Finite Group Databasebeta

← Group #13156500

Character table — Group #13156500

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117
size111122222222222222222244444444444444444444444488888888881212121212121212121212121212121212121212121212121212121212121212121212121212181824242424242424243636363636727272727272108108
order12223334466666666612121212333666666666121212121212121212121212366612121212121244888824242424242424242424242424242424242424242424242424242424242424244412121212121212122661212441212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1-1-111-1-1
χ31111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111111111-1-1-1-1-1-1111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-111
χ511111111111111111111111111111111111111111111111111111111-1-111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111111111111111111111111111-1-111-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-111
χ711111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111
χ811111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111111-1-1
χ92222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2000000000000000000000000000000000000002200000000-2-2-22200000000
χ102222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-200000000000000000000000000000000000000-2-200000000222-2-200000000
χ11222222-12222-1-122-122-1-1-1-12-1-12-1-1-1-12-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1002222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122000000002-1-1-1-100000000
χ12222222-12222-1-122-122-1-1-1-12-1-12-1-1-1-12-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-10022-2-2-1-1-1-111112222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-200000000-2111100000000
χ13222222-12222-1-122-122-1-1-1-12-1-12-1-1-1-12-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-100-2-2221111-1-1-1-1-2-2-2-2111111112222-1-1-1-1-1-1-1-1-2-200000000-2111100000000
χ14222222-12222-1-122-122-1-1-1-12-1-12-1-1-1-12-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-100-2-2-2-211111111-2-2-2-211111111-2-2-2-21111111122000000002-1-1-1-100000000
χ15222222-1-2-222-1-122-12211112-1-12-1-1-1-12-1-12-2-21111-2-21111-1-1-1-1-2-2111100000033−3−333−3−300003333−3−3−3−300003333−3−3−3−32200000000-211-1-100000000
χ16222222-1-2-222-1-122-12211112-1-12-1-1-1-12-1-12-2-21111-2-21111-1-1-1-1-2-2111100000033−3−3−3−33300003333−3−3−3−30000−3−3−3−33333-2-2000000002-1-11100000000
χ17222222-1-2-222-1-122-12211112-1-12-1-1-1-12-1-12-2-21111-2-21111-1-1-1-1-2-21111000000−3−33333−3−30000−3−3−3−3333300003333−3−3−3−3-2-2000000002-1-11100000000
χ18222222-1-2-222-1-122-12211112-1-12-1-1-1-12-1-12-2-21111-2-21111-1-1-1-1-2-21111000000−3−333−3−3330000−3−3−3−333330000−3−3−3−333332200000000-211-1-100000000
χ1922222-12222-1222-12-122222-12-1-122-1-1-12-1-12-122-1-12-122-1-1-1-1-1-1-1-1-1-1-1-122002200002222000000000000-1-1-1-1-1-1-1-1-1-1-1-100-1-122-1-1-1-10000002-1-10000
χ2022222-12222-1222-12-122222-12-1-122-1-1-12-1-12-122-1-12-122-1-1-1-1-1-1-1-1-1-1-1-12200-2-20000-2-2-2-200000000000011111111111100-1-122-1-1-1-1000000-2110000
χ2122222-12222-1222-12-122222-12-1-122-1-1-12-1-12-122-1-12-122-1-1-1-1-1-1-1-1-1-1-1-1-2-2002200002222000000000000-1-1-1-1-1-1-1-1-1-1-1-10011-2-21111000000-2110000
χ2222222-12222-1222-12-122222-12-1-122-1-1-12-1-12-122-1-12-122-1-1-1-1-1-1-1-1-1-1-1-1-2-200-2-20000-2-2-2-20000000000001111111111110011-2-211110000002-1-10000
χ232222-12222-1222-1222-12222-1-12-1-1-122-1-12-1-12-1-122-12-1-122-1-1-1-1-1-1-1-1-1-122220022220000-1-1-1-1-1-1-1-1-1-1-1-10000000000000022-1-1-1-1-1-1000002000-1-100
χ242222-12222-1222-1222-12222-1-12-1-1-122-1-12-1-12-1-122-12-1-122-1-1-1-1-1-1-1-1-1-122-2-200-2-2-2-200001111111111110000000000000022-1-1-1-1-1-100000-20001100
χ252222-12222-1222-1222-12222-1-12-1-1-122-1-12-1-12-1-122-12-1-122-1-1-1-1-1-1-1-1-1-1-2-2220022220000-1-1-1-1-1-1-1-1-1-1-1-100000000000000-2-211111100000-20001100
χ262222-12222-1222-1222-12222-1-12-1-1-122-1-12-1-12-1-122-12-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-200-2-2-2-2000011111111111100000000000000-2-2111111000002000-1-100
χ2722-2-222200-2-22-2-22-2-220000222-22-22-2-2-2-2200000000000022-2-2000000002−2−i2i22−22−2−i2i2−i2i222−2−222−2−222−2−2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i22i−2i000000000002i−2i00000000
χ2822-2-222200-2-22-2-22-2-220000222-22-22-2-2-2-2200000000000022-2-2000000002−2i2−i22−22−2i2−i2i2−i222−2−222−2−222−2−2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2−2i2i00000000000−2i2i00000000
χ2922-2-222200-2-22-2-22-2-220000222-22-22-2-2-2-2200000000000022-2-200000000−22−i2i2−22−22−i2i2−i2i2−2−222−2−222−2−222−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−2i2i00000000000−2i2i00000000
χ3022-2-222200-2-22-2-22-2-220000222-22-22-2-2-2-2200000000000022-2-200000000−22i2−i2−22−22i2−i2i2−i2−2−222−2−222−2−222i2i2−i2−i2i2i2−i2−i2i2i2−i2−i22i−2i000000000002i−2i00000000
χ3122-2-222-100-2-2-11-221-2233−3−32-1-1-2-11-11-2112003−33−3003−33−3-1-1110033−3−3002−2−i2i2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ722−2−2ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23−i2−i2i2i2ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ72i−2i000000000−i3i3−ii00000000
χ3222-2-222-100-2-2-11-221-2233−3−32-1-1-2-11-11-2112003−33−3003−33−3-1-1110033−3−3002−2i2−i2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ722−2−2ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23i2i2−i2−i2−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−2i2i000000000i3−i3i−i00000000
χ3322-2-222-100-2-2-11-221-2233−3−32-1-1-2-11-11-2112003−33−3003−33−3-1-1110033−3−300−22−i2i2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−2−222−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−i2−i2i2i2ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7−2i2i000000000i3−i3i−i00000000
χ3422-2-222-100-2-2-11-221-2233−3−32-1-1-2-11-11-2112003−33−3003−33−3-1-1110033−3−300−22i2−i2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−2−222−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23i2i2−i2−i2−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ72i−2i000000000−i3i3−ii00000000
χ3522-2-222-100-2-2-11-221-22−3−3332-1-1-2-11-11-211200−33−3300−33−33-1-11100−3−333002−2−i2i2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2322−2−2ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−i2−i2i2i2ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ232i−2i000000000i3−i3−ii00000000
χ3622-2-222-100-2-2-11-221-22−3−3332-1-1-2-11-11-211200−33−3300−33−33-1-11100−3−333002−2i2−i2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2322−2−2ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7i2i2−i2−i2−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−2i2i000000000−i3i3i−i00000000
χ3722-2-222-100-2-2-11-221-22−3−3332-1-1-2-11-11-211200−33−3300−33−33-1-11100−3−33300−22−i2i2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−2−222−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−i2−i2i2i2ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23−2i2i000000000−i3i3i−i00000000
χ3822-2-222-100-2-2-11-221-22−3−3332-1-1-2-11-11-211200−33−3300−33−33-1-11100−3−33300−22i2−i2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−2−222−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7i2i2−i2−i2−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ232i−2i000000000i3−i3−ii00000000
χ392-22-22222-2-2-2-2-22-222-22-22-2222-2-2-2-2-2222-22-222-2-2-22-2-2222-2-222-22-22-2000000000000000000000000000000000000000000000000000000000002i−2i
χ402-22-22222-2-2-2-2-22-222-22-22-2222-2-2-2-2-2222-22-222-2-2-22-2-2222-2-222-22-22-200000000000000000000000000000000000000000000000000000000000−2i2i
χ412-22-2222-22-2-2-2-22-222-2-22-22222-2-2-2-2-2222-2-22-2-2222-222-2-22-2-22-22-22-222i−2i000000000000000000000000000000000000002i−2i2i−2i2i2i−2i−2i0000000000000
χ422-22-2222-22-2-2-2-22-222-2-22-22222-2-2-2-2-2222-2-22-2-2222-222-2-22-2-22-22-22-22−2i2i00000000000000000000000000000000000000−2i2i−2i2i−2i−2i2i2i0000000000000
χ432-22-22-12-22-21-2-2212-1-2-22-22-12-11-2-211-12-11-2-1-2-2-1-1212211-111-11-11-11-12i−2i0000000000000000000000003−33−33−33−33−33−300−ii2i−2i−i−iii0000000−i3i30000
χ442-22-22-12-22-21-2-2212-1-2-22-22-12-11-2-211-12-11-2-1-2-2-1-1212211-111-11-11-11-12i−2i000000000000000000000000−33−33−33−33−33−3300−ii2i−2i−i−iii0000000i3−i30000
χ452-22-22-12-22-21-2-2212-1-2-22-22-12-11-2-211-12-11-2-1-2-2-1-1212211-111-11-11-11-1−2i2i0000000000000000000000003−33−33−33−33−33−300i−i−2i2iii−i−i0000000i3−i30000
χ462-22-22-12-22-21-2-2212-1-2-22-22-12-11-2-211-12-11-2-1-2-2-1-1212211-111-11-11-11-1−2i2i000000000000000000000000−33−33−33−33−33−3300i−i−2i2iii−i−i0000000−i3i30000
χ472-22-2-122-221-2-2-2-1-2221-22-22-1-12111-2-2-1-121121122-1-2-1-1-2-2-111-11-11-11-12i−2i000000000000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3000000000000002i−2i−ii−i−iii0000000003−300
χ482-22-2-122-221-2-2-2-1-2221-22-22-1-12111-2-2-1-121121122-1-2-1-1-2-2-111-11-11-11-12i−2i000000000000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3000000000000002i−2i−ii−i−iii000000000−3300
χ492-22-2-122-221-2-2-2-1-2221-22-22-1-12111-2-2-1-121121122-1-2-1-1-2-2-111-11-11-11-1−2i2i000000000000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i300000000000000−2i2ii−iii−i−i000000000−3300
χ502-22-2-122-221-2-2-2-1-2221-22-22-1-12111-2-2-1-121121122-1-2-1-1-2-2-111-11-11-11-1−2i2i000000000000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i300000000000000−2i2ii−iii−i−i0000000003−300
χ5144444-24-4-44-2444-24-24-4-4-4-4-24-2-244-2-2-24-2-2-42-4-422-42-4-422-2-2-2-22222220000000000000000000000000000000000000000000000000000000000000
χ5244444-2-2444-2-2-24-2-2-24-2-2-2-2-2-21-2-2-211-2-21-24-2-2-2114-2-2-2111111-2-211110000440000-2-2-2-2000000000000-2-2-2-21111111100000000000000000000000
χ5344444-2-2444-2-2-24-2-2-24-2-2-2-2-2-21-2-2-211-2-21-24-2-2-2114-2-2-2111111-2-211110000-4-4000022220000000000002222-1-1-1-1-1-1-1-100000000000000000000000
χ5444444-2-2-4-44-2-2-24-2-2-242222-2-21-2-2-211-2-21-2-4222-1-1-4222-1-1111122-1-1-1-100000000002323−23−230000000000000000−3−3−3−3333300000000000000000000000
χ5544444-2-2-4-44-2-2-24-2-2-242222-2-21-2-2-211-2-21-2-4222-1-1-4222-1-1111122-1-1-1-10000000000−23−23232300000000000000003333−3−3−3−300000000000000000000000
χ564444-244-4-4-2444-2444-2-4-4-4-4-2-24-2-2-244-2-24-22-422-4-42-422-4-4-2-2-2-22222220000000000000000000000000000000000000000000000000000000000000
χ574444-24-244-24-2-2-24-24-2-2-2-2-2-21-2-211-2-2-21-2-2-2411-2-2-2411-2-21111-2-21111004400-2-2-2-20000-2-2-2-21111111100000000000000000000000000000000000
χ584444-24-244-24-2-2-24-24-2-2-2-2-2-21-2-211-2-2-21-2-2-2411-2-2-2411-2-21111-2-2111100-4-400222200002222-1-1-1-1-1-1-1-100000000000000000000000000000000000
χ594444-24-2-4-4-24-2-2-24-24-22222-21-2-211-2-2-21-2-22-4-1-1222-4-1-122111122-1-1-1-10000002323−23−2300000000−3−3−3−3333300000000000000000000000000000000000
χ604444-24-2-4-4-24-2-2-24-24-22222-21-2-211-2-2-21-2-22-4-1-1222-4-1-122111122-1-1-1-1000000−23−232323000000003333−3−3−3−300000000000000000000000000000000000
χ614444-2-2444-2-244-2-24-2-244441-2-21-2-2-2-21-2-21-2-2-2-2-2-2-2-2-2-2-2-211111111114400000000000000000000000000000000000000-2-2-2-211110000000000000
χ624444-2-2444-2-244-2-24-2-244441-2-21-2-2-2-21-2-21-2-2-2-2-2-2-2-2-2-2-2-21111111111-4-4000000000000000000000000000000000000002222-1-1-1-10000000000000
χ634444-2-24-4-4-2-244-2-24-2-2-4-4-4-41-2-21-2-2-2-21-2-212222222222221111-1-1-1-1-1-1000000000000000000000000000000000000000000003-33-30000000000000
χ644444-2-24-4-4-2-244-2-24-2-2-4-4-4-41-2-21-2-2-2-21-2-212222222222221111-1-1-1-1-1-100000000000000000000000000000000000000000000-33-330000000000000
χ6544-4-44-2400-424-4-4-2-4240000-24-224-4-222-42-2000000000000-2-2220000000000−2i22i20000−2i22i2−2i22i2000000000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200000000000000000000000
χ6644-4-44-2400-424-4-4-2-4240000-24-224-4-222-42-2000000000000-2-22200000000002i2−2i200002i2−2i22i2−2i2000000000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.