Finite Group Databasebeta

← Group #13172354

Character table — Group #13172354

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size111122222222222222444444444444444444888888888888881212121212121212121212121212181818181818181824242424242424242424242424242424242424243636363636363636363636363636108108
order12222233366666666633366666666666666636666666666666224444661212121212124444121212126666666121212121212121212121212122244666612121212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1
χ3111111111111111111111111111111111111111111111111111-11-11111111111111111111-1-111-1-1-1111-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ4111111111111111111111111111111111111111111111111111-11-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-1-11-111-1-1-1-1-1-111-1-11111-1-1-1-1-1-111
χ511111111111111111111111111111111111111111111111111-11-1111-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-111111-11-1-111111111-1-11111-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111111111111111111111-11-11-1-1-1-1-1-1-1-1-1-111111111-111-1-1111-1-1-11-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-111-1-1-1-11111-1-111
χ811111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ91111-1-1111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1111-1-1-1-111-1-11-111-1-111-1-111-1-1-1-1-1-11111111-11-1-1-1-1-1-1-111-1-11-11-111-1-111-1-1111-1
χ101111-1-1111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1111-1-1-1-111-1-1-1111-1-1-1-111-1-11111111111111-1-11-1-1-1-1-1-1-1-111-111-1-1-11111-1-1-1-1-11
χ111111-1-1111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1111-1-1-1-11-1-111-111-1-111-1-111-1-1-1-1-1-11-1-111-1-111-1-11-1-11111-1-1-11-11-1-111-1-11111-11
χ121111-1-1111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1111-1-1-1-11-1-11-1111-1-1-1-111-1-11111111-1-111-1-11-11-11-1-111-1-1111-1-1111-1-1-1-111-1-11-1
χ131111-1-1111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1111-1-1-1-1-111-11-1-1-11111-1-1-1-1111111-111-1-111-11-11-111-1-111-1-11-1-1111-1-1-1-111-1-1-11
χ141111-1-1111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1111-1-1-1-1-111-1-11-1-111-1-11111-1-1-1-1-1-1-111-1-111-1-111-111-1-1-1-111-11-11-1-111-1-111111-1
χ151111-1-1111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1111-1-1-1-1-1-1111-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-111-111111111-1-1-111-1-1-11111-1-1-1-11-1
χ161111-1-1111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1111-1-1-1-1-1-111-11-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-11111111-1-1111-11-111-1-111-1-111-11
χ1722222222-1222-1-1-1222-12-12222-1-1-122-1-1-1-12-1-1-1-122-1-1-1-1-1-1-1-1-1020222000022220000000002-100-1-1-1-1-10200-1-1-1-1-1-12200-1-1-1-100000000
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χ1922222222-1222-1-1-1222-12-12222-1-1-122-1-1-1-12-1-1-1-122-1-1-1-1-1-1-1-1-10-20-22200002222000000000-2100111-1-10-20011-1-1-1-1-2-200111100000000
χ2022222222-1222-1-1-1222-12-12222-1-1-122-1-1-1-12-1-1-1-122-1-1-1-1-1-1-1-1-10-20-2-2-20000-2-2-2-2000000000-2100111110-2001111112200-1-1-1-100000000
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χ27222222-1222-1-122222-1-1-12-1-12222-1-1-122-1-1-12-1-1-1-1-122-1-1-1-1-1-1-1-20-20221111-1-1-1-1-2-2-2-21111-2001100022-201100-1-1-1-10000000000001100
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χ292222-2-222-1222-1-1-1222-12-1-2-2-2-211-122-1-1-1-12-1-111-2-211-1-1-11111020-22-2000022-2-20000000002-100-1-11-110-20011-1-1112-200-1-11100000000
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χ322222-2-222-1222-1-1-1222-12-1-2-2-2-211-122-1-1-1-12-1-111-2-211-1-1-111110-202-220000-2-222000000000-210011-11-10200-1-111-1-12-200-1-11100000000
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χ362222-2-22-12-122222-1-122-1-1-2-211-2-22-1-1-1-122-1-1-1-2-21111-1-1-11111-2-22200-2-22200000000000011-21111200-1-1-1-1-1-10000002-20000-1-1110000
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χ392222-2-2-1222-1-122222-1-1-1211-2-2-2-2-1-1-122-1-1-12-11111-2-2-1-1-11111-20202-211-1-1-1-111-2-222-1-1-1-1-200110002-220-1-100-1-1110000000000001100
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χ4122-2-22-2222-22-22-2-22-2-22222-22-22-22-2-2-2-2-2-22222-22-22-22-2-222-2-2000000000000002i−2i2i−2i2i2i−2i−2i000000000000000000000000000000002i−2i00
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χ4322-2-22-2-122-2-112-2-22-21-1-12-112-22-2-111-2-211-12-1-11-112-2-111-1-111000000−i3i3−i3i33−33−32i−2i2i−2i−i−iii000−i3i30000000−i3i3003−33−3000000000000−ii00
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χ944-4-4400-244-42-2-4-44-442-2-2400000022-2-442-22-4-200000022-20000000000000000000000−232323−23000000000000000000000000000000000000
χ95888888-4-4-4-4-4-4-4-4-4-4-4-4222-4-4-4-4-4-4222222222-1222222-1-1-1-1-1-1-10000000000000000000000000000000000000000000000000000000000
χ968888-8-8-4-4-4-4-4-4-4-4-4-4-4-4222444444222222222-1-2-2-2-2-2-2-1-1-111110000000000000000000000000000000000000000000000000000000000
χ9788-8-88-8-4-4-44-44-444-444222-44-44-442-2-2-2-2-2-222-12-22-22-2-111-1-1110000000000000000000000000000000000000000000000000000000000
χ9888-8-8-88-4-4-44-44-444-4442224-44-44-42-2-2-2-2-2-222-1-22-22-22-11111-1-10000000000000000000000000000000000000000000000000000000000
χ998-88-8008-4-4-4-8-84-44448-4-420000004-442-2-444-22000000-22-200000000000000000000000000000000000000000000000000000000000000
χ1008-88-800-48-48444-44-8-8-42-4-4000000-2-44-442-2442000000-22-200000000000000000000000000000000000000000000000000000000000000
χ1018-88-800-4-48-444-88-844-4-42-400000042-2-44-44-242000000-22-200000000000000000000000000000000000000000000000000000000000000
χ1028-88-800-4-4-4-4444-4444-4222000000-22-22-22-2-2-2-10000001-11−3i33i3−3i33i30000000000000000000000000000000000000000000000000000000000
χ1038-88-800-4-4-4-4444-4444-4222000000-22-22-22-2-2-2-10000001-113i3−3i33i3−3i30000000000000000000000000000000000000000000000000000000000
χ1048-8-88008-4-44-8844-44-4-8-4-4200000044-4-224-44-22000000-2-2200000000000000000000000000000000000000000000000000000000000000
χ1058-8-8800-48-4-84-444-4-8842-4-4000000-24-44-4-22442000000-2-2200000000000000000000000000000000000000000000000000000000000000
χ1068-8-8800-4-4844-4-8-884-44-42-40000004-224-44-4-242000000-2-2200000000000000000000000000000000000000000000000000000000000000
χ1078-8-8800-4-4-444-444-44-44222000000-2-22-22-22-2-2-100000011-1−3i33i33i3−3i30000000000000000000000000000000000000000000000000000000000
χ1088-8-8800-4-4-444-444-44-44222000000-2-22-22-22-2-2-100000011-13i3−3i3−3i33i30000000000000000000000000000000000000000000000000000000000

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