Finite Group Databasebeta

← Group #13170593

Character table — Group #13170593

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126
size112222244444412121212121218182244444888888242424242424363633666661212121212123636363636365454112222244444412121212121218182244444888888242424242424363633666661212121212123636363636365454
order1233466361212121244121212128836331266361212121212121212121224242266466661212121244121212128822664666612121212441212121288666612666612121212121212121212242422664666612121212441212121288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111-111-1-1-1-111111111111111-111-1-1-1-111111111111111-111-1-1-1-111111111111111-111-1-1-1-111111111111111-111-1-1-1-111111111111111-111-1-1-1-1
χ31111111111111-11-1-111-1-11111111111111-11-1-111-1-11111111111111-11-1-111-1-11111111111111-11-1-111-1-11111111111111-11-1-111-1-11111111111111-11-1-111-1-1
χ41111111111111-1-1-1-1-1-1111111111111111-1-1-1-1-1-1111111111111111-1-1-1-1-1-1111111111111111-1-1-1-1-1-1111111111111111-1-1-1-1-1-1111111111111111-1-1-1-1-1-111
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χ6222-122-1-1-12-1-1-10200-1-100222-122-1-1-12-1-1-10200-1-100222-122-1-1-12-1-1-10200-1-100222-122-1-1-12-1-1-10200-1-100222-122-1-1-12-1-1-10200-1-100222-122-1-1-12-1-1-10200-1-100
χ7222-122-1-1-12-1-1-10-2001100222-122-1-1-12-1-1-10-2001100222-122-1-1-12-1-1-10-2001100222-122-1-1-12-1-1-10-2001100222-122-1-1-12-1-1-10-2001100222-122-1-1-12-1-1-10-2001100
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χ9222-1-22-1-1-1-21110000i3−i300222-1-22-1-1-1-21110000i3−i300222-1-22-1-1-1-21110000i3−i300222-1-22-1-1-1-21110000i3−i300222-1-22-1-1-1-21110000i3−i300222-1-22-1-1-1-21110000i3−i300
χ1022-122-12-1-1-12-1-120-1-1000022-122-12-1-1-12-1-120-1-1000022-122-12-1-1-12-1-120-1-1000022-122-12-1-1-12-1-120-1-1000022-122-12-1-1-12-1-120-1-1000022-122-12-1-1-12-1-120-1-10000
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χ22111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ2311111111111111-111-1-1-1-111111111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111111111111111111-111-1-1-1-111111111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111
χ241111111111111-11-1-111-1-11111111111111-11-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1111111111111111-11-1-111-1-11111111111111-11-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-111
χ251111111111111-1-1-1-1-1-1111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111111111111-1-1-1-1-1-1111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ262222-22222-2-2-2-2000000002222-22222-2-2-2-200000000-2-2-2-22-2-2-2-22222000000002222-22222-2-2-2-2000000002222-22222-2-2-2-200000000-2-2-2-22-2-2-2-2222200000000
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χ3744-2-24-2-211-2-2110000000044-2-24-2-211-2-21100000000-4-422-422-1-122-1-10000000044-2-24-2-211-2-2110000000044-2-24-2-211-2-21100000000-4-422-422-1-122-1-100000000
χ3844-2-2-4-2-21122-1-10000000044-2-2-4-2-21122-1-100000000-4-422422-1-1-2-2110000000044-2-2-4-2-21122-1-10000000044-2-2-4-2-21122-1-100000000-4-422422-1-1-2-21100000000
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χ7622-12-2-12-1-11-21100i3−i3000022-12-2-12-1-11-21100i3−i3000022-12-2-12-1-11-21100i3−i30000-2-21-221-211-12-1-100−i3i30000-2-21-221-211-12-1-100−i3i30000-2-21-221-211-12-1-100−i3i30000
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χ782-2220-2-22-20000000000−222-2220-2-22-20000000000−222-2220-2-22-20000000000−22-22-2-2022-2200000000002−2-22-2-2022-2200000000002−2-22-2-2022-2200000000002−2
χ7944-2-24-2-211-2-2110000000044-2-24-2-211-2-2110000000044-2-24-2-211-2-21100000000-4-422-422-1-122-1-100000000-4-422-422-1-122-1-100000000-4-422-422-1-122-1-100000000
χ8044-2-2-4-2-21122-1-10000000044-2-2-4-2-21122-1-10000000044-2-2-4-2-21122-1-100000000-4-422422-1-1-2-21100000000-4-422422-1-1-2-21100000000-4-422422-1-1-2-21100000000
χ814-44-20-42-220000000000004-44-20-42-220000000000004-44-20-42-22000000000000-44-4204-22-2000000000000-44-4204-22-2000000000000-44-4204-22-2000000000000
χ824-4-2402-4-220000000000004-4-2402-4-220000000000004-4-2402-4-22000000000000-442-40-242-2000000000000-442-40-242-2000000000000-442-40-242-2000000000000
χ834-4-2-20221-1003i−3i000000004-4-2-20221-1003i−3i000000004-4-2-20221-1003i−3i00000000-44220-2-2-1100−3i3i00000000-44220-2-2-1100−3i3i00000000-44220-2-2-1100−3i3i00000000
χ844-4-2-20221-100−3i3i000000004-4-2-20221-100−3i3i000000004-4-2-20221-100−3i3i00000000-44220-2-2-11003i−3i00000000-44220-2-2-11003i−3i00000000-44220-2-2-11003i−3i00000000
χ85111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111
χ8611111111111111-111-1-1-1-111111111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111111111111111111-111-1-1-1-1
χ871111111111111-11-1-111-1-11111111111111-11-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1111111111111111-11-1-111-1-1
χ881111111111111-1-1-1-1-1-1111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111111111111-1-1-1-1-1-111
χ892222-22222-2-2-2-2000000002222-22222-2-2-2-200000000-2-2-2-22-2-2-2-2222200000000-2-2-2-22-2-2-2-2222200000000-2-2-2-22-2-2-2-22222000000002222-22222-2-2-2-200000000
χ90222-122-1-1-12-1-1-10200-1-100222-122-1-1-12-1-1-10200-1-100-2-2-21-2-2111-21110-2001100-2-2-21-2-2111-21110-2001100-2-2-21-2-2111-21110-2001100222-122-1-1-12-1-1-10200-1-100
χ91222-122-1-1-12-1-1-10-2001100222-122-1-1-12-1-1-10-2001100-2-2-21-2-2111-21110200-1-100-2-2-21-2-2111-21110200-1-100-2-2-21-2-2111-21110200-1-100222-122-1-1-12-1-1-10-2001100
χ92222-1-22-1-1-1-21110000−i3i300222-1-22-1-1-1-21110000−i3i300-2-2-212-21112-1-1-10000i3−i300-2-2-212-21112-1-1-10000i3−i300-2-2-212-21112-1-1-10000i3−i300222-1-22-1-1-1-21110000−i3i300
χ93222-1-22-1-1-1-21110000i3−i300222-1-22-1-1-1-21110000i3−i300-2-2-212-21112-1-1-10000−i3i300-2-2-212-21112-1-1-10000−i3i300-2-2-212-21112-1-1-10000−i3i300222-1-22-1-1-1-21110000i3−i300
χ9422-122-12-1-1-12-1-120-1-1000022-122-12-1-1-12-1-120-1-10000-2-21-2-21-2111-211-20110000-2-21-2-21-2111-211-20110000-2-21-2-21-2111-211-2011000022-122-12-1-1-12-1-120-1-10000
χ9522-122-12-1-1-12-1-1-2011000022-122-12-1-1-12-1-1-20110000-2-21-2-21-2111-21120-1-10000-2-21-2-21-2111-21120-1-10000-2-21-2-21-2111-21120-1-1000022-122-12-1-1-12-1-1-20110000
χ9622-12-2-12-1-11-21100−i3i3000022-12-2-12-1-11-21100−i3i30000-2-21-221-211-12-1-100i3−i30000-2-21-221-211-12-1-100i3−i30000-2-21-221-211-12-1-100i3−i3000022-12-2-12-1-11-21100−i3i30000
χ9722-12-2-12-1-11-21100i3−i3000022-12-2-12-1-11-21100i3−i30000-2-21-221-211-12-1-100−i3i30000-2-21-221-211-12-1-100−i3i30000-2-21-221-211-12-1-100−i3i3000022-12-2-12-1-11-21100i3−i30000
χ982-2220-2-22-200000000002−22-2220-2-22-200000000002−2-22-2-2022-220000000000−22-22-2-2022-220000000000−22-22-2-2022-220000000000−222-2220-2-22-200000000002−2
χ992-2220-2-22-20000000000−222-2220-2-22-20000000000−22-22-2-2022-2200000000002−2-22-2-2022-2200000000002−2-22-2-2022-2200000000002−22-2220-2-22-20000000000−22
χ10044-2-24-2-211-2-2110000000044-2-24-2-211-2-21100000000-4-422-422-1-122-1-100000000-4-422-422-1-122-1-100000000-4-422-422-1-122-1-10000000044-2-24-2-211-2-21100000000
χ10144-2-2-4-2-21122-1-10000000044-2-2-4-2-21122-1-100000000-4-422422-1-1-2-21100000000-4-422422-1-1-2-21100000000-4-422422-1-1-2-2110000000044-2-2-4-2-21122-1-100000000
χ1024-44-20-42-220000000000004-44-20-42-22000000000000-44-4204-22-2000000000000-44-4204-22-2000000000000-44-4204-22-20000000000004-44-20-42-22000000000000
χ1034-4-2402-4-220000000000004-4-2402-4-22000000000000-442-40-242-2000000000000-442-40-242-2000000000000-442-40-242-20000000000004-4-2402-4-22000000000000
χ1044-4-2-20221-1003i−3i000000004-4-2-20221-1003i−3i00000000-44220-2-2-1100−3i3i00000000-44220-2-2-1100−3i3i00000000-44220-2-2-1100−3i3i000000004-4-2-20221-1003i−3i00000000
χ1054-4-2-20221-100−3i3i000000004-4-2-20221-100−3i3i00000000-44220-2-2-11003i−3i00000000-44220-2-2-11003i−3i00000000-44220-2-2-11003i−3i000000004-4-2-20221-100−3i3i00000000
χ106222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2111111111111111111111000000000000000000000
χ10722222222222222-222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111000000000000000000000-2-2-2-2-2-2-2-2-2-2-2-2-2-22-2-2222211111111111111-111-1-1-1-1000000000000000000000
χ1082222222222222-22-2-222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-111000000000000000000000-2-2-2-2-2-2-2-2-2-2-2-2-22-222-2-2221111111111111-11-1-111-1-1000000000000000000000
χ1092222222222222-2-2-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1000000000000000000000-2-2-2-2-2-2-2-2-2-2-2-2-2222222-2-21111111111111-1-1-1-1-1-111000000000000000000000
χ1104444-44444-4-4-4-400000000-2-2-2-22-2-2-2-2222200000000000000000000000000000-4-4-4-44-4-4-4-44444000000002222-22222-2-2-2-200000000000000000000000000000
χ111444-244-2-2-24-2-2-20400-2-200-2-2-21-2-2111-21110-2001100000000000000000000000-4-4-42-4-4222-42220-4002200222-122-1-1-12-1-1-10200-1-100000000000000000000000
χ112444-244-2-2-24-2-2-20-4002200-2-2-21-2-2111-21110200-1-100000000000000000000000-4-4-42-4-4222-42220400-2-200222-122-1-1-12-1-1-10-2001100000000000000000000000
χ113444-2-44-2-2-2-42220000−2i32i300-2-2-212-21112-1-1-10000i3−i300000000000000000000000-4-4-424-42224-2-2-200002i3−2i300222-1-22-1-1-1-21110000−i3i300000000000000000000000
χ114444-2-44-2-2-2-422200002i3−2i300-2-2-212-21112-1-1-10000−i3i300000000000000000000000-4-4-424-42224-2-2-20000−2i32i300222-1-22-1-1-1-21110000i3−i300000000000000000000000
χ11544-244-24-2-2-24-2-240-2-20000-2-21-2-21-2111-211-20110000000000000000000000000-4-42-4-42-4222-422-4022000022-122-12-1-1-12-1-120-1-10000000000000000000000000
χ11644-244-24-2-2-24-2-2-40220000-2-21-2-21-2111-21120-1-10000000000000000000000000-4-42-4-42-4222-42240-2-2000022-122-12-1-1-12-1-1-20110000000000000000000000000
χ11744-24-4-24-2-22-42200−2i32i30000-2-21-221-211-12-1-100i3−i30000000000000000000000000-4-42-442-422-24-2-2002i3−2i3000022-12-2-12-1-11-21100−i3i30000000000000000000000000
χ11844-24-4-24-2-22-422002i3−2i30000-2-21-221-211-12-1-100−i3i30000000000000000000000000-4-42-442-422-24-2-200−2i32i3000022-12-2-12-1-11-21100i3−i30000000000000000000000000
χ1194-4440-4-44-4000000000022−22-22-2-2022-220000000000−22000000000000000000000-44-4-4044-440000000000−22222-2220-2-22-200000000002−2000000000000000000000
χ1204-4440-4-44-40000000000−2222-22-2-2022-2200000000002−2000000000000000000000-44-4-4044-44000000000022−222-2220-2-22-20000000000−22000000000000000000000
χ12188-4-48-4-422-4-42200000000-4-422-422-1-122-1-100000000000000000000000000000-8-844-844-2-244-2-20000000044-2-24-2-211-2-21100000000000000000000000000000
χ12288-4-4-8-4-42244-2-200000000-4-422422-1-1-2-21100000000000000000000000000000-8-844844-2-2-4-4220000000044-2-2-4-2-21122-1-100000000000000000000000000000
χ1238-88-40-84-44000000000000-44-4204-22-2000000000000000000000000000000000-88-8408-44-40000000000004-44-20-42-22000000000000000000000000000000000
χ1248-8-4804-8-44000000000000-442-40-242-2000000000000000000000000000000000-884-80-484-40000000000004-4-2402-4-22000000000000000000000000000000000
χ1258-8-4-40442-2006i−6i00000000-44220-2-2-1100−3i3i00000000000000000000000000000-88440-4-4-2200−6i6i000000004-4-2-20221-1003i−3i00000000000000000000000000000
χ1268-8-4-40442-200−6i6i00000000-44220-2-2-11003i−3i00000000000000000000000000000-88440-4-4-22006i−6i000000004-4-2-20221-100−3i3i00000000000000000000000000000

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