Finite Group Databasebeta

← Group #13170645

Character table — Group #13170645

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size1122222224444444444466666688888812121212121212121212121224242424242436363636363636363610811222222244444444444666666888888121212121212121212121212242424242424363636363636363636108
order123334666333666121212121224661212361212121224666661212121212666121212226666824248226664666666666121212121224661212661212121224666661212121212666121212226666824248
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1111111-1-111111-1-1-11-1-1-111-1-1-1-1111111111111111111111111111111111-1111111-1-111111-1-1-11-1-1-111-1-1-1-1
χ311111111111111111111111111111111-111-1-11111111-1-1-1111-1111-1-1-1-1-1-111111111111111111111111111111111-111-1-11111111-1-1-1111-1111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-11-1-1111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111111111-1-11-1-1111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-1-1-111111111-111-1-1-111-1-1111111-1-1-1-1-1-1111-111111111111111111111-1-1-1-1-1-111111111-111-1-1-111-1-1111111-1-1-1-1-1-1111-1
χ611111111111111111111-1-1-1-1-1-11111111-1-111-1-1-1-1-1-1-1111-1-1-1-1111-1-1-1-1-1111111111111111111111-1-1-1-1-1-11111111-1-111-1-1-1-1-1-1-1111-1-1-1-1111-1-1-1-1-11
χ711111111111111111111-1-1-1-1-1-1111111-11-1-1-1-1-1-111-1-1-1-1-11111-1-1-111-1-1-1111111111111111111111-1-1-1-1-1-1111111-11-1-1-1-1-1-111-1-1-1-1-11111-1-1-111-1-1-11
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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χ2722-12222-12-12-1-12-12222-1000000-1-1-1-1-1-1220220002200-1-1-1-1-1-10000002-1-1022-12222-12-12-1-12-12222-1000000-1-1-1-1-1-1220220002200-1-1-1-1-1-10000002-1-10
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χ782222-1-2-1222-1-1-1-121-211-2-221122-1-11-21100-2i3−i311-100-1-10i3−i30000000−i3i30000-2-2-2-2121-2-2-21111-2-12-1-122-2-1-1-2-211-12-1-1002−i3i3-1-1100110−i3i30000000i3−i30000
χ79222-12222-1-1-122-1-12-1-1-122222-1-1-1-12-1-1-102-100-1-12-1-1-1-10002-1-102-1-1000000-2-2-21-2-2-2-2111-2-211-2111-2-2-2-2-21111-21110-210011-21111000-2110-211000000
χ80222-12222-1-1-122-1-12-1-1-122222-1-1-1-12-1-1-10-2-100-1-1211-1-1000-2110-211000000-2-2-21-2-2-2-2111-2-211-2111-2-2-2-2-21111-21110210011-2-1-1110002-1-102-1-1000000
χ81222-12222-1-1-122-1-12-1-1-12-2-2-2-211-1-12-1-1-10210011-2-1-1110002-1-10-211000000-2-2-21-2-2-2-2111-2-211-2111-22222-1-111-21110-2-100-1-1211-1-1000-21102-1-1000000
χ82222-12222-1-1-122-1-12-1-1-12-2-2-2-211-1-12-1-1-10-210011-21111000-21102-1-1000000-2-2-21-2-2-2-2111-2-211-2111-22222-1-111-211102-100-1-12-1-1-1-10002-1-10-211000000
χ83222-12-222-1-1-122-1-1-2111-22-22211-1-1-211100-100-1-1-2−i3i3110000−i3i300−i3i3000000-2-2-21-22-2-2111-2-2112-1-1-12-22-2-2-1-1112-1-1-100100112i3−i3-1-10000i3−i300i3−i3000000
χ84222-12-222-1-1-122-1-1-2111-22-22211-1-1-211100-100-1-1-2i3−i3110000i3−i300i3−i3000000-2-2-21-22-2-2111-2-2112-1-1-12-22-2-2-1-1112-1-1-100100112−i3i3-1-10000−i3i300−i3i3000000
χ85222-12-222-1-1-122-1-1-2111-2-22-2-2-1-1-1-1-211100100112−i3i3-1-10000−i3i300i3−i3000000-2-2-21-22-2-2111-2-2112-1-1-122-22211112-1-1-100-100-1-1-2i3−i3110000i3−i300−i3i3000000
χ86222-12-222-1-1-122-1-1-2111-2-22-2-2-1-1-1-1-211100100112i3−i3-1-10000i3−i300−i3i3000000-2-2-21-22-2-2111-2-2112-1-1-122-22211112-1-1-100-100-1-1-2−i3i3110000−i3i300i3−i3000000
χ8722-12222-12-12-1-12-12222-1000000-1-1-1-1-1-1220220002200-1-1-1-1-1-10000002-1-10-2-21-2-2-2-21-21-211-21-2-2-2-21000000111111-2-20-2-2000-2-200111111000000-2110
χ8822-12222-12-12-1-12-12222-1000000-1-1-1-1-1-12-2022000-2-200-1-1-1111000000-2110-2-21-2-2-2-21-21-211-21-2-2-2-21000000111111-220-2-20002200111-1-1-10000002-1-10
χ8922-12222-12-12-1-12-12222-1000000-1-1-1-1-1-1-220-2-20002200111-1-1-1000000-2110-2-21-2-2-2-21-21-211-21-2-2-2-210000001111112-2022000-2-200-1-1-11110000002-1-10
χ9022-12222-12-12-1-12-12222-1000000-1-1-1-1-1-1-2-20-2-2000-2-2001111110000002-1-10-2-21-2-2-2-21-21-211-21-2-2-2-21000000111111220220002200-1-1-1-1-1-1000000-2110
χ91444-2-24-24-2-21-2-21-2-2-211444-2-2-2-211-2-21100-20011-200110000000000000000-4-4-422-42-422-122-1222-1-1-4-4-42222-1-122-1-100200-1-1200-1-10000000000000000
χ92444-2-24-24-2-21-2-21-2-2-2114-4-4222211-2-21100200-1-1200-1-10000000000000000-4-4-422-42-422-122-1222-1-1-444-2-2-2-2-1-122-1-100-20011-200110000000000000000
χ93444-2-2-4-24-2-21-2-21-222-1-1-44-4-2-2221122-1-100-20011200-1-10000000000000000-4-4-42242-422-122-12-2-2114-4422-2-2-1-1-2-21100200-1-1-200110000000000000000
χ94444-2-2-4-24-2-21-2-21-222-1-1-4-4422-2-21122-1-100200-1-1-200110000000000000000-4-4-42242-422-122-12-2-21144-4-2-222-1-1-2-21100-20011200-1-10000000000000000
χ9544-244-44-24-24-2-24-2-4-4-4-42000000-2-222220000000000000000000000000000-4-42-4-44-42-42-422-424444-200000022-2-2-2-20000000000000000000000000000
χ9644-24-24-2-24-2-211-2-2-24-2-2-2000000111-211400-2-20000000-2110000000000000-4-42-42-422-422-1-1222-4222000000-1-1-12-1-1-4002200000002-1-10000000000000
χ9744-24-24-2-24-2-211-2-2-24-2-2-2000000111-211-4002200000002-1-10000000000000-4-42-42-422-422-1-1222-4222000000-1-1-12-1-1400-2-20000000-2110000000000000
χ9844-24-2-4-2-24-2-211-2-22-422200000011-12-1-1000−2i32i300000000i3−i30000000000000-4-42-42422-422-1-122-24-2-2-2000000-1-11-2110002i3−2i300000000−i3i30000000000000
χ9944-24-2-4-2-24-2-211-2-22-422200000011-12-1-10002i3−2i300000000−i3i30000000000000-4-42-42422-422-1-122-24-2-2-2000000-1-11-211000−2i32i300000000i3−i30000000000000
χ10044-2-2444-2-21-2-2-2-214-2-2-2-200000011-211104000000-2-200000-2110000000000-4-422-4-4-422-12222-1-42222000000-1-12-1-1-10-400000022000002-1-10000000000
χ10144-2-2444-2-21-2-2-2-214-2-2-2-200000011-21110-400000022000002-1-10000000000-4-422-4-4-422-12222-1-42222000000-1-12-1-1-104000000-2-200000-2110000000000
χ10244-2-24-44-2-21-2-2-2-21-42222000000112-1-1-100000000−2i32i3000000i3−i30000000000-4-422-44-422-12222-14-2-2-2-2000000-1-1-2111000000002i3−2i3000000−i3i30000000000
χ10344-2-24-44-2-21-2-2-2-21-42222000000112-1-1-1000000002i3−2i3000000−i3i30000000000-4-422-44-422-12222-14-2-2-2-2000000-1-1-211100000000−2i32i3000000i3−i30000000000
χ1044-44440-4-4-4444-4-4-4000000000004-400000000000000000000000000000000-44-4-4-40444-4-4-444400000000000-4400000000000000000000000000000000
χ1054-444-202-4-44-2-222-40000000−2i32i300-22000000000−2i32i3000000000000000000000-44-4-420-244-422-2-2400000002i3−2i3002-20000000002i3−2i3000000000000000000000
χ1064-444-202-4-44-2-222-400000002i3−2i300-220000000002i3−2i3000000000000000000000-44-4-420-244-422-2-240000000−2i32i3002-2000000000−2i32i3000000000000000000000
χ1074-44-240-4-42-2-24-42200000000023−23-220000000000000023−230000000000000000-44-42-4044-222-44-2-2000000000−23232-200000000000000−23230000000000000000
χ1084-44-240-4-42-2-24-422000000000−2323-2200000000000000−23230000000000000000-44-42-4044-222-44-2-200000000023−232-20000000000000023−230000000000000000
χ1094-44-2-202-42-21-22-12003i−3i000−2i32i323−231-1003i−3i00000i3−i3000−330000000000000000-44-4220-24-22-12-21-200−3i3i0002i3−2i3−2323-1100−3i3i00000−i3i30003−30000000000000000
χ1104-44-2-202-42-21-22-12003i−3i0002i3−2i3−23231-1003i−3i00000−i3i30003−30000000000000000-44-4220-24-22-12-21-200−3i3i000−2i32i323−23-1100−3i3i00000i3−i3000−330000000000000000
χ1114-44-2-202-42-21-22-1200−3i3i000−2i32i3−23231-100−3i3i00000i3−i30003−30000000000000000-44-4220-24-22-12-21-2003i−3i0002i3−2i323−23-11003i−3i00000−i3i3000−330000000000000000
χ1124-44-2-202-42-21-22-1200−3i3i0002i3−2i323−231-100−3i3i00000−i3i3000−330000000000000000-44-4220-24-22-12-21-2003i−3i000−2i32i3−2323-11003i−3i00000i3−i30003−30000000000000000
χ1134-4-2440-42-4-24-22-4200000000000-22000000000000000000000000000006−60-442-4-404-242-42-24-2000000000002-200000000000000000000000000000−660
χ1144-4-2440-42-4-24-22-4200000000000-2200000000000000000000000000000−660-442-4-404-242-42-24-2000000000002-2000000000000000000000000000006−60
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
χ1178-8-48-4044-8-4-42-244000000000002-200000000000000000000000000000000-884-840-4-4844-22-4-400000000000-2200000000000000000000000000000000
χ1188-8-4-480-8442-4-444-2000000000002-200000000000000000000000000000000-8844-808-4-4-244-4-4200000000000-2200000000000000000000000000000000
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).