Finite Group Databasebeta

← Group #13156669

Character table — Group #13156669

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
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χ3111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-11-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-111
χ51111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111
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χ914-4-444-2-200-422-4224-2-2-2-2122-1122-1-2-20003i−3i00−3i3i022−22−22221-11-10000−3i3i3i−3i−222−2−222−2ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ23000000000000000000000000000000000000
χ924-4-444-2-200-422-4224-2-2-2-2122-1122-1-2-20003i−3i00−3i3i0−222222−221-11-10000−3i3i3i−3i2−2−222−2−22−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ23000000000000000000000000000000000000
χ934-4-444-2-200-422-4224-2-2-2-2122-1122-1-2-2000−3i3i003i−3i022−22−22221-11-100003i−3i−3i3i−222−2−222−2−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ23000000000000000000000000000000000000
χ944-4-444-2-200-422-4224-2-2-2-2122-1122-1-2-2000−3i3i003i−3i0−222222−221-11-100003i−3i−3i3i2−2−222−2−222ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ23000000000000000000000000000000000000
χ954-4-44-244002-4-42-4-4-244-2-2422-4422-4-2-200000000000000-22-2200000000000000000000000022−22−2222000000000000000000−222−20000000000
χ964-4-44-244002-4-42-4-4-244-2-2422-4422-4-2-200000000000000-22-22000000000000000000000000−222222−220000000000000000002−2−220000000000
χ978888-4-4-488-4-4-4-4-4-4-4-4-4222222222222-4-4-422-4-422-40000-1-1-1-12222-1-1-1-10000000000000000000000000000000000000000000000000000
χ988888-4-4-4-8-8-4-4-4-4-4-4-4-4-4222222222222444-2-244-2-240000-1-1-1-1-2-2-2-211110000000000000000000000000000000000000000000000000000
χ9988-8-8-4-4-48-8444-4-4-4444222-2-2-2-2222-2-2-444-2-2-4-42240000-111-12-22-2-1-1110000000000000000000000000000000000000000000000000000
χ10088-8-8-4-4-4-88444-4-4-4444222-2-2-2-2222-2-24-4-42244-2-2-40000-111-1-22-2211-1-10000000000000000000000000000000000000000000000000000
χ1018-88-8-48-400-48-44-844-84-42-4-42-444-244-20000000000000022-2-2000000000000000000000000000000000000000000000000000000000000
χ1028-88-8-4-4800-4-4844-844-82-4-42-4-44-244-240000000000000022-2-2000000000000000000000000000000000000000000000000000000000000
χ1038-88-8-4-4-400-4-4-4444444222222-2-2-2-2-2-20006i−6i006i−6i00000-1-1110000−3i3i−3i3i0000000000000000000000000000000000000000000000000000
χ1048-88-8-4-4-400-4-4-4444444222222-2-2-2-2-2-2000−6i6i00−6i6i00000-1-11100003i−3i3i−3i0000000000000000000000000000000000000000000000000000
χ1058-8-88-48-4004-844-84-48-4-42-44-24-44-24-42000000000000002-22-2000000000000000000000000000000000000000000000000000000000000
χ1068-8-88-4-480044-844-8-4-482-4-4-244-4-2442-4000000000000002-22-2000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-400444444-4-4-4222-2-2-22-2-2-2220006i−6i00−6i6i00000-11-1100003i−3i−3i3i0000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-400444444-4-4-4222-2-2-22-2-2-222000−6i6i006i−6i00000-11-110000−3i3i3i−3i0000000000000000000000000000000000000000000000000000

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