Finite Group Databasebeta

← Group #13172181

Character table — Group #13172181

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117
size1111222222222222444444444444444444444666666666688888888888881212121212121212121212121212121212121212121212121218181818242424242424242424242424363636363636363636365454727272108
order12223336666666662333666666666666666664444441212121236666666666664441212121212121212121212121212121212121212121244441212121212121212121212122244661212121222612124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-11-111-1-111111111111111111111-1-1-1-11-11111-1-1-1-11-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-1-1111111111111111111-11-1-11111-1-1-1-1111111111111-1-1-1-111-11-1-1-1-11111-111-1-1-1-1-1-1-1-1-11-11-1
χ411111111111111111111111111111111111111111-1-111111111111111111-1-1-1-1-1-1-111-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-11-11
χ51111111111111111111111111111111111111-1-1-1-111-1-1-1-111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-11-1-1-1-111-1-1-11-1-1
χ61111111111111111111111111111111111111-1-1-1-111-1-1-1-11111111111111-11-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-1-111-1-1-1-1-1-1-1111-111
χ71111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111111111-11-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-11-1-1-1-111111-1-1-11111-1-111-1-1-11
χ81111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1111-1
χ91111111111111111-1111-1-1-1-11111-1-1-1-11111111-1-11111111-1-1-1-1-1111-1-1-1-11-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-11-1-1111-1-111-1-111-1111-1-1-1-1-1-111-11
χ101111111111111111-1111-1-1-1-11111-1-1-1-11111111-1-11111111-1-1-1-1-1111-1-1-1-1-1-11-1-111-1-1111111-1-11111-1-1-1-1-1-111-11-1-111-1-1-1-1111-11-111-1-11111-1-11-1
χ111111111111111111-1111-1-1-1-11111-1-1-1-11111111-1-1-1-111111-1-1-1-1-1111-1-1-1-111-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111-111-1-11111-1-1-11-1-1-1-11111111-1-1-1
χ121111111111111111-1111-1-1-1-11111-1-1-1-11111111-1-1-1-111111-1-1-1-1-1111-1-1-1-1-1111111-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-111-1-1-111-1-111-1-111-1-111-1-1-1-1-1111
χ131111111111111111-1111-1-1-1-11111-1-1-1-111111-1-11111-1-1-1-11-1-1-1-1-1111-1-1-1-11-1-1-1-1-1-1111111-1-111-1-1-1-1111111-1-11-1-1111-1-111-1-1-1-111-1-111-1-111-111-1
χ141111111111111111-1111-1-1-1-11111-1-1-1-111111-1-11111-1-1-1-11-1-1-1-1-1111-1-1-1-1-1-11-1-111111111-1-111-1-1-1-111111111-11-1-111-1-1-1-111-11-1-1-1-11111-1-11-1-11
χ151111111111111111-1111-1-1-1-11111-1-1-1-111111-1-111-1-1-1-1-1-11-1-1-1-1-1111-1-1-1-111-111-1-111-1-1-1-1-1-111-1-1-1-11111-1-1111-111-1-11111-1-11-11-111-1-111-1-1-1-111
χ161111111111111111-1111-1-1-1-11111-1-1-1-111111-1-111-1-1-1-1-1-11-1-1-1-1-1111-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-111-1-1-111-1-11111-1111-1-1-1-11111-1-1
χ17222222-122-12-1-122222-1-122-1-12-1-1-1-1-1-1-122-1-1-1222222-1-1-1-1-1222-1-1-1-1-1-1-1-1-1020-1-100-1-1-1-1222222-1-1-1-1-1-1-1-122000020-1-1-1-100002000-1-1-1-100000000
χ18222222-122-12-1-122222-1-122-1-12-1-1-1-1-1-1-122-1-1-12222-2-2-1-1-1-1-1222-1-1-1-1-1-1-1-1-10-201100-1-111-2-22222-1-1-1-1-1-1-1-1-2-20000-2011110000-2000111100000000
χ19222222-122-12-1-122222-1-122-1-12-1-1-1-1-1-1-122-1-1-1-2-2-2-2221111-1222-1-1-1-1-1-1-1-1-1020-1-10011-1-122-2-2-2-211111111-2-2000020-1-1-1-10000-2000111100000000
χ20222222-122-12-1-122222-1-122-1-12-1-1-1-1-1-1-122-1-1-1-2-2-2-2-2-21111-1222-1-1-1-1-1-1-1-1-10-2011001111-2-2-2-2-2-211111111220000-20111100002000-1-1-1-100000000
χ21222222-122-12-1-1222-22-1-1-2-2112-1-1-1111122-1-1-122-2-222-1-1-1-1-1-2-2-211-1-1-111110-20110011-1-12222-2-2-1-1-1-11111-2-20000-20-1-11100002000-1-11100000000
χ22222222-122-12-1-1222-22-1-1-2-2112-1-1-1111122-1-1-122-2-2-2-2-1-1-1-1-1-2-2-211-1-1-11111020-1-1001111-2-222-2-2-1-1-1-111112200002011-1-10000-200011-1-100000000
χ23222222-122-12-1-1222-22-1-1-2-2112-1-1-1111122-1-1-1-2-222221111-1-2-2-211-1-1-111110-201100-1-1-1-122-2-2221111-1-1-1-1220000-20-1-1110000-200011-1-100000000
χ24222222-122-12-1-1222-22-1-1-2-2112-1-1-1111122-1-1-1-2-222-2-21111-1-2-2-211-1-1-11111020-1-100-1-111-2-2-2-2221111-1-1-1-1-2-200002011-1-100002000-1-11100000000
χ2522222-12-1-1222222-12-12-1-1-122-12-1-1-1-1-1-1-1-122-12222002222-12-1-122-1-1-1-1-1-1-12020022220000-1-1-1-1-1-1-1-1-1-1-1-10000-1-1020000-1-1-1-1022000000000-10-10
χ2622222-12-1-1222222-12-12-1-1-122-12-1-1-1-1-1-1-1-122-12222002222-12-1-122-1-1-1-1-1-1-1-20-200-2-2220000-1-1-1-1-1-1-1-1-1-1-1-10000110-2000011110-2-20000000001010
χ2722222-12-1-1222222-12-12-1-1-122-12-1-1-1-1-1-1-1-122-1-2-2-2-200-2-2-2-2-12-1-122-1-1-1-1-1-1-12020022-2-200001111111111110000-1-1020000-1-1-1-10-2-20000000001010
χ2822222-12-1-1222222-12-12-1-1-122-12-1-1-1-1-1-1-1-122-1-2-2-2-200-2-2-2-2-12-1-122-1-1-1-1-1-1-1-20-200-2-2-2-200001111111111110000110-200001111022000000000-10-10
χ2922222-12-1-1222222-1-2-12-111-2-2-12-1-11111-1-122-122-2-2002222-1-211-2-2-1-1-1111120-200-2-2-2-20000-1-111-1-1-1-111110000-11020000-1-11102-2000000000-1010
χ3022222-12-1-1222222-1-2-12-111-2-2-12-1-11111-1-122-122-2-2002222-1-211-2-2-1-1-11111-2020022-2-20000-1-111-1-1-1-1111100001-10-2000011-1-10-2200000000010-10
χ3122222-12-1-1222222-1-2-12-111-2-2-12-1-11111-1-122-1-2-22200-2-2-2-2-1-211-2-2-1-1-1111120-200-2-222000011-1-11111-1-1-1-10000-11020000-1-1110-2200000000010-10
χ3222222-12-1-1222222-1-2-12-111-2-2-12-1-11111-1-122-1-2-22200-2-2-2-2-1-211-2-2-1-1-11111-202002222000011-1-11111-1-1-1-100001-10-2000011-1-102-2000000000-1010
χ332222-122222-122-1-122-1-122222-1-1222222-1-1-1-120000220000-1-1-1-1-1-1-1-1-1-1-1-1-122222-1-10022-1-1000000000000002222-1-1-1-1-1-1-1-1-1-100020000-1-1000-100
χ342222-122222-122-1-122-1-122222-1-1222222-1-1-1-120000220000-1-1-1-1-1-1-1-1-1-1-1-1-1-22-222110022-1-100000000000000-2-2-2-2-11-1-1-1-11111000-2000011000100
χ352222-122222-122-1-122-1-122222-1-1222222-1-1-1-120000-2-20000-1-1-1-1-1-1-1-1-1-1-1-1-12-22-2-2-1-100-2-21100000000000000-2-2221-11111-1-1-1-1000-2000011000100
χ362222-122222-122-1-122-1-122222-1-1222222-1-1-1-120000-2-20000-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-21100-2-2110000000000000022-2-2111111111100020000-1-1000-100
χ372222-122222-122-1-12-2-1-12-2-2-2-2-1-122-2-2-2-2-1-1-1-120000220000-111111-1-1-111112-2-2-2-2110022-1-100000000000000-2-22-21-1-1-111-1-1110002000011000-100
χ382222-122222-122-1-12-2-1-12-2-2-2-2-1-122-2-2-2-2-1-1-1-120000220000-111111-1-1-11111-2-22-2-2-1-10022-1-10000000000000022-2211-1-11111-1-1000-20000-1-1000100
χ392222-122222-122-1-12-2-1-12-2-2-2-2-1-122-2-2-2-2-1-1-1-120000-2-20000-111111-1-1-1111122-2221100-2-21100000000000000222-2-1-111-1-1-1-111000-20000-1-1000100
χ402222-122222-122-1-12-2-1-12-2-2-2-2-1-122-2-2-2-2-1-1-1-120000-2-20000-111111-1-1-11111-22222-1-100-2-21100000000000000-2-2-22-1111-1-111-1-10002000011000-100
χ4122-2-22222-2-2-22-22-2-202220000-222-200002-2-2-2-2002i−2i2i−2i00002000002-2-2000000000002i−2i2i−2i2i−2i002i−2i00002i2i−2i−2i2-20000002i−2i0000000000002-200000000
χ4222-2-22222-2-2-22-22-2-202220000-222-200002-2-2-2-2002i−2i−2i2i00002000002-2-2000000000002i−2i−2i2i−2i2i002i−2i00002i2i−2i−2i-22000000−2i2i000000000000-2200000000
χ4322-2-22222-2-2-22-22-2-202220000-222-200002-2-2-2-200−2i2i2i−2i00002000002-2-200000000000−2i2i2i−2i2i−2i00−2i2i0000−2i−2i2i2i-220000002i−2i000000000000-2200000000
χ4422-2-22222-2-2-22-22-2-202220000-222-200002-2-2-2-200−2i2i−2i2i00002000002-2-200000000000−2i2i−2i2i−2i2i00−2i2i0000−2i−2i2i2i2-2000000−2i2i0000000000002-200000000
χ4522-2-222-12-21-2-112-2-202-1-100−i3i3-2-1-11−i3−i3i3i32-2111002i−2i2i−2i33−3−3-1000−i3i3-111−i3−i3i3i30003−300−ii−ii2i−2i002i−2i33−3−3−i−iii2-2000000−ii3−300000000−i3i3-1100000000
χ4622-2-222-12-21-2-112-2-202-1-100−i3i3-2-1-11−i3−i3i3i32-2111002i−2i−2i2i33−3−3-1000−i3i3-111−i3−i3i3i3000−3300−iii−i−2i2i002i−2i33−3−3−i−iii-22000000i−i−3300000000i3−i31-100000000
χ4722-2-222-12-21-2-112-2-202-1-100−i3i3-2-1-11−i3−i3i3i32-211100−2i2i2i−2i−3−333-1000−i3i3-111−i3−i3i3i30003−300i−i−ii2i−2i00−2i2i−3−333ii−i−i-22000000−ii3−300000000i3−i31-100000000
χ4822-2-222-12-21-2-112-2-202-1-100−i3i3-2-1-11−i3−i3i3i32-211100−2i2i−2i2i−3−333-1000−i3i3-111−i3−i3i3i3000−3300i−ii−i−2i2i00−2i2i−3−333ii−i−i2-2000000i−i−3300000000−i3i3-1100000000
χ4922-2-222-12-21-2-112-2-202-1-100i3−i3-2-1-11i3i3−i3−i32-2111002i−2i2i−2i−3−333-1000i3−i3-111i3i3−i3−i3000−3300−ii−ii2i−2i002i−2i−3−333−i−iii2-2000000−ii−3300000000i3−i3-1100000000
χ5022-2-222-12-21-2-112-2-202-1-100i3−i3-2-1-11i3i3−i3−i32-2111002i−2i−2i2i−3−333-1000i3−i3-111i3i3−i3−i30003−300−iii−i−2i2i002i−2i−3−333−i−iii-22000000i−i3−300000000−i3i31-100000000
χ5122-2-222-12-21-2-112-2-202-1-100i3−i3-2-1-11i3i3−i3−i32-211100−2i2i2i−2i33−3−3-1000i3−i3-111i3i3−i3−i3000−3300i−i−ii2i−2i00−2i2i33−3−3ii−i−i-22000000−ii−3300000000−i3i31-100000000
χ5222-2-222-12-21-2-112-2-202-1-100i3−i3-2-1-11i3i3−i3−i32-211100−2i2i−2i2i33−3−3-1000i3−i3-111i3i3−i3−i30003−300i−ii−i−2i2i00−2i2i33−3−3ii−i−i2-2000000i−i3−300000000i3−i3-1100000000
χ532-2-22222-2222-2-2-2-2-202220000-2-2-220000-222-2-22i−2i00002i−2i2i−2i200000-22-2000000000000000002i−2i002i−2i2i−2i0000002i−2i000000000000000000002i−2i2-20000
χ542-2-22222-2222-2-2-2-2-202220000-2-2-220000-222-2-22i−2i00002i−2i2i−2i200000-22-2000000000000000002i−2i002i−2i2i−2i000000−2i2i00000000000000000000−2i2i-220000
χ552-2-22222-2222-2-2-2-2-202220000-2-2-220000-222-2-2−2i2i0000−2i2i−2i2i200000-22-200000000000000000−2i2i00−2i2i−2i2i0000002i−2i000000000000000000002i−2i-220000
χ562-2-22222-2222-2-2-2-2-202220000-2-2-220000-222-2-2−2i2i0000−2i2i−2i2i200000-22-200000000000000000−2i2i00−2i2i−2i2i000000−2i2i00000000000000000000−2i2i2-20000
χ5744444-2-2-2-2-24-2-244-24-2-21-2-2-2-2-2-2111111-2-2-2-21444400-2-2-2-214-2-2-2-211111110000000-2-20000-2-2-2-21111111100000000000000000000000000000000
χ5844444-2-2-2-2-24-2-244-24-2-21-2-2-2-2-2-2111111-2-2-2-21-4-4-4-400222214-2-2-2-2111111100000002200002222-1-1-1-1-1-1-1-100000000000000000000000000000000
χ5944444-2-2-2-2-24-2-244-2-4-2-212222-2-211-1-1-1-1-2-2-2-2144-4-400-2-2-2-21-42222111-1-1-1-10000000220000-2-2221111-1-1-1-100000000000000000000000000000000
χ6044444-2-2-2-2-24-2-244-2-4-2-212222-2-211-1-1-1-1-2-2-2-21-4-4440022221-42222111-1-1-1-10000000-2-2000022-2-2-1-1-1-1111100000000000000000000000000000000
χ614444-24-244-2-2-2-2-2-244-21-244-2-2-21-2-2-2-2-2-2-2-211-200004400001-2-2-2111111111040-2-20000-2-2-2-2000000000000000000-20111100000000000000000000
χ624444-24-244-2-2-2-2-2-244-21-244-2-2-21-2-2-2-2-2-2-2-211-20000-4-400001-2-2-21111111110-40220000222200000000000000000020-1-1-1-100000000000000000000
χ634444-24-244-2-2-2-2-2-24-4-21-2-4-422-21-2-22222-2-211-200004400001222-1-1111-1-1-1-10-40220000-2-2-2-20000000000000000002011-1-100000000000000000000
χ644444-24-244-2-2-2-2-2-24-4-21-2-4-422-21-2-22222-2-211-20000-4-400001222-1-1111-1-1-1-1040-2-200002222000000000000000000-20-1-11100000000000000000000
χ654444-2-24-2-24-244-2-2-241-2-2-2-2441-2-2-2-2-2-2-211-2-2-200000000001-211-2-2111111140400-2-20000000000000000000000-2-20-2000011110000000000000000
χ664444-2-24-2-24-244-2-2-241-2-2-2-2441-2-2-2-2-2-2-211-2-2-200000000001-211-2-21111111-40-40022000000000000000000000022020000-1-1-1-10000000000000000
χ674444-2-24-2-24-244-2-2-2-41-2-222-4-41-2-2-2222211-2-2-2000000000012-1-122111-1-1-1-140-400220000000000000000000000-220-2000011-1-10000000000000000
χ684444-2-24-2-24-244-2-2-2-41-2-222-4-41-2-2-2222211-2-2-2000000000012-1-122111-1-1-1-1-40400-2-200000000000000000000002-2020000-1-1110000000000000000
χ6944-4-44-24-22-4-44-44-420-24-2000024-220000-22-4-42004i−4i000000-200000-222000000000004i−4i000000−2i2i0000−2i−2i2i2i00000000000000000000000000000000
χ7044-4-44-24-22-4-44-44-420-24-2000024-220000-22-4-4200−4i4i000000-200000-22200000000000−4i4i0000002i−2i00002i2i−2i−2i00000000000000000000000000000000
χ7144-4-44-2-2-222-4-224-420-2-2100−2i32i32-21-1i3i3−i3−i3-2222-1004i−4i002323−23−231000−2i32i31-1-1i3i3−i3−i30000000−2i2i000000−2i2i−3−333ii−i−i00000000000000000000000000000000
χ7244-4-44-2-2-222-4-224-420-2-2100−2i32i32-21-1i3i3−i3−i3-2222-100−4i4i00−23−2323231000−2i32i31-1-1i3i3−i3−i300000002i−2i0000002i−2i33−3−3−i−iii00000000000000000000000000000000
χ7344-4-44-2-2-222-4-224-420-2-21002i3−2i32-21-1−i3−i3i3i3-2222-1004i−4i00−23−23232310002i3−2i31-1-1−i3−i3i3i30000000−2i2i000000−2i2i33−3−3ii−i−i00000000000000000000000000000000
χ7444-4-44-2-2-222-4-224-420-2-21002i3−2i32-21-1−i3−i3i3i3-2222-100−4i4i002323−23−2310002i3−2i31-1-1−i3−i3i3i300000002i−2i0000002i−2i−3−333−i−iii00000000000000000000000000000000
χ7544-4-4-2444-4-424-4-22-40-2-2400002-24-40000-2222-400004i−4i0000-200000-22200000000000004i−4i−2i2i00000000000000000000−2i2i0000000000000000000000
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Here i is the imaginary unit (i² = −1).