Finite Group Databasebeta

← Group #13170642

Character table — Group #13170642

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
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order123334666333666121212121224661212361212121222666666612121266666624668121224248226664666666666121212121224661212661212121222666666612121266666624668121224248
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1111-1-1111111-111-1-1-11-1-1-111-1-1-1111111111111111111111111111111111-1111-1-1111111-111-1-1-11-1-1-111-1-1-1
χ311111111111111111111111111111111-111-1-11111111-11-1-1111-111-1-1-1-1-1-111111111111111111111111111111111-111-1-11111111-11-1-1111-111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-11-1-111111111111111111111111111111111111-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-11-1-1111
χ511111111111111111111-1-1-1-1-1-111111111-11111-1-1-1-1-1111111-1-1-1-11-1-111-111111111111111111111-1-1-1-1-1-111111111-11111-1-1-1-1-1111111-1-1-1-11-1-111-1
χ611111111111111111111-1-1-1-1-1-11111111-1-111-1-1-1-1-1-1-11-111-1-11-111-1-1-1-1-1111111111111111111111-1-1-1-1-1-11111111-1-111-1-1-1-1-1-1-11-111-1-11-111-1-1-1-1-11
χ711111111111111111111-1-1-1-1-1-1111111-11-1-1-111-1-1-1-1-1-11-1-111-11-1-1-111-1-1111111111111111111111-1-1-1-1-1-1111111-11-1-1-111-1-1-1-1-1-11-1-111-11-1-1-111-1-11
χ811111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1
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χ22222-122-1222-1-1-1-122222-1000000-1-1-1-1-1-1-2-20-2-2-2-2000001111110000200-1-10222-122-1222-1-1-1-122222-1000000-1-1-1-1-1-1-2-20-2-2-2-2000001111110000200-1-10
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χ3644-24-244-2-21-2-2-2-21-2-211444-2-2-2-211-2-21100-2000011-211000000000000000044-24-244-2-21-2-2-2-21-2-211444-2-2-2-211-2-21100-2000011-2110000000000000000
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χ782222-1-22-12-12-12-1-11-211-2-221122-1-1-211100-200i3−i311-1-1-10000i3−i300−i3i3000000-2-2-2-212-21-21-21-211-12-1-122-2-1-1-2-2112-1-1-100200−i3i3-1-11110000−i3i300i3−i3000000
χ79222-122-1222-1-1-1-122222-1000000-1-1-1-1-1-1220222200000-1-1-1-1-1-10000200-1-10-2-2-21-2-21-2-2-21111-2-2-2-2-21000000111111-2-20-2-2-2-2000001111110000-200110
χ80222-122-1222-1-1-1-122222-1000000-1-1-1-1-1-12-2022-2-200000-11-1-1110000-200110-2-2-21-2-21-2-2-21111-2-2-2-2-21000000111111-220-2-222000001-111-1-10000200-1-10
χ81222-122-1222-1-1-1-122222-1000000-1-1-1-1-1-1-220-2-222000001-111-1-10000-200110-2-2-21-2-21-2-2-21111-2-2-2-2-210000001111112-2022-2-200000-11-1-1110000200-1-10
χ82222-122-1222-1-1-1-122222-1000000-1-1-1-1-1-1-2-20-2-2-2-2000001111110000200-1-10-2-2-21-2-21-2-2-21111-2-2-2-2-21000000111111220222200000-1-1-1-1-1-10000-200110
χ8322-122222-1-1-12-12-12-1-1-122222-1-1-1-1-12-1-120-1-1-100-1-12-1-120-1-10002000-1-1000-2-21-2-2-2-2-2111-21-21-2111-2-2-2-2-211111-211-201110011-211-2011000-200011000
χ8422-122222-1-1-12-12-12-1-1-122222-1-1-1-1-12-1-1-20-11100-1-12-1-1-2011000-200011000-2-21-2-2-2-2-2111-21-21-2111-2-2-2-2-211111-211201-1-10011-21120-1-10002000-1-1000
χ8522-122222-1-1-12-12-12-1-1-12-2-2-2-211-1-1-12-1-1201-1-10011-21120-1-1000-200011000-2-21-2-2-2-2-2111-21-21-2111-22222-1-1111-211-20-11100-1-12-1-1-20110002000-1-1000
χ8622-122222-1-1-12-12-12-1-1-12-2-2-2-211-1-1-12-1-1-201110011-211-20110002000-1-1000-2-21-2-2-2-2-2111-21-21-2111-22222-1-1111-21120-1-1-100-1-12-1-120-1-1000-200011000
χ8722-122-222-1-1-12-12-1-2111-22-22211-1-11-21100-1−i3i300-1-1-21100−i3i30000000−i3i3000-2-21-2-22-2-2111-21-212-1-1-12-22-2-2-1-111-12-1-1001i3−i300112-1-100i3−i30000000i3−i3000
χ8822-122-222-1-1-12-12-1-2111-22-22211-1-11-21100-1i3−i300-1-1-21100i3−i30000000i3−i3000-2-21-2-22-2-2111-21-212-1-1-12-22-2-2-1-111-12-1-1001−i3i300112-1-100−i3i30000000−i3i3000
χ8922-122-222-1-1-12-12-1-2111-2-22-2-2-1-1-1-11-211001−i3i300112-1-100−i3i30000000i3−i3000-2-21-2-22-2-2111-21-212-1-1-122-2221111-12-1-100-1i3−i300-1-1-21100i3−i30000000−i3i3000
χ9022-122-222-1-1-12-12-1-2111-2-22-2-2-1-1-1-11-211001i3−i300112-1-100i3−i30000000−i3i3000-2-21-2-22-2-2111-21-212-1-1-122-2221111-12-1-100-1−i3i300-1-1-21100−i3i30000000i3−i3000
χ91444-24-4-2444-2-2-2-24-4-4-4-42000000-2-222220000000000000000000000000000-4-4-42-442-4-4-42222-44444-200000022-2-2-2-20000000000000000000000000000
χ92444-2-24-2-24-2-21-21-2-24-2-2-200000011-211104000-2-2000000-200110000000000-4-4-422-422-422-12-122-4222000000-1-12-1-1-10-400022000000200-1-10000000000
χ93444-2-24-2-24-2-21-21-2-24-2-2-200000011-21110-400022000000200-1-10000000000-4-4-422-422-422-12-122-4222000000-1-12-1-1-104000-2-2000000-200110000000000
χ94444-2-2-4-2-24-2-21-21-22-4222000000112-1-1-100000−2i32i3000000000i3−i30000000000-4-4-422422-422-12-12-24-2-2-2000000-1-1-2111000002i3−2i3000000000−i3i30000000000
χ95444-2-2-4-2-24-2-21-21-22-4222000000112-1-1-1000002i3−2i3000000000−i3i30000000000-4-4-422422-422-12-12-24-2-2-2000000-1-1-211100000−2i32i3000000000i3−i30000000000
χ9644-24-244-2-21-2-2-2-21-2-211444-2-2-2-211-2-21100-2000011-2110000000000000000-4-42-42-4-422-12222-122-1-1-4-4-42222-1-122-1-10020000-1-12-1-10000000000000000
χ9744-24-244-2-21-2-2-2-21-2-2114-4-4222211-2-2110020000-1-12-1-10000000000000000-4-42-42-4-422-12222-122-1-1-444-2-2-2-2-1-122-1-100-2000011-2110000000000000000
χ9844-24-2-44-2-21-2-2-2-2122-1-1-44-4-2-2221122-1-100-20000112-1-10000000000000000-4-42-424-422-12222-1-2-2114-4422-2-2-1-1-2-2110020000-1-1-2110000000000000000
χ9944-24-2-44-2-21-2-2-2-2122-1-1-4-4422-2-21122-1-10020000-1-1-2110000000000000000-4-42-424-422-12222-1-2-21144-4-2-222-1-1-2-21100-20000112-1-10000000000000000
χ10044-2-244-24-2-21-21-2-24-2-2-2-2000000111-211400-2-20000000-2011000000000000-4-422-4-42-422-12-122-42222000000-1-1-12-1-1-40022000000020-1-1000000000000
χ10144-2-244-24-2-21-21-2-24-2-2-2-2000000111-211-40022000000020-1-1000000000000-4-422-4-42-422-12-122-42222000000-1-1-12-1-1400-2-20000000-2011000000000000
χ10244-2-24-4-24-2-21-21-2-2-4222200000011-12-1-1000−2i32i3000000000i3−i3000000000000-4-422-442-422-12-1224-2-2-2-2000000-1-11-2110002i3−2i3000000000−i3i3000000000000
χ10344-2-24-4-24-2-21-21-2-2-4222200000011-12-1-10002i3−2i3000000000−i3i3000000000000-4-422-442-422-12-1224-2-2-2-2000000-1-11-211000−2i32i3000000000i3−i3000000000000
χ1044-44440-4-4-4444-4-4-4000000000004-400000000000000000000000000000000-44-4-4-40444-4-4-444400000000000-4400000000000000000000000000000000
χ1054-444-20-42-4-24-2-4220000000−2i32i300-2200000000000−2i32i30000000000000000000-44-4-4204-242-424-2-200000002i3−2i3002-2000000000002i3−2i30000000000000000000
χ1064-444-20-42-4-24-2-42200000002i3−2i300-22000000000002i3−2i30000000000000000000-44-4-4204-242-424-2-20000000−2i32i3002-200000000000−2i32i30000000000000000000
χ1074-44-2402-4-44-2-222-400000000000-2200000000000000000000000000000i6−i60-44-42-40-244-422-2-24000000000002-200000000000000000000000000000−i6i60
χ1084-44-2402-4-44-2-222-400000000000-2200000000000000000000000000000−i6i60-44-42-40-244-422-2-24000000000002-200000000000000000000000000000i6−i60
χ1094-4-2440-4-42-2-242-4200000000023−23-220000000000000023−230000000000000000-442-4-4044-222-4-24-2000000000−23232-200000000000000−23230000000000000000
χ1104-4-2440-4-42-2-242-42000000000−2323-2200000000000000−23230000000000000000-442-4-4044-222-4-24-200000000023−232-20000000000000023−230000000000000000
χ1114-4-24-20-4221-2-222-1003i−3i000−2i32i323−231-1003i−3i0000000i3−i30−330000000000000000-442-4204-2-2-122-2-2100−3i3i0002i3−2i3−2323-1100−3i3i0000000−i3i303−30000000000000000
χ1124-4-24-20-4221-2-222-1003i−3i0002i3−2i3−23231-1003i−3i0000000−i3i303−30000000000000000-442-4204-2-2-122-2-2100−3i3i000−2i32i323−23-1100−3i3i0000000i3−i30−330000000000000000
χ1134-4-24-20-4221-2-222-100−3i3i000−2i32i3−23231-100−3i3i0000000i3−i303−30000000000000000-442-4204-2-2-122-2-21003i−3i0002i3−2i323−23-11003i−3i0000000−i3i30−330000000000000000
χ1144-4-24-20-4221-2-222-100−3i3i0002i3−2i323−231-100−3i3i0000000−i3i30−330000000000000000-442-4204-2-2-122-2-21003i−3i000−2i32i3−2323-11003i−3i0000000i3−i303−30000000000000000
χ11588-4-4-48-4-4-4222222-4-422-4000000-1-122-1-10000000000000000000000000000-8-8444-8444-2-2-2-2-2-244-2-2400000011-2-2110000000000000000000000000000
χ11688-4-4-4-8-4-4-422222244-2-24000000-1-1-2-2110000000000000000000000000000-8-84448444-2-2-2-2-2-2-4-422-40000001122-1-10000000000000000000000000000
χ1178-88-4-4044-8-4-424-24000000000002-200000000000000000000000000000000-88-8440-4-4844-2-42-400000000000-2200000000000000000000000000000000
χ1188-8-4-4804-84-42-4-244000000000002-200000000000000000000000000000000-8844-80-48-44-242-4-400000000000-2200000000000000000000000000000000
χ1198-8-4-4-40444222-2-2-2006i−6i0000000-1100−3i3i0000000000000000000000000000-884440-4-4-4-2-2-222200−6i6i00000001-1003i−3i0000000000000000000000000000
χ1208-8-4-4-40444222-2-2-200−6i6i0000000-11003i−3i0000000000000000000000000000-884440-4-4-4-2-2-2222006i−6i00000001-100−3i3i0000000000000000000000000000

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