Finite Group Databasebeta

← Group #10590357

Character table — Group #10590357

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11222224444441212121212121818112222244444412121212121218181122222444444121212121212181811222224444441212121212121818
order1233466361212121224661212884412124121212121212121244121212128822664666612121212246612128844121241212121212121212441212121288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111-111-1-1-1-111111111111111-111-1-1-1-111111111111111-111-1-1-1-111111111111111-111-1-1-1-1
χ31111111111111-11-1-111-1-11111111111111-11-1-111-1-11111111111111-11-1-111-1-11111111111111-11-1-111-1-1
χ41111111111111-1-1-1-1-1-1111111111111111-1-1-1-1-1-1111111111111111-1-1-1-1-1-1111111111111111-1-1-1-1-1-111
χ52222-22222-2-2-2-2000000002222-22222-2-2-2-2000000002222-22222-2-2-2-2000000002222-22222-2-2-2-200000000
χ6222-12-12-1-1-12-1-120-1-10000222-12-12-1-1-12-1-120-1-10000222-12-12-1-1-12-1-120-1-10000222-12-12-1-1-12-1-120-1-10000
χ7222-12-12-1-1-12-1-1-20110000222-12-12-1-1-12-1-1-20110000222-12-12-1-1-12-1-1-20110000222-12-12-1-1-12-1-1-20110000
χ8222-1-2-12-1-11-21100−i3i30000222-1-2-12-1-11-21100−i3i30000222-1-2-12-1-11-21100−i3i30000222-1-2-12-1-11-21100−i3i30000
χ9222-1-2-12-1-11-21100i3−i30000222-1-2-12-1-11-21100i3−i30000222-1-2-12-1-11-21100i3−i30000222-1-2-12-1-11-21100i3−i30000
χ1022-1222-1-1-12-1-1-10200-1-10022-1222-1-1-12-1-1-10200-1-10022-1222-1-1-12-1-1-10200-1-10022-1222-1-1-12-1-1-10200-1-100
χ1122-1222-1-1-12-1-1-10-200110022-1222-1-1-12-1-1-10-200110022-1222-1-1-12-1-1-10-200110022-1222-1-1-12-1-1-10-2001100
χ1222-12-22-1-1-1-21110000−i3i30022-12-22-1-1-1-21110000−i3i30022-12-22-1-1-1-21110000−i3i30022-12-22-1-1-1-21110000−i3i300
χ1322-12-22-1-1-1-21110000i3−i30022-12-22-1-1-1-21110000i3−i30022-12-22-1-1-1-21110000i3−i30022-12-22-1-1-1-21110000i3−i300
χ142-2220-2-22-20000000000−i2i22-2220-2-22-20000000000−i2i22-2220-2-22-20000000000−i2i22-2220-2-22-20000000000−i2i2
χ152-2220-2-22-20000000000i2−i22-2220-2-22-20000000000i2−i22-2220-2-22-20000000000i2−i22-2220-2-22-20000000000i2−i2
χ1644-2-24-2-211-2-2110000000044-2-24-2-211-2-2110000000044-2-24-2-211-2-2110000000044-2-24-2-211-2-21100000000
χ1744-2-2-4-2-21122-1-10000000044-2-2-4-2-21122-1-10000000044-2-2-4-2-21122-1-10000000044-2-2-4-2-21122-1-100000000
χ184-44-202-4-220000000000004-44-202-4-220000000000004-44-202-4-220000000000004-44-202-4-22000000000000
χ194-4-240-42-220000000000004-4-240-42-220000000000004-4-240-42-220000000000004-4-240-42-22000000000000
χ204-4-2-20221-1003i−3i000000004-4-2-20221-1003i−3i000000004-4-2-20221-1003i−3i000000004-4-2-20221-1003i−3i00000000
χ214-4-2-20221-100−3i3i000000004-4-2-20221-100−3i3i000000004-4-2-20221-100−3i3i000000004-4-2-20221-100−3i3i00000000
χ22111111111111111111111iiiiiiiiiiiiiiiiiiiii-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i
χ2311111111111111-111-1-1-1-1iiiiiiiiiiiiii−iii−i−i−i−i-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111−i−i−i−i−i−i−i−i−i−i−i−i−i−ii−i−iiiii
χ241111111111111-11-1-111-1-1iiiiiiiiiiiii−ii−i−iii−i−i-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-111−i−i−i−i−i−i−i−i−i−i−i−i−ii−iii−i−iii
χ251111111111111-1-1-1-1-1-111iiiiiiiiiiiii−i−i−i−i−i−iii-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiii−i−i
χ262222-22222-2-2-2-2000000002i2i2i2i−2i2i2i2i2i−2i−2i−2i−2i00000000-2-2-2-22-2-2-2-2222200000000−2i−2i−2i−2i2i−2i−2i−2i−2i2i2i2i2i00000000
χ27222-12-12-1-1-12-1-120-1-100002i2i2i−i2i−i2i−i−i−i2i−i−i2i0−i−i0000-2-2-21-21-2111-211-20110000−2i−2i−2ii−2ii−2iiii−2iii−2i0ii0000
χ28222-12-12-1-1-12-1-1-201100002i2i2i−i2i−i2i−i−i−i2i−i−i−2i0ii0000-2-2-21-21-2111-21120-1-10000−2i−2i−2ii−2ii−2iiii−2iii2i0−i−i0000
χ29222-1-2-12-1-11-21100−i3i300002i2i2i−i−2i−i2i−i−ii−2iii003−30000-2-2-2121-211-12-1-100i3−i30000−2i−2i−2ii2ii−2iii−i2i−i−i00−330000
χ30222-1-2-12-1-11-21100i3−i300002i2i2i−i−2i−i2i−i−ii−2iii00−330000-2-2-2121-211-12-1-100−i3i30000−2i−2i−2ii2ii−2iii−i2i−i−i003−30000
χ3122-1222-1-1-12-1-1-10200-1-1002i2i−i2i2i2i−i−i−i2i−i−i−i02i00−i−i00-2-21-2-2-2111-21110-2001100−2i−2ii−2i−2i−2iiii−2iiii0−2i00ii00
χ3222-1222-1-1-12-1-1-10-20011002i2i−i2i2i2i−i−i−i2i−i−i−i0−2i00ii00-2-21-2-2-2111-21110200-1-100−2i−2ii−2i−2i−2iiii−2iiii02i00−i−i00
χ3322-12-22-1-1-1-21110000−i3i3002i2i−i2i−2i2i−i−i−i−2iiii00003−300-2-21-22-21112-1-1-10000i3−i300−2i−2ii−2i2i−2iiii2i−i−i−i0000−3300
χ3422-12-22-1-1-1-21110000i3−i3002i2i−i2i−2i2i−i−i−i−2iiii0000−3300-2-21-22-21112-1-1-10000−i3i300−2i−2ii−2i2i−2iiii2i−i−i−i00003−300
χ352-2220-2-22-20000000000−i2i22i−2i2i2i0−2i−2i2i−2i00000000002−2-22-2-2022-220000000000i2−i2−2i2i−2i−2i02i2i−2i2i0000000000−22
χ362-2220-2-22-20000000000i2−i22i−2i2i2i0−2i−2i2i−2i0000000000−22-22-2-2022-220000000000−i2i2−2i2i−2i−2i02i2i−2i2i00000000002−2
χ3744-2-24-2-211-2-211000000004i4i−2i−2i4i−2i−2iii−2i−2iii00000000-4-422-422-1-122-1-100000000−4i−4i2i2i−4i2i2i−i−i2i2i−i−i00000000
χ3844-2-2-4-2-21122-1-1000000004i4i−2i−2i−4i−2i−2iii2i2i−i−i00000000-4-422422-1-1-2-21100000000−4i−4i2i2i4i2i2i−i−i−2i−2iii00000000
χ394-44-202-4-220000000000004i−4i4i−2i02i−4i−2i2i000000000000-44-420-242-2000000000000−4i4i−4i2i0−2i4i2i−2i000000000000
χ404-4-240-42-220000000000004i−4i−2i4i0−4i2i−2i2i000000000000-442-404-22-2000000000000−4i4i2i−4i04i−2i2i−2i000000000000
χ414-4-2-20221-1003i−3i000000004i−4i−2i−2i02i2ii−i00-3300000000-44220-2-2-1100−3i3i00000000−4i4i2i2i0−2i−2i−ii003-300000000
χ424-4-2-20221-100−3i3i000000004i−4i−2i−2i02i2ii−i003-300000000-44220-2-2-11003i−3i00000000−4i4i2i2i0−2i−2i−ii00-3300000000
χ43111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ4411111111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111111111111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111
χ451111111111111-11-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1111111111111111-11-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-111
χ461111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ472222-22222-2-2-2-200000000-2-2-2-22-2-2-2-22222000000002222-22222-2-2-2-200000000-2-2-2-22-2-2-2-2222200000000
χ48222-12-12-1-1-12-1-120-1-10000-2-2-21-21-2111-211-20110000222-12-12-1-1-12-1-120-1-10000-2-2-21-21-2111-211-20110000
χ49222-12-12-1-1-12-1-1-20110000-2-2-21-21-2111-21120-1-10000222-12-12-1-1-12-1-1-20110000-2-2-21-21-2111-21120-1-10000
χ50222-1-2-12-1-11-21100−i3i30000-2-2-2121-211-12-1-100i3−i30000222-1-2-12-1-11-21100−i3i30000-2-2-2121-211-12-1-100i3−i30000
χ51222-1-2-12-1-11-21100i3−i30000-2-2-2121-211-12-1-100−i3i30000222-1-2-12-1-11-21100i3−i30000-2-2-2121-211-12-1-100−i3i30000
χ5222-1222-1-1-12-1-1-10200-1-100-2-21-2-2-2111-21110-200110022-1222-1-1-12-1-1-10200-1-100-2-21-2-2-2111-21110-2001100
χ5322-1222-1-1-12-1-1-10-2001100-2-21-2-2-2111-21110200-1-10022-1222-1-1-12-1-1-10-2001100-2-21-2-2-2111-21110200-1-100
χ5422-12-22-1-1-1-21110000−i3i300-2-21-22-21112-1-1-10000i3−i30022-12-22-1-1-1-21110000−i3i300-2-21-22-21112-1-1-10000i3−i300
χ5522-12-22-1-1-1-21110000i3−i300-2-21-22-21112-1-1-10000−i3i30022-12-22-1-1-1-21110000i3−i300-2-21-22-21112-1-1-10000−i3i300
χ562-2220-2-22-20000000000−i2i2-22-2-2022-220000000000i2−i22-2220-2-22-20000000000−i2i2-22-2-2022-220000000000i2−i2
χ572-2220-2-22-20000000000i2−i2-22-2-2022-220000000000−i2i22-2220-2-22-20000000000i2−i2-22-2-2022-220000000000−i2i2
χ5844-2-24-2-211-2-21100000000-4-422-422-1-122-1-10000000044-2-24-2-211-2-21100000000-4-422-422-1-122-1-100000000
χ5944-2-2-4-2-21122-1-100000000-4-422422-1-1-2-2110000000044-2-2-4-2-21122-1-100000000-4-422422-1-1-2-21100000000
χ604-44-202-4-22000000000000-44-420-242-20000000000004-44-202-4-22000000000000-44-420-242-2000000000000
χ614-4-240-42-22000000000000-442-404-22-20000000000004-4-240-42-22000000000000-442-404-22-2000000000000
χ624-4-2-20221-1003i−3i00000000-44220-2-2-1100−3i3i000000004-4-2-20221-1003i−3i00000000-44220-2-2-1100−3i3i00000000
χ634-4-2-20221-100−3i3i00000000-44220-2-2-11003i−3i000000004-4-2-20221-100−3i3i00000000-44220-2-2-11003i−3i00000000
χ64111111111111111111111−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiiiiiiiiiiiiiiii
χ6511111111111111-111-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−ii−i−iiiii-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111iiiiiiiiiiiiii−iii−i−i−i−i
χ661111111111111-11-1-111-1-1−i−i−i−i−i−i−i−i−i−i−i−i−ii−iii−i−iii-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-111iiiiiiiiiiiii−ii−i−iii−i−i
χ671111111111111-1-1-1-1-1-111−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiii−i−i-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1iiiiiiiiiiiii−i−i−i−i−i−iii
χ682222-22222-2-2-2-200000000−2i−2i−2i−2i2i−2i−2i−2i−2i2i2i2i2i00000000-2-2-2-22-2-2-2-22222000000002i2i2i2i−2i2i2i2i2i−2i−2i−2i−2i00000000
χ69222-12-12-1-1-12-1-120-1-10000−2i−2i−2ii−2ii−2iiii−2iii−2i0ii0000-2-2-21-21-2111-211-201100002i2i2i−i2i−i2i−i−i−i2i−i−i2i0−i−i0000
χ70222-12-12-1-1-12-1-1-20110000−2i−2i−2ii−2ii−2iiii−2iii2i0−i−i0000-2-2-21-21-2111-21120-1-100002i2i2i−i2i−i2i−i−i−i2i−i−i−2i0ii0000
χ71222-1-2-12-1-11-21100−i3i30000−2i−2i−2ii2ii−2iii−i2i−i−i00−330000-2-2-2121-211-12-1-100i3−i300002i2i2i−i−2i−i2i−i−ii−2iii003−30000
χ72222-1-2-12-1-11-21100i3−i30000−2i−2i−2ii2ii−2iii−i2i−i−i003−30000-2-2-2121-211-12-1-100−i3i300002i2i2i−i−2i−i2i−i−ii−2iii00−330000
χ7322-1222-1-1-12-1-1-10200-1-100−2i−2ii−2i−2i−2iiii−2iiii0−2i00ii00-2-21-2-2-2111-21110-20011002i2i−i2i2i2i−i−i−i2i−i−i−i02i00−i−i00
χ7422-1222-1-1-12-1-1-10-2001100−2i−2ii−2i−2i−2iiii−2iiii02i00−i−i00-2-21-2-2-2111-21110200-1-1002i2i−i2i2i2i−i−i−i2i−i−i−i0−2i00ii00
χ7522-12-22-1-1-1-21110000−i3i300−2i−2ii−2i2i−2iiii2i−i−i−i0000−3300-2-21-22-21112-1-1-10000i3−i3002i2i−i2i−2i2i−i−i−i−2iiii00003−300
χ7622-12-22-1-1-1-21110000i3−i300−2i−2ii−2i2i−2iiii2i−i−i−i00003−300-2-21-22-21112-1-1-10000−i3i3002i2i−i2i−2i2i−i−i−i−2iiii0000−3300
χ772-2220-2-22-20000000000−i2i2−2i2i−2i−2i02i2i−2i2i0000000000−22-22-2-2022-220000000000i2−i22i−2i2i2i0−2i−2i2i−2i00000000002−2
χ782-2220-2-22-20000000000i2−i2−2i2i−2i−2i02i2i−2i2i00000000002−2-22-2-2022-220000000000−i2i22i−2i2i2i0−2i−2i2i−2i0000000000−22
χ7944-2-24-2-211-2-21100000000−4i−4i2i2i−4i2i2i−i−i2i2i−i−i00000000-4-422-422-1-122-1-1000000004i4i−2i−2i4i−2i−2iii−2i−2iii00000000
χ8044-2-2-4-2-21122-1-100000000−4i−4i2i2i4i2i2i−i−i−2i−2iii00000000-4-422422-1-1-2-211000000004i4i−2i−2i−4i−2i−2iii2i2i−i−i00000000
χ814-44-202-4-22000000000000−4i4i−4i2i0−2i4i2i−2i000000000000-44-420-242-20000000000004i−4i4i−2i02i−4i−2i2i000000000000
χ824-4-240-42-22000000000000−4i4i2i−4i04i−2i2i−2i000000000000-442-404-22-20000000000004i−4i−2i4i0−4i2i−2i2i000000000000
χ834-4-2-20221-1003i−3i00000000−4i4i2i2i0−2i−2i−ii003-300000000-44220-2-2-1100−3i3i000000004i−4i−2i−2i02i2ii−i00-3300000000
χ844-4-2-20221-100−3i3i00000000−4i4i2i2i0−2i−2i−ii00-3300000000-44220-2-2-11003i−3i000000004i−4i−2i−2i02i2ii−i003-300000000

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