Finite Group Databasebeta

← Group #13156512

Character table — Group #13156512

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111222222222222224444444444444444444444666688888888888812121212121212121212121212121212181818182424242424242424242424242424242424243636363654545454727272727272
order122233344666666666333666666666121212121212121212128888366612121212121212122424242424242424242424242424242444444412121212121212121212121212121212121212128888226666
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
χ92222222-2-2222222222222222222222-2-2-2-2-2-2-2-2-2-200002222-2-2-2-2-2-2-2-2000000000000000022-2-200000000000000000022-2-20000000000
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χ12222222-1222-122-12-1222-1-12-1-1-12-1-12-1222-1-1-12-1-1-12222-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000-2001100-2-200001111000000000-20011
χ13222222-1222-122-12-1222-1-12-1-1-12-1-12-1222-1-1-12-1-1-1-2-2-2-2-1-1-1-122-1-1-1-1-1-1-2-2-2-211111111111100000200-1-100220000-1-1-1-1000000000-20011
χ14222222-1222-122-12-1222-1-12-1-1-12-1-12-1222-1-1-12-1-1-1-2-2-2-2-1-1-1-122-1-1-1-1-1-1-2-2-2-211111111111100000-2001100-2-200001111000000000200-1-1
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χ854-44-4-24400442-4-4-4-4-22-2-24-2-24-422-42200000000000000-2-2220000000000000000000000004-400000000000000000000-22000000000000
χ864-44-4-24400442-4-4-4-4-22-2-24-2-24-422-42200000000000000-2-222000000000000000000000000-44000000000000000000002-2000000000000
χ874-4-4444-200-42-4-424-2-444-2-2-422-2-4224-2000000000022−22−2222-22-220000000022−22−2222−222−2−2−22222−2−2000000000000000000000000000000000000
χ884-4-4444-200-42-4-424-2-444-2-2-422-2-4224-20000000000−222222−22-22-2200000000−222222−222−2−2222−2−2−2−222000000000000000000000000000000000000
χ894-4-444-24002-4-42-4-24-44-24-22-42-22-42-24000000000022−22−2222-22-2200000000−222−222−22−2222−2−22222−2−2000000000000000000000000000000000000
χ904-4-444-24002-4-42-4-24-44-24-22-42-22-42-240000000000−222222−22-22-22000000002−2−22−222222−2222−2−2−2−222000000000000000000000000000000000000
χ914-4-444-2-20022-422-2-2-44-2-2122-1122-1-2-200003i−3i00−3i3i22−22−22221-11-10000−3i3i3i−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
χ924-4-444-2-20022-422-2-2-44-2-2122-1122-1-2-200003i−3i00−3i3i−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
χ934-4-444-2-20022-422-2-2-44-2-2122-1122-1-2-20000−3i3i003i−3i22−22−22221-11-100003i−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
χ944-4-444-2-20022-422-2-2-44-2-2122-1122-1-2-20000−3i3i003i−3i−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
χ954-4-44-24400-4-42-4-4442-2-2-2422-4422-4-2-200000000000000-22-22000000000000000000000000004-400000000000000000000-220000000000
χ964-4-44-24400-4-42-4-4442-2-2-2422-4422-4-2-200000000000000-22-2200000000000000000000000000-44000000000000000000002-20000000000
χ978888-4-4-488-4-4-4-4-4-4-4-4-4222222222222-4-4-4-422-4-4220000-1-1-1-12222-1-1-1-10000000000000000000000000000000000000000000000000000
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
χ9988-8-8-4-4-48-844-4-4-44444222-2-2-2-2222-2-2-4444-2-2-4-4220000-111-12-22-2-1-1110000000000000000000000000000000000000000000000000000
χ10088-8-8-4-4-4-8844-4-4-44444222-2-2-2-2222-2-24-4-4-42244-2-20000-111-1-22-2211-1-10000000000000000000000000000000000000000000000000000
χ1018-88-8-48-4008-44-84-84-44-42-4-42-444-244-20000000000000022-2-2000000000000000000000000000000000000000000000000000000000000
χ1028-88-8-4-4800-4844-84-8-442-4-42-4-44-244-240000000000000022-2-2000000000000000000000000000000000000000000000000000000000000
χ1038-88-8-4-4-400-4-444444-44222222-2-2-2-2-2-200006i−6i006i−6i0000-1-1110000−3i3i−3i3i0000000000000000000000000000000000000000000000000000
χ1048-88-8-4-4-400-4-444444-44222222-2-2-2-2-2-20000−6i6i00−6i6i0000-1-11100003i−3i3i−3i0000000000000000000000000000000000000000000000000000
χ1058-8-88-48-400-844-848-44-4-42-44-24-44-24-42000000000000002-22-2000000000000000000000000000000000000000000000000000000000000
χ1068-8-88-4-48004-844-8-484-42-4-4-244-4-2442-4000000000000002-22-2000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-40044444-4-44-4222-2-2-22-2-2-22200006i−6i00−6i6i0000-11-1100003i−3i−3i3i0000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-40044444-4-44-4222-2-2-22-2-2-2220000−6i6i006i−6i0000-11-110000−3i3i3i−3i0000000000000000000000000000000000000000000000000000

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