Finite Group Databasebeta

← Group #13156539

Character table — Group #13156539

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
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χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
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χ3111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-111
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
χ71111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-111
χ81111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-11111-1111-1-1
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χ864-44-4-24-2002-4-2-42-2422-21-221-1-222-12-2000−3i3i00−3i3i02i2−2i22i2−2i211-1-10000−3i3i−3i3i−i2i2−i2i2−i2i2−i2i2−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ23−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ23000000000000000000000000000000000000
χ874-4-4444-200442-42-4-4-2-44-2-242-22-2-422-4000000000022−22−2222-22-220000000022−22−2222−222−2−2−22222−2−2000000000000000000000000000000000000
χ884-4-4444-200442-42-4-4-2-44-2-242-22-2-422-40000000000−222222−22-22-2200000000−222222−222−2−2222−2−2−2−222000000000000000000000000000000000000
χ894-4-444-24004-2-42-4-424-4-24-2-2-442-22-42200000000000000-22-22000000000000000000000000−2i22i22i2−2i2000000000000000000i2−i2−i2i20000000000
χ904-4-444-24004-2-42-4-424-4-24-2-2-442-22-42200000000000000-22-220000000000000000000000002i2−2i2−2i22i2000000000000000000−i2i2i2−i20000000000
χ914-4-44-24400-24-4-4-42-442-2-24-22-2-4422-42000000000022−22−2222-22-2200000000−222−222−22−2222−2−22222−2−2000000000000000000000000000000000000
χ924-4-44-24400-24-4-4-42-442-2-24-22-2-4422-420000000000−222222−22-22-22000000002−2−22−222222−2222−2−2−2−222000000000000000000000000000000000000
χ934-4-44-24-200-242-422-4-22-21-2-2-112-22-1220003i−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
χ944-4-44-24-200-242-422-4-22-21-2-2-112-22-1220003i−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
χ954-4-44-24-200-242-422-4-22-21-2-2-112-22-122000−3i3i003i−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
χ964-4-44-24-200-242-422-4-22-21-2-2-112-22-122000−3i3i003i−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
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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
χ9988-8-8-4-4-48-8444-4-4444-4222-2-2-2-2-2222-2-444-2-2-4-42240000-111-12-22-2-1-1110000000000000000000000000000000000000000000000000000
χ10088-8-8-4-4-4-88444-4-4444-4222-2-2-2-2-2222-24-4-42244-2-2-40000-111-1-22-2211-1-10000000000000000000000000000000000000000000000000000
χ1018-88-88-4-400-84-4448-44-8-4-424-442-244-2-40000000000000022-2-2000000000000000000000000000000000000000000000000000000000000
χ1028-88-8-4-48004484-8-4-4-842-4-4-2-44-44-24420000000000000022-2-2000000000000000000000000000000000000000000000000000000000000
χ1038-88-8-4-4-40044-444-4-444222-22-22-2-2-2-220006i−6i006i−6i00000-1-1110000−3i3i−3i3i0000000000000000000000000000000000000000000000000000
χ1048-88-8-4-4-40044-444-4-444222-22-22-2-2-2-22000−6i6i00−6i6i00000-1-11100003i−3i3i−3i0000000000000000000000000000000000000000000000000000
χ1058-8-888-4-4008-4444-84-4-8-4-42-44-4-2244-24000000000000002-22-2000000000000000000000000000000000000000000000000000000000000
χ1068-8-88-4-4800-4-4-84-844842-4-424-44-4-244-2000000000000002-22-2000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-400-4-444444-442222-22-22-2-2-2-20006i−6i00−6i6i00000-11-1100003i−3i−3i3i0000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-400-4-444444-442222-22-22-2-2-2-2000−6i6i006i−6i00000-11-110000−3i3i3i−3i0000000000000000000000000000000000000000000000000000

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