Finite Group Databasebeta

← Group #13172093

Character table — Group #13172093

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
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order12222233366666666633366666666666666666664444366666666666244412121212121212121212121212121212444466661212121212121212121212124444244412121212446121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111-11-11111111111111111-1-1-1-11111-1-11-1-1111-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1-111-1-1
χ311111111111111111111111111111111111111111111111111111111-11-111111111111111111-1-1-1-1-1-1-1-111-111-1-1-11111-1-1-1-1-11-11-1-1-1-1-1-1-1-111
χ411111111111111111111111111111111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1
χ51111111111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-11111111111111-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11-1-1111-1-1-1-11111-11-11-1-1-1-111-1-111
χ71111111111111111111111111111111111111111-1-1-1-1111111111111-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1111111111-11-1-1-1-1-11111-1-1
χ81111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111
χ91111-1-1111111111111111-1-1-1-1-1-1111-1-1-1-111111111-1-11-1-1-1-1111-1-1-1-111-1-111-1-111-1-11111-1-1-1-111-1-111111-1-1-11-1-1-111-1-11111-1-11111-1-1-1-1-111-1
χ101111-1-1111111111111111-1-1-1-1-1-1111-1-1-1-111111111-1-11-1-1-1-1111-1-1-1-11-1-1111-1-111-1-11111-1-1-1-1-1-1111111-11-11-1-1-1-1-1-111-1-1-1-1-111-1-1-11111-11-11
χ111111-1-1111111111111111-1-1-1-1-1-1111-1-1-1-111111111-1-11-1-1-1-1111-1-1-1-1-111-111-1-111-1-11111-1-1-1-1-1-111-1-1-1-11-11-1111111-1-1-1-1-1-11-1-11-1-111111-11-1
χ121111-1-1111111111111111-1-1-1-1-1-1111-1-1-1-111111111-1-11-1-1-1-1111-1-1-1-1-1-11111-1-111-1-11111-1-1-1-111-1-1-1-1-1-1-1111-1111-1-111111111-1-111-1-1-1-11-1-11
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χ914-44-4-44-2-24-2-422-4242-21-2-22-22-2-441-2222-2-222-1-1-2200001-112-2-11-1-1-1110000000000000000000000000000000000003i−3i−3i3i000000000000000000
χ924-44-4-44-2-24-2-422-4242-21-2-22-22-2-441-2222-2-222-1-1-2200001-112-2-11-1-1-111000000000000000000000000000000000000−3i3i3i−3i000000000000000000
χ934-4-440044-2-4-2-44242-4-44-2-2000000-42-200002-2-44224i−4i00-2000022-200000000−2i2i004i−4i00−2i−2i2i2i000000000000000000000000000000000000000000
χ944-4-440044-2-4-2-44242-4-44-2-2000000-42-200002-2-4422−4i4i00-2000022-2000000002i−2i00−4i4i002i2i−2i−2i000000000000000000000000000000000000000000
χ954-4-44004-24-442-2-44-4-42-24-20000002-4400002-22-22-40000-2000022-20000000000000000000000004i−4i00000000000000000000000000−2i2i00000000
χ964-4-44004-24-442-2-44-4-42-24-20000002-4400002-22-22-40000-2000022-2000000000000000000000000−4i4i000000000000000000000000002i−2i00000000
χ974-4-4400-24424-44-4-2-42-4-2-2400000022-20000-442-2-424i−4i00-2000022-2000000004i−4i00−2i2i00−2i−2i2i2i000000000000000000000000000000000000000000
χ984-4-4400-24424-44-4-2-42-4-2-2400000022-20000-442-2-42−4i4i00-2000022-200000000−4i4i002i−2i002i2i−2i−2i000000000000000000000000000000000000000000
χ994-4-4400-24-22-2-442-222-4-21-20000002-113-3-332-22-22-14i−4i0010000-1-113-3-330000−2i2i00−2i2i00ii−i−i3i−3i−3i3i00000000000000000000000000000000000000
χ1004-4-4400-24-22-2-442-222-4-21-20000002-113-3-332-22-22-1−4i4i0010000-1-113-3-3300002i−2i002i−2i00−i−iii−3i3i3i−3i00000000000000000000000000000000000000
χ1014-4-4400-24-22-2-442-222-4-21-20000002-11-333-32-22-22-14i−4i0010000-1-11-333-30000−2i2i00−2i2i00ii−i−i−3i3i3i−3i00000000000000000000000000000000000000
χ1024-4-4400-24-22-2-442-222-4-21-20000002-11-333-32-22-22-1−4i4i0010000-1-11-333-300002i−2i002i−2i00−i−iii3i−3i−3i3i00000000000000000000000000000000000000
χ103888888-4-4-4-4-4-4-4-4-4-4-4-4222-4-4-4-4-4-422222222222220000-12222-1-1-1-1-1-1-10000000000000000000000000000000000000000000000000000000000
χ1048888-8-8-4-4-4-4-4-4-4-4-4-4-4-4222444444222-2-2-2-22222220000-1-2-2-2-2-1-1-111110000000000000000000000000000000000000000000000000000000000
χ10588-8-8008-4-4-84-44-4-8484-4-4200000044400002-2-44-2-40000200002-2-200000000000000000000000000000000000000000000000000000000000000
χ10688-8-800-4-484-8-4484-8-442-4-4000000-2440000-442-24-40000200002-2-200000000000000000000000000000000000000000000000000000000000000
χ10788-8-800-4-4-444-44-444-44222000000-2-2-26-66-62-22-2-220000-10000-111-33-330000000000000000000000000000000000000000000000000000000000
χ10888-8-800-4-4-444-44-444-44222000000-2-2-2-66-662-22-2-220000-10000-1113-33-30000000000000000000000000000000000000000000000000000000000
χ1098-88-88-8-4-4-4-444444-44-4222-44-44-4422-222-2-2-2-2-2-22-20000-12-22-21-11-1-1110000000000000000000000000000000000000000000000000000000000
χ1108-88-8-88-4-4-4-444444-44-42224-44-44-422-2-2-222-2-2-2-22-20000-1-22-221-1111-1-10000000000000000000000000000000000000000000000000000000000
χ1118-8-88008-4-4-8-44-4484-84-4-4200000044-40000-224-4-24000020000-2-2200000000000000000000000000000000000000000000000000000000000000
χ1128-8-8800-4-48484-4-8-4-8442-4-4000000-24-400004-4-2244000020000-2-2200000000000000000000000000000000000000000000000000000000000000
χ1138-8-8800-4-4-44-44-44-4444222000000-2-226-6-66-22-22-2-20000-1000011-1-333-30000000000000000000000000000000000000000000000000000000000
χ1148-8-8800-4-4-44-44-44-4444222000000-2-22-666-6-22-22-2-20000-1000011-13-3-330000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).