Finite Group Databasebeta

← Group #13156589

Character table — Group #13156589

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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χ914-4-444-2-2002-22-2-422-441-2-2-112-22-2-12200003i−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
χ924-4-444-2-2002-22-2-422-441-2-2-112-22-2-12200003i−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
χ934-4-444-2-2002-22-2-422-441-2-2-112-22-2-1220000−3i3i003i−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
χ944-4-444-2-2002-22-2-422-441-2-2-112-22-2-1220000−3i3i003i−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
χ954-4-44-24400-44-442-4-42-24-2-2-442-22-2-42200000000000000-22-220000000000000000000000004-400000000000000000000-22000000000000
χ964-4-44-24400-44-442-4-42-24-2-2-442-22-2-42200000000000000-22-22000000000000000000000000-44000000000000000000002-2000000000000
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
χ9988-8-8-4-4-48-84444-4-4-444222-2-2-2-2-2-2222-4444-2-2-4-4220000-111-12-22-2-1-1110000000000000000000000000000000000000000000000000000
χ10088-8-8-4-4-4-884444-4-4-444222-2-2-2-2-2-22224-4-4-42244-2-20000-111-1-22-2211-1-10000000000000000000000000000000000000000000000000000
χ1018-88-8-48-4008-8-444-84-44-4-42-44-442-244-20000000000000022-2-2000000000000000000000000000000000000000000000000000000000000
χ1028-88-8-4-4800-448-844-8-44-42-4-442-2-444-240000000000000022-2-2000000000000000000000000000000000000000000000000000000000000
χ1038-88-8-4-4-400-44-44444-442222-22-22-2-2-2-200006i−6i006i−6i0000-1-1110000−3i3i−3i3i0000000000000000000000000000000000000000000000000000
χ1048-88-8-4-4-400-44-44444-442222-22-22-2-2-2-20000−6i6i00−6i6i0000-1-11100003i−3i3i−3i0000000000000000000000000000000000000000000000000000
χ1058-8-88-48-400-884-44-844-4-4-424-44-4-2244-2000000000000002-22-2000000000000000000000000000000000000000000000000000000000000
χ1068-8-88-4-48004-4-8844-84-4-42-44-4-224-44-24000000000000002-22-2000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-4004-44-44444-4222-22-22-22-2-2-200006i−6i00−6i6i0000-11-1100003i−3i−3i3i0000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-4004-44-44444-4222-22-22-22-2-2-20000−6i6i006i−6i0000-11-110000−3i3i3i−3i0000000000000000000000000000000000000000000000000000

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