Finite Group Databasebeta

← Group #13172239

Character table — Group #13172239

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size111122222222222222444444444444444444444466668888888888889999121212121212121212121212121212121212121212121212121212121818181818182424242424242424242424243636363636365454545472727272
order1222223336666666663336666666666666666666444436666666666644444444121212121212121212121212121212121212121212121212441212121212121212121212121212121244441212444412121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-11-11-11111-1-1-1-11111111111111111-1-1-1-1-1-11-11-11111-1-1-1-11-11-1-1-1-1-1-1-11-11-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-11-11-1-1-1-111111111111111111111-1-1-1-1-1-1-11-11-1-1-1-11111-11-11-1-1-1-1-1-1-11-11
χ51111111111111111111111111111111111111111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111
χ71111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-11-11-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-11111-1-1-1-1-11-11-1-11111-11-11
χ81111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-11-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-111111-11-1-1-111111-11-1
χ91111-1-1111111111111111-1-1-1-1-1-11111-1-1-1-11111111-1-11-1-1-1-1111-1-1-1-111111-1-1111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-11111-111-111-1-111-1-11-1-11-1-111-1-1-111-1
χ101111-1-1111111111111111-1-1-1-1-1-11111-1-1-1-11111111-1-11-1-1-1-1111-1-1-1-11111-111-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-111111-1-11-1-111-1-111-111-1-1-111-1-11-1-11
χ111111-1-1111111111111111-1-1-1-1-1-11111-1-1-1-11111111-1-11-1-1-1-1111-1-1-1-1-1-1-1-111-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111-1-111
χ121111-1-1111111111111111-1-1-1-1-1-11111-1-1-1-11111111-1-11-1-1-1-1111-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-11111-1-1
χ131111-1-1111111111111111-1-1-1-1-1-11111-1-1-1-111111-1-1111-1-1-1-1111-1-1-1-111111-1-1111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-11111-111-111-1-111-1-1-111-1-1-1-1-1111-1-11
χ141111-1-1111111111111111-1-1-1-1-1-11111-1-1-1-111111-1-1111-1-1-1-1111-1-1-1-11111-111-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-111111-1-11-1-111-1-1111-1-11-1-1-1-111-111-1
χ151111-1-1111111111111111-1-1-1-1-1-11111-1-1-1-111111-1-1111-1-1-1-1111-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111-1-1111111-1-111-1-1
χ161111-1-1111111111111111-1-1-1-1-1-11111-1-1-1-111111-1-1111-1-1-1-1111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-111-1-11111-1-1-1-111
χ1722222222-122-1-12222-12-1-12222-1-122-1-12222-1-1-1-120000-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1000000000000000022-1-1-1-12222-1-1-1-1-1-1-1-10000-1-100000000
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χ1922222222-122-1-12222-12-1-12222-1-122-1-12222-1-1-1-120000-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22-22-2-1-1-1-111110000000000000000-2-211112-22-2-1-1-1-1111100001100000000
χ2022222222-122-1-12222-12-1-12222-1-122-1-12222-1-1-1-120000-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-22-221111-1-1-1-10000000000000000-2-21111-22-221111-1-1-1-100001100000000
χ212222222-122-1222-12-12-12-122-1-122-1-12-1-1-1-1-122-1-1-12222-122-1-1-1-1-1-1-1-1-1000002020000222222-1-122-1-1-1-1-1-1-1-1-1-10000000-10-10000-1-1-1-102020000000-10-1
χ222222222-122-1222-12-12-12-122-1-122-1-12-1-1-1-1-122-1-1-12222-122-1-1-1-1-1-1-1-1-100000-20-20000-2-2-2-222-1-122-1-1-1-1-1-1-1-1-1-10000000101000011110-20-20000000101
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χ242222222-122-1222-12-12-12-122-1-122-1-12-1-1-1-1-122-1-1-1-2-2-2-2-122-1-1-1-1-1-1-1-1-100000-20-20000-2-2-2-2-2-211-2-2111111111100000001010000111102020000000-10-1
χ25222222-122-1222-12-122-1-12-1-12222-1-1-12-1-1-1-1-1-122-12222-1-1-122-1-1-1-1-1-1-10000202022220000-1-122-1-122-1-1-1-1-1-1-1-1000000-10-10-1-1-1-100002020000000-10-10
χ26222222-122-1222-12-122-1-12-1-12222-1-1-12-1-1-1-1-1-122-12222-1-1-122-1-1-1-1-1-1-10000-20-20-2-2-2-20000-1-122-1-122-1-1-1-1-1-1-1-1000000101011110000-20-200000001010
χ27222222-122-1222-12-122-1-12-1-12222-1-1-12-1-1-1-1-1-122-1-2-2-2-2-1-1-122-1-1-1-1-1-1-1000020202222000011-2-211-2-211111111000000-10-10-1-1-1-10000-20-200000001010
χ28222222-122-1222-12-122-1-12-1-12222-1-1-12-1-1-1-1-1-122-1-2-2-2-2-1-1-122-1-1-1-1-1-1-10000-20-20-2-2-2-2000011-2-211-2-2111111110000001010111100002020000000-10-10
χ292222-2-222-122-1-12222-12-1-1-2-2-2-21122-1-1-2-2-2-2-1-1-1-120000-11111-1-1-1111122222-2-22-1-111-1-1110000000000000000-2-2-1-1-1-1-222-2-1-111-1-11100001100000000
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χ312222-2-222-122-1-12222-12-1-1-2-2-2-21122-1-1-2-2-2-2-1-1-1-120000-11111-1-1-11111-2-2-2-222-2-2-1-11111-1-10000000000000000221111-2-222-1-11111-1-10000-1-100000000
χ322222-2-222-122-1-12222-12-1-1-2-2-2-21122-1-1-2-2-2-2-1-1-1-120000-11111-1-1-11111-2-2-2-2-2-22211-1-1-1-111000000000000000022111122-2-211-1-1-1-1110000-1-100000000
χ332222-2-22-122-1222-12-12-12-1-2-211-2-2-1-12-1111122-1-1-122-2-2-1-2-211-1-1-111110000020-20000-2-22222-1-1-2-211-1-1-1-11111000000010-1000011-1-1020-2000000010-1
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χ352222-2-22-122-1222-12-12-12-1-2-211-2-2-1-12-1111122-1-1-1-2-222-1-2-211-1-1-111110000020-20000-2-222-2-21122-1-11111-1-1-1-1000000010-1000011-1-10-2020000000-101
χ362222-2-22-122-1222-12-12-12-1-2-211-2-2-1-12-1111122-1-1-1-2-222-1-2-211-1-1-1111100000-202000022-2-2-2-21122-1-11111-1-1-1-10000000-1010000-1-111020-2000000010-1
χ372222-2-2-122-1222-12-122-1-1211-2-2-2-2-1-1-121111-1-122-122-2-2-111-2-2-1-1-11111000020-2022-2-20000-1-12211-2-2-1-1-1-1111100000010-10-1-111000020-2000000010-10
χ382222-2-2-122-1222-12-122-1-1211-2-2-2-2-1-1-121111-1-122-122-2-2-111-2-2-1-1-111110000-2020-2-2220000-1-12211-2-2-1-1-1-11111000000-101011-1-10000-2020000000-1010
χ392222-2-2-122-1222-12-122-1-1211-2-2-2-2-1-1-121111-1-122-1-2-222-111-2-2-1-1-11111000020-2022-2-2000011-2-2-1-1221111-1-1-1-100000010-10-1-1110000-2020000000-1010
χ402222-2-2-122-1222-12-122-1-1211-2-2-2-2-1-1-121111-1-122-1-2-222-111-2-2-1-1-111110000-2020-2-222000011-2-2-1-1221111-1-1-1-1000000-101011-1-1000020-2000000010-10
χ4122-2-22-222222-2-2-2-2-2-222222-22-22-22-22222-2-2-2-2-2-2-2000022-22-22-2-222-2-222-2-200000000000000000000000000002-222-2-200000000000000002-200000000
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χ1054-4-4400-2-2422-44-2-222-41-2-2000000-11223-3-332-22-2-1004i−4i10000-1-113-3-3300000000000000000000−2i2i−2i2i3i−3i−3i3iii−i−i00000000000000000000000000000000
χ1064-4-4400-2-2422-44-2-222-41-2-2000000-11223-3-332-22-2-100−4i4i10000-1-113-3-33000000000000000000002i−2i2i−2i−3i3i3i−3i−i−iii00000000000000000000000000000000
χ1074-4-4400-2-2422-44-2-222-41-2-2000000-1122-333-32-22-2-1004i−4i10000-1-11-333-300000000000000000000−2i2i−2i2i−3i3i3i−3iii−i−i00000000000000000000000000000000
χ1084-4-4400-2-2422-44-2-222-41-2-2000000-1122-333-32-22-2-100−4i4i10000-1-11-333-3000000000000000000002i−2i2i−2i3i−3i−3i3i−i−iii00000000000000000000000000000000
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χ1108888-8-8-4-4-4-4-4-4-4-4-4-4-4-42224444442222-2-2-2-2222220000-1-2-2-2-2-1-1-111110000000000000000000000000000000000000000000000000000000000000000
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χ11288-8-8-88-4-4-4-4-4444444-42224-44-44-42-222-2-222-2-2-2-2-20000-1-22-22-11111-1-10000000000000000000000000000000000000000000000000000000000000000
χ1138-88-8008-4-4-84-44-848-44-4-42000000444-20000-442-2-4000020000-22-200000000000000000000000000000000000000000000000000000000000000000000
χ1148-88-800-48-44-8-444-8-484-42-400000044-2400002-2-44-4000020000-22-200000000000000000000000000000000000000000000000000000000000000000000
χ1158-88-800-4-4-444-4444-4-44222000000-2-2-2-26-66-62-22-220000-100001-11-33-330000000000000000000000000000000000000000000000000000000000000000
χ1168-88-800-4-4-444-4444-4-44222000000-2-2-2-2-66-662-22-220000-100001-113-33-30000000000000000000000000000000000000000000000000000000000000000
χ1178-8-88008-4-4-844-48-4-844-4-420000004-44-200004-4-224000020000-2-2200000000000000000000000000000000000000000000000000000000000000000000
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χ1198-8-8800-4-4-4444-4-4-4444222000000-22-2-26-6-66-22-22-20000-1000011-1-333-30000000000000000000000000000000000000000000000000000000000000000
χ1208-8-8800-4-4-4444-4-4-4444222000000-22-2-2-666-6-22-22-20000-1000011-13-3-330000000000000000000000000000000000000000000000000000000000000000

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