Finite Group Databasebeta

← Group #13156653

Character table — Group #13156653

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
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order1222333446666666663336666666661212121212121212121288883666121212121212121224242424242424242424242424242424888844121212121212121212121212121212122424242444444412121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-11-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-111
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
χ71111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-11-1-111
χ81111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-11111-1-1-1-111111-111-1-1
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χ874-4-4444-200-4-42-44-4-2424-2-2422-2-422-4-20000000000−2i22i22i2−2i2-22-2200000000−2i22i22i2−2i2i2−i2−i2i2i2i2−i2−i2−i2−i2i2i2000000000000000000000000000000000000
χ884-4-4444-200-4-42-44-4-2424-2-2422-2-422-4-200000000002i2−2i2−2i22i2-22-22000000002i2−2i2−2i22i2−i2i2i2−i2−i2−i2i2i2i2i2−i2−i2000000000000000000000000000000000000
χ894-4-444-2400-42-4-4424-2-4-24-2-2-42-22-42240000000000−2i22i22i2−2i2-22-2200000000i2−i2−i2i2−2i22i22i2−2i2i2i2−i2−i2−i2−i2i2i2000000000000000000000000000000000000
χ904-4-444-2400-42-4-4424-2-4-24-2-2-42-22-422400000000002i2−2i2−2i22i2-22-2200000000−i2i2i2−i22i2−2i2−2i22i2−i2−i2i2i2i2i2−i2−i2000000000000000000000000000000000000
χ914-4-444-2-200-422-442-2-22-2-21-22-1122-12-20003i−3i00−3i3i0−2i22i22i2−2i21-11-10000−3i3i3i−3ii2−i2−i2i2i2−i2−i2i2ζ5−2ζ7+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
χ924-4-444-2-200-422-442-2-22-2-21-22-1122-12-20003i−3i00−3i3i02i2−2i2−2i22i21-11-10000−3i3i3i−3i−i2i2i2−i2−i2i2i2−i2−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
χ934-4-444-2-200-422-442-2-22-2-21-22-1122-12-2000−3i3i003i−3i0−2i22i22i2−2i21-11-100003i−3i−3i3ii2−i2−i2i2i2−i2−i2i2−2ζ5+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
χ944-4-444-2-200-422-442-2-22-2-21-22-1122-12-2000−3i3i003i−3i02i2−2i2−2i22i21-11-100003i−3i−3i3i−i2i2i2−i2−i2i2i2−i22ζ5−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
χ954-4-44-244002-4-42-2-444-4-2-24-22-4422-42-200000000000000-22-22000000000000000000000000−2i22i22i2−2i2000000000000000000i2−i2−i2i20000000000
χ964-4-44-244002-4-42-2-444-4-2-24-22-4422-42-200000000000000-22-220000000000000000000000002i2−2i2−2i22i2000000000000000000−i2i2i2−i20000000000
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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
χ9988-8-8-4-4-48-8-4-4-4444444222-2-2-2-2222-2-2-444-2-2-4-42240000-111-12-22-2-1-1110000000000000000000000000000000000000000000000000000
χ10088-8-8-4-4-4-88-4-4-4444444222-2-2-2-2222-2-24-4-42244-2-2-40000-111-1-22-2211-1-10000000000000000000000000000000000000000000000000000
χ1018-88-8-48-4004-84-4484-8-4-42-442-444-24-4-20000000000000022-2-2000000000000000000000000000000000000000000000000000000000000
χ1028-88-8-4-480044-8-44-4-8482-4-4-2-4-44-244240000000000000022-2-2000000000000000000000000000000000000000000000000000000000000
χ1038-88-8-4-4-400444-44-444-4222-222-2-2-2-22-20006i−6i006i−6i00000-1-1110000−3i3i−3i3i0000000000000000000000000000000000000000000000000000
χ1048-88-8-4-4-400444-44-444-4222-222-2-2-2-22-2000−6i6i00−6i6i00000-1-11100003i−3i3i−3i0000000000000000000000000000000000000000000000000000
χ1058-8-88-48-4004-844-4-8-484-42-4-4-24-44-2442000000000000002-22-2000000000000000000000000000000000000000000000000000000000000
χ1068-8-88-4-480044-84-448-4-82-4-4244-4-244-2-4000000000000002-22-2000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-4004444-44-4-442222-2-22-2-2-2-220006i−6i00−6i6i00000-11-1100003i−3i−3i3i0000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-4004444-44-4-442222-2-22-2-2-2-22000−6i6i006i−6i00000-11-110000−3i3i3i−3i0000000000000000000000000000000000000000000000000000

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