Finite Group Databasebeta

← Group #13155897

Character table — Group #13155897

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105
size111122222222222222444444444444444444444488888888888812121212121212121212121212121212121212122424242424242424242424242424242424363636363636363654547272727272108
order12223334466666666633366666666612121212121212121212366612121212121212124488242424242424242424242424242424244121212121212121212121212121212122288242424244446612122
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-111-1
χ3111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111-111-1-11
χ51111111111111111111111111111111111111111111111111111-1-111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-111-1-1-1
χ61111111111111111111111111111111111111111111111111111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-11
χ71111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1111
χ81111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111111-1
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χ13222222-122222-1-12-1222-1-122-1-1-1-1-1-12-122-1-1-12-1-12-1-1-1-1-1-122-1-1-1-100-2-2-2-2-2-2111111111111222-1-10000-1-1-1-10000-2-200000000011000
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χ914-4-44-2-244-4222-442-4-2-21-2-2-1-1222-2-221-4-22224-2-2-221-1-11-221-111-1-1-44000000000000000000000002-22-20000-1-1110000000000000000
χ924-4-44-2-24-44222-442-4-2-21-2-2-1-1222-2-22142-2-2-2-4222-21-1-112-2-11-1-1110000000000000000000000000000000003-3-330000000000000000
χ934-4-44-2-24-44222-442-4-2-21-2-2-1-1222-2-22142-2-2-2-4222-21-1-112-2-11-1-111000000000000000000000000000000000-333-30000000000000000
χ948888-4-4-488-4-4-4-4-4-4-4-4-4222222222222-4-4-422-4-422-4-1-1-1-12222-1-1-1-100000000000000000000000000000000000000000000000000000
χ958888-4-4-4-8-8-4-4-4-4-4-4-4-4-4222222222222444-2-244-2-24-1-1-1-1-2-2-2-2111100000000000000000000000000000000000000000000000000000
χ9688-8-88-4-400-88-4-44444-8-4-424-44-424-2-2400000000002-22-20000000000000000000000000000000000000000000000000000000000000
χ9788-8-8-4-48004-4-48-84-8442-4-4-224-4-4444-200000000002-22-20000000000000000000000000000000000000000000000000000000000000
χ9888-8-8-4-4-4004-4-4-444444222-22-222-2-2-2-20006i−6i006i−6i0-11-110000−3i3i−3i3i00000000000000000000000000000000000000000000000000000
χ9988-8-8-4-4-4004-4-4-444444222-22-222-2-2-2-2000−6i6i00−6i6i0-11-1100003i−3i3i−3i00000000000000000000000000000000000000000000000000000
χ1008-88-88-4-4008-8444-4-44-8-4-42-44-44-24-224000000000022-2-20000000000000000000000000000000000000000000000000000000000000
χ1018-88-8-4-4800-444-8-8-48442-4-42-2-44444-4-2000000000022-2-20000000000000000000000000000000000000000000000000000000000000
χ1028-88-8-4-4-400-44444-4-4442222-22-2-2-2-22-20006i−6i00−6i6i0-1-11100003i−3i−3i3i00000000000000000000000000000000000000000000000000000
χ1038-88-8-4-4-400-44444-4-4442222-22-2-2-2-22-2000−6i6i006i−6i0-1-1110000−3i3i3i−3i00000000000000000000000000000000000000000000000000000
χ1048-8-88-4-4-48-84444-444-4-4222-2-2-2-2-222-224-44-2-2-4-4224-111-12-22-2-1-11100000000000000000000000000000000000000000000000000000
χ1058-8-88-4-4-4-884444-444-4-4222-2-2-2-2-222-22-44-42244-2-2-4-111-1-22-2211-1-100000000000000000000000000000000000000000000000000000

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