Finite Group Databasebeta

← Group #13156651

Character table — Group #13156651

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111222222222222224444444444444444444444666688888888888812121212121212121212121212121212181818182424242424242424242424242424242424243636363654545454727272727272
order1222333446666666663336666666661212121212121212121288883666121212121212121224242424242424242424242424242424444444121212121212121212121212121212121212121288884412121212
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
χ3111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1
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
χ71111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-111-1-11111-1-1-1-1-1-1-1-11111-11-1-111
χ81111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-111-1-1-1-11111-1-1-1-111111-111-1-1
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χ13222222-12222-122-122-12-1-122-1-12-1-1-1-122-1-12222220000-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-22-222-2-2-1-111-1-1-1-1111111110000000000
χ14222222-12222-122-122-12-1-122-1-12-1-1-1-122-1-12222220000-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-2-22-2-22211-1-11111-1-1-1-111110000000000
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χ874-4-4444-200-4-42-4-4-24424-2-2-44-2-2-4222200000000000000-22-22000000000000000000000000004-4000000000000000000-22000000000000
χ884-4-4444-200-4-42-4-4-24424-2-2-44-2-2-4222200000000000000-22-2200000000000000000000000000-440000000000000000002-2000000000000
χ894-4-444-2400-42-4-4244-2-4-24-22-24-22-42-420000000000−2i22i22i2−2i2-22-2200000000−2i22i22i2−2i2i2−i2−i2i2i2i2−i2−i2−i2−i2i2i2000000000000000000000000000000000000
χ904-4-444-2400-42-4-4244-2-4-24-22-24-22-42-4200000000002i2−2i2−2i22i2-22-22000000002i2−2i2−2i22i2−i2i2i2−i2−i2−i2i2i2i2i2−i2−i2000000000000000000000000000000000000
χ914-4-44-244002-4-42-44-24-4-2-242-2-2422-42-40000000000−2i22i22i2−2i2-22-2200000000i2−i2−i2i2−2i22i22i2−2i2i2i2−i2−i2−i2−i2i2i2000000000000000000000000000000000000
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χ934-4-44-2-240022-4224-2-2-41-2-2-11-2-2-1222200003i−3i00−3i3i−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
χ944-4-44-2-240022-4224-2-2-41-2-2-11-2-2-1222200003i−3i00−3i3i2i2−2i2−2i22i21-11-10000−3i3i3i−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
χ954-4-44-2-240022-4224-2-2-41-2-2-11-2-2-122220000−3i3i003i−3i−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
χ964-4-44-2-240022-4224-2-2-41-2-2-11-2-2-122220000−3i3i003i−3i2i2−2i2−2i22i21-11-100003i−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
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χ988888-4-4-4-8-8-4-4-4-4-4-4-4-4-42222222222224444-2-244-2-20000-1-1-1-1-2-2-2-211110000000000000000000000000000000000000000000000000000
χ9988-8-8-4-4-48-8-4-4-4444444222-2-2-2-2222-2-244-44-2-2-4-4220000-111-12-22-2-1-1110000000000000000000000000000000000000000000000000000
χ10088-8-8-4-4-4-88-4-4-4444444222-2-2-2-2222-2-2-4-44-42244-2-20000-111-1-22-2211-1-10000000000000000000000000000000000000000000000000000
χ1018-88-88-4-400-8448-44-84-4-4-42-444-244-2-420000000000000022-2-2000000000000000000000000000000000000000000000000000000000000
χ1028-88-8-48-4004-84-4844-8-4-42-4-44-244-242-40000000000000022-2-2000000000000000000000000000000000000000000000000000000000000
χ1038-88-8-4-4-400444-4-4444-42222-2-2-2-2-2-22200006i−6i006i−6i0000-1-1110000−3i3i−3i3i0000000000000000000000000000000000000000000000000000
χ1048-88-8-4-4-400444-4-4444-42222-2-2-2-2-2-2220000−6i6i00−6i6i0000-1-11100003i−3i3i−3i0000000000000000000000000000000000000000000000000000
χ1058-8-888-4-400-844-84-48-44-4-424-4-4244-24-2000000000000002-22-2000000000000000000000000000000000000000000000000000000000000
χ1068-8-88-48-4004-844-8-4-484-42-44-42-44-24-24000000000000002-22-2000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-40044444-4-4-44222-2222-2-2-2-2-200006i−6i00−6i6i0000-11-1100003i−3i−3i3i0000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-40044444-4-4-44222-2222-2-2-2-2-20000−6i6i006i−6i0000-11-110000−3i3i3i−3i0000000000000000000000000000000000000000000000000000

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