Finite Group Databasebeta

← Group #13172300

Character table — Group #13172300

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size111122222222222222444444444444444444888888888888881212121212121212121212121212181818181818181824242424242424242424242424242424242424243636363636363636363636363636108108
order1222223336666666663336666666666666663666666666666622244466661212121222226666666666666612121212121212121212444466121212121212121224
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-111-1111111111111111111-1-11111-1-111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111-111-1111-1-111-1-1-1-1-1-1-1-1-1-11-11111-1-1111-11111-1-11111-1-1-1-11111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111-1-11-1-111-1-111-1-1-1-1-1-1-1-1-1-11-1-1-111-1-1-1-11-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1111111
χ511111111111111111111111111111111111111111111111111-111-111-1-111-1-111-1-1-1-1-1-1-1-1-1111-1-11111-1111-1-11111-1-111-1-1-1-1-1-11111-1-1
χ611111111111111111111111111111111111111111111111111-11-1-11-1-1-111-1-111-1-1-1-1-1-1-1-1-11-1-1-1-111-1-1-11-1-1-1-111-1-111-1-1-1-11111-1-1-1-111
χ711111111111111111111111111111111111111111111111111-1-11-1-11-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111
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
χ91111-1-1111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1111-1-1-1-1111-1-1-11111-1-1-1-111-1-111111111111111-1-1-1-1-1-1-1-1-1-11-11-1-1-111-1-111-1-1-11
χ101111-1-1111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1111-1-1-1-111-1-1-111111-1-1-1-111-1-1111111-1-11111-1-1-1-111-1-1-1-111-11-11-1-1-1-111-1-1111-1
χ111111-1-1111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1111-1-1-1-11-11-11-111-1-1-1-111-1-111-1-1-1-11-11111-1-111-11-1-1-1-111-1-11-1-111111-1-1-1-1111-1
χ121111-1-1111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1111-1-1-1-11-1-1-11111-1-1-1-111-1-111-1-1-1-11-1-1-111-1-1-1-1-1111-1-11111-111-111-1-11111-1-1-11
χ131111-1-1111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1111-1-1-1-1-1111-1-1-1-11111-1-1-1-111-1-1-1-1-1111-1-111111-1-1-111-1-1-1-1-111-111-1-11111-1-11-1
χ141111-1-1111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1111-1-1-1-1-11-11-11-1-11111-1-1-1-111-1-1-1-1-11-1-1-1-111-1-11-11111-1-1111-1-111111-1-1-1-111-11
χ151111-1-1111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1111-1-1-1-1-1-1111-1-1-1-1-1111111-1-11111-1-111-1-1-1-11111-1-11111-1-1-11-11-1-1-1-111-1-111-11
χ161111-1-1111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1111-1-1-1-1-1-1-1111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-111111111111-11-1-1-111-1-111-1-11-1
χ1722222222-122-1-122-1222-1-12222-1-122-1-1-1-12-1-1-122-1-1-1-1-1-1-1-1-1-1-1220220-1-1-1-1-1-1-1-12222-1-1-1-12200-1-1-1-1002200-1-1-1-1000000-1-10000000000
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χ1922222222-122-1-122-1222-1-12222-1-122-1-1-1-12-1-1-122-1-1-1-1-1-1-1-1-1-1-1-220-22011-1-111-1-1-2-2-2-21111-220011-1-100-220011-1-1000000110000000000
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χ242222222-122-1222-122-1-12-122-1-122-1-122-1-1-12-1-1-1-122-1-1-1-1-1-1-1-1-10-2-20-2-200-2-200-2-20000000001-2100111101-210011110022000000-1-1-1-100
χ25222222-122-1222-122-12-1-12-1-12222-1-1-1-122-1-12-1-1-1-1-122-1-1-1-1-1-1-12022022200220000000000-10-12-1-100-1-1-10-12-1-100-1-1220000-1-1-1-1000000
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χ27222222-122-1222-122-12-1-12-1-12222-1-1-1-122-1-12-1-1-1-1-122-1-1-1-1-1-1-1-202-202-2-200-2-2000000000010-121100-1-110-121100-1-1-2-200001111000000
χ28222222-122-1222-122-12-1-12-1-12222-1-1-1-122-1-12-1-1-1-1-122-1-1-1-1-1-1-1-20-2-20-2-2-200-2-20000000000101-2110011101-2110011220000-1-1-1-1000000
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χ312222-2-222-122-1-122-1222-1-1-2-2-2-21122-1-1-1-12-1-1-1-2-21111-1-1-11111-2202-2011-1-1-1-111-2-2221111-220011-1-1002-200-1-111000000-1-10000000000
χ322222-2-222-122-1-122-1222-1-1-2-2-2-21122-1-1-1-12-1-1-1-2-21111-1-1-11111-2-202201111-1-1-1-122-2-2-1-1-1-1-2-2001111002200-1-1-1-1000000110000000000
χ332222-2-22-122-1222-122-1-12-1-2-211-2-2-1-122-1-1-12-1-111-2-211-1-1-111110220-2-2002200-2-2000000000-12-100-1-1-1-101-21001111002-2000000-1-11100
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χ352222-2-22-122-1222-122-1-12-1-2-211-2-2-1-122-1-1-12-1-111-2-211-1-1-111110-2202-200-2-2002200000000012-10011-1-10-1-2100-1-11100-2200000011-1-100
χ362222-2-22-122-1222-122-1-12-1-2-211-2-2-1-122-1-1-12-1-111-2-211-1-1-111110-2-202200-2-200220000000001-210011110-12-100-1-1-1-1002-2000000-1-11100
χ372222-2-2-122-1222-122-12-1-1211-2-2-2-2-1-1-1-122-1-12-11111-2-2-1-1-11111202-20-22200-2-20000000000-10-12-1-100-1-1101-21100112-20000-1-111000000
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χ392222-2-2-122-1222-122-12-1-1211-2-2-2-2-1-1-1-122-1-12-11111-2-2-1-1-11111-20220-2-2-20022000000000010-121100-1-1-101-2-1-10011-22000011-1-1000000
χ402222-2-2-122-1222-122-12-1-1211-2-2-2-2-1-1-1-122-1-12-11111-2-2-1-1-11111-20-2202-2-200220000000000101-2110011-10-12-1-100-1-12-20000-1-111000000
χ412-2-222-2222-2-2-2-2222-2-22222-22-22-2-2-2-2-2-2-222222-22-22-22-2-222-2-2000000000000002-22-222-2-20000000000000000000000002-20000000000
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χ432-2-222-222-1-2-21122-1-2-22-1-12-22-2-11-2-211112-1-1-12-2-11-11-111-1-111000000−i3i3−i3i3−i3i3−i3i32-22-2-1-1110000−i3i3−i3i3000000−i3i3−i3i3000000-110000000000
χ442-2-222-222-1-2-21122-1-2-22-1-12-22-2-11-2-211112-1-1-12-2-11-11-111-1-111000000−i3i3i3−i3−i3i3i3−i3-22-2211-1-10000−i3i3i3−i3000000−i3i3i3−i30000001-10000000000
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χ482-2-22-22222-2-2-2-2222-2-2222-22-22-22-2-2-2-2-2-22222-22-22-222-2-2-2-22200000000000000-222-2-2-2220000000000000000000000002-20000000000
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χ934-4-44-44-2-2422-4-4-2-24221-2-22-22-2-44-1-122221-2-21-112-22-21-1-1-1-1110000000000000000000000000000003-300000000-330000000000000000
χ944-4-44-44-2-2422-4-4-2-24221-2-22-22-2-44-1-122221-2-21-112-22-21-1-1-1-111000000000000000000000000000000-33000000003-30000000000000000
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
χ9788-8-8008-4-484-44-844-8-4-4-42000000-44-442-244-22000000-22-200000000000000000000000000000000000000000000000000000000000000
χ9888-8-800-48-4-4-8-444-8448-42-4000000-442-2-444-242000000-22-200000000000000000000000000000000000000000000000000000000000000
χ9988-8-800-4-48-448-844-84-42-4-40000002-2-44-44-2442000000-22-200000000000000000000000000000000000000000000000000000000000000
χ10088-8-800-4-4-4-44-444444-42220000002-22-22-2-2-2-2-10000001-11−3i33i3−3i33i30000000000000000000000000000000000000000000000000000000000
χ10188-8-800-4-4-4-44-444444-42220000002-22-22-2-2-2-2-10000001-113i3−3i33i3−3i30000000000000000000000000000000000000000000000000000000000
χ1028-88-8008-4-4-8-44-4-84484-4-420000004-44-4-2244-22000000-2-2200000000000000000000000000000000000000000000000000000000000000
χ1038-88-800-48-4484-44-84-4-8-42-40000004-4-224-44-242000000-2-2200000000000000000000000000000000000000000000000000000000000000
χ1048-88-800-4-484-4-8844-8-442-4-4000000-224-44-4-2442000000-2-2200000000000000000000000000000000000000000000000000000000000000
χ1058-88-800-4-4-44-44-4444-44222000000-22-22-22-2-2-2-100000011-1−3i33i33i3−3i30000000000000000000000000000000000000000000000000000000000
χ1068-88-800-4-4-44-44-4444-44222000000-22-22-22-2-2-2-100000011-13i3−3i3−3i33i30000000000000000000000000000000000000000000000000000000000
χ1078-8-888-8-4-4-44444-4-4-444222-44-44-44-2-2-2-2-2-2222-12-22-22-2-111-1-1110000000000000000000000000000000000000000000000000000000000
χ1088-8-88-88-4-4-44444-4-4-4442224-44-44-4-2-2-2-2-2-2222-1-22-22-22-11111-1-10000000000000000000000000000000000000000000000000000000000

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