-22i2i2i−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−i0000000000000000000000000000−2i2i-221−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000
χ3322-2-222-2-2−2i−2i2i2i−2i2i−2i2i20000000022-2-2-22-2−2i−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−i00000000000000000000000000002i−2i-22−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000
χ3422-2-222-2-2−2i−2i2i2i−2i2i−2i2i20000000022-2-2-22-2−2i−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−i0000000000000000000000000000−2i2i2-21+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000
χ3522-2-222-2-2−2i−2i2i2i−2i2i−2i2i20000000022-2-2-22-2−2i−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+i00000000000000000000000000002i−2i-221+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000
χ3622-2-222-2-2−2i−2i2i2i−2i2i−2i2i20000000022-2-2-22-2−2i−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+i0000000000000000000000000000−2i2i2-2−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000
χ3722-2-2-2-2222i−2i2i−2i2i−2i−2i2i222-2-22i−2i2i−2i2-22-2-2-222i−2i−2i2i2i−2i2i−2i0000000022-2-22i−2i2i−2i0000000000000000000000000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13
χ3822-2-2-2-2222i−2i2i−2i2i−2i−2i2i222-2-22i−2i2i−2i2-22-2-2-222i−2i−2i2i2i−2i2i−2i0000000022-2-22i−2i2i−2i000000000000000000000000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13
χ3922-2-2-2-2222i−2i2i−2i2i−2i−2i2i2-2-222−2i2i−2i2i2-22-2-2-222i−2i−2i2i2i−2i2i−2i00000000-2-222−2i2i−2i2i000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000002ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13000000000000000000000000
χ4022-2-2-2-2222i−2i2i−2i2i−2i−2i2i2-2-222−2i2i−2i2i2-22-2-2-222i−2i−2i2i2i−2i2i−2i00000000-2-222−2i2i−2i2i00000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ232ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13000000000000000000000000
χ4122-2-2-2-2222i−2i2i−2i2i−2i−2i2i-1-2-222−2i2i−2i2i-11-1111-1−iii−i−ii−ii0000000011-1-1i−ii−iζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ2300002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1333−3−3−i3−i3i3i3−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13000000000000000000000000
χ4222-2-2-2-2222i−2i2i−2i2i−2i−2i2i-1-2-222−2i2i−2i2i-11-1111-1−iii−i−ii−ii0000000011-1-1i−ii−iζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ230000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−3−333i3i3−i3−i3ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13000000000000000000000000
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χ4422-2-2-2-2222i−2i2i−2i2i−2i−2i2i-1-2-222−2i2i−2i2i-11-1111-1−iii−i−ii−ii0000000011-1-1i−ii−i−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ230000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1333−3−3−i3−i3i3i3ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13000000000000000000000000
χ4522-2-2-2-222−2i2i−2i2i−2i2i2i−2i222-2-2−2i2i−2i2i2-22-2-2-22−2i2i2i−2i−2i2i−2i2i0000000022-2-2−2i2i−2i2i000000000000000000000000000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23
χ4622-2-2-2-222−2i2i−2i2i−2i2i2i−2i222-2-2−2i2i−2i2i2-22-2-2-22−2i2i2i−2i−2i2i−2i2i0000000022-2-2−2i2i−2i2i0000000000000000000000000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23
χ4722-2-2-2-222−2i2i−2i2i−2i2i2i−2i2-2-2222i−2i2i−2i2-22-2-2-22−2i2i2i−2i−2i2i−2i2i00000000-2-2222i−2i2i−2i00000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ132ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23000000000000000000000000
χ4822-2-2-2-222−2i2i−2i2i−2i2i2i−2i2-2-2222i−2i2i−2i2-22-2-2-22−2i2i2i−2i−2i2i−2i2i00000000-2-2222i−2i2i−2i000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000002ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23000000000000000000000000
χ4922-2-2-2-222−2i2i−2i2i−2i2i2i−2i-1-2-2222i−2i2i−2i-11-1111-1i−i−iii−ii−i0000000011-1-1−ii−ii−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ130000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2333−3−3i3i3−i3−i3ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23000000000000000000000000
χ5022-2-2-2-222−2i2i−2i2i−2i2i2i−2i-1-2-2222i−2i2i−2i-11-1111-1i−i−iii−ii−i0000000011-1-1−ii−ii−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ1300002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−3−333−i3−i3i3i3−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23000000000000000000000000
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χ1114-44-4-44-44−4i4i−4i4i4i−4i−4i4i-20000000022-2-22-222i−2i2i−2i2i−2i−2i2i2+2i−2−2i2+2i−2−2i2−2i−2+2i2−2i−2+2i00000000−1−i1+i1+i−1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i1−i−1+i−1+i1−i000000000000000000000000000000000000000000000000
χ1124-44-4-44-44−4i4i−4i4i4i−4i−4i4i-20000000022-2-22-222i−2i2i−2i2i−2i−2i2i−2−2i2+2i−2−2i2+2i−2+2i2−2i−2+2i2−2i000000001+i−1−i−1−i1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i−1+i1−i1−i−1+i000000000000000000000000000000000000000000000000
χ1134-4-444-4-444444-4-4-4-4400000000-444-44-4-444-4-444-4-400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1144-4-444-4-444444-4-4-4-4-2000000002-2-22-222-2-222-2-2220000000000000000i6−i6i6−i6−i6i6−i6i6−i6i6−i6i6i6−i6i6−i6000000000000000000000000000000000000000000000000
χ1154-4-444-4-444444-4-4-4-4-2000000002-2-22-222-2-222-2-2220000000000000000−i6i6−i6i6i6−i6i6−i6i6−i6i6−i6−i6i6−i6i6000000000000000000000000000000000000000000000000
χ1164-4-444-4-44-4-4-4-44444400000000-444-44-4-4-4-444-4-44400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1174-4-444-4-44-4-4-4-44444-2000000002-2-22-22222-2-222-2-200000000000000006−66−6−66−666−66−6−66−66000000000000000000000000000000000000000000000000
χ1184-4-444-4-44-4-4-4-44444-2000000002-2-22-22222-2-222-2-20000000000000000−66−666−66−6−66−666−66−6000000000000000000000000000000000000000000000000
χ1194-4-44-444-44-4-44-4-444-2-444-4-4-4442222-2-2-2-22-2-22-222000000002-2-2222-2-20000000000000000000000000000000000000000000000000000000000000000
χ1204-4-44-444-4-444-444-4-4-2-444-444-4-42222-2-2-22-222-22-2-2000000002-2-22-2-2220000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.