Finite Group Databasebeta

← Group #13156308

Character table — Group #13156308

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105
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χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-111
χ31111111111111111111111111111111111111111111111111111111111111111111111-1-11-111-1-111-1-11111-1-1-1-111-1-1-1-1-1-1-111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111111111-1-1-11-1-111-1-111-1-1-1-11111-1-1-111-1-1-1-1-1-111-1-1
χ51111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-11-1-11111-1-1-1-1-1-1
χ61111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1
χ71111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-111-1-11111-1-1-1-1-1-1-111-1-1-1-1-1-11111
χ81111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-111-1-1-1-1111111-1-1-1-1-1-1-111-1-111
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χ924-4-44-24-200-22-42224-2-4-21-2-21-1-22-12220000−3i3i003i−3i11-1-10000−3i3i3i−3i−2i22i2i2−i2i2−i2i2−i2i2−i2ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ23−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ2300000000000000000000000000000000000
χ934-4-44-24-200-22-42224-2-4-21-2-21-1-22-12220000−3i3i003i−3i11-1-10000−3i3i3i−3i2i2−2i2−i2i2−i2i2−i2i2−i2i2−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ232ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ2300000000000000000000000000000000000
χ948888-4-4-488-4-4-4-4-4-4-4-4-4222222222222-4-4-4-422-4-422-1-1-1-12222-1-1-1-100000000000000000000000000000000000000000000000000000
χ958888-4-4-4-8-8-4-4-4-4-4-4-4-4-42222222222224444-2-244-2-2-1-1-1-1-2-2-2-2111100000000000000000000000000000000000000000000000000000
χ9688-8-8-4-4-48-84-4-4-444444222-2-2-2-2222-2-2-4-44-42244-2-2-111-12-22-2-1-11100000000000000000000000000000000000000000000000000000
χ9788-8-8-4-4-4-884-4-4-444444222-2-2-2-2222-2-244-44-2-2-4-422-111-1-22-2211-1-100000000000000000000000000000000000000000000000000000
χ988-88-88-4-4004-8448-44-8-4-4-4244-4-244-2-4200000000002-22-20000000000000000000000000000000000000000000000000000000000000
χ998-88-8-4-4800-844-8-4844-42-4-4-24-44-2442-400000000002-22-20000000000000000000000000000000000000000000000000000000000000
χ1008-88-8-4-4-4004444-4-444-4222-2-22-2-2-2-22200006i−6i006i−6i-11-110000−3i3i−3i3i00000000000000000000000000000000000000000000000000000
χ1018-88-8-4-4-4004444-4-444-4222-2-22-2-2-2-2220000−6i6i00−6i6i-11-1100003i−3i3i−3i00000000000000000000000000000000000000000000000000000
χ1028-8-888-4-400-4-844-84-484-4-42-4-44244-24-2000000000022-2-20000000000000000000000000000000000000000000000000000000000000
χ1038-8-88-4-4800844-84-8-4-442-4-42-44-4-244-24000000000022-2-20000000000000000000000000000000000000000000000000000000000000
χ1048-8-88-4-4-400-444444-4-4422222-22-2-2-2-2-200006i−6i00−6i6i-1-1110000−3i3i3i−3i00000000000000000000000000000000000000000000000000000
χ1058-8-88-4-4-400-444444-4-4422222-22-2-2-2-2-20000−6i6i006i−6i-1-11100003i−3i−3i3i00000000000000000000000000000000000000000000000000000

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