Finite Group Databasebeta

← Group #13138907

Character table — Group #13138907

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83
size111122222222224444446666666612121212121212121212121212121212121212121212121212121212181836363636363636363636363636363672727272727272727272
order122234466612121212882424242433666666366612121212121212122424242424242424242424242424242422444446688121224242424441212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111
χ511111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111-1-1-1-1-1-111-1-111-1-1
χ611111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-111-1-1-1-111-1-111-1-111
χ711111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1111-1-1-1-111
χ811111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111111-1-1-11111-1-1
χ9222222222222222222222-12-12-1-12-1-1-1-12-1-1-12-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10002200000000000020-1-1-1-10000
χ10222222222222222222222-12-12-1-12-1-1-1-12-1-1-12-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000-2-2000000000000-2011110000
χ1122222222222222222222-12-12-122-1-1-1-1-1-12-1-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000220000000000020000-1-1-1-1
χ1222222222222222222222-12-12-122-1-1-1-1-1-12-1-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000-2-200000000000-200001111
χ1322222222222222-2-2-2-2-2-22-12-12-1-12-1-1-1-12-1-1-12-1-1-1-2-2-2-211111111111100022000000000000-20-1-1110000
χ1422222222222222-2-2-2-2-2-22-12-12-1-12-1-1-1-12-1-1-12-1-1-1-2-2-2-2111111111111000-2-20000000000002011-1-10000
χ1522222222222222-2-2-2-2-2-2-12-12-122-1-1-1-1-1-12-1-1-12-1-11111-2-2-2-211111111000002200000000000-20000-1-111
χ1622222222222222-2-2-2-2-2-2-12-12-122-1-1-1-1-1-12-1-1-12-1-11111-2-2-2-21111111100000-2-2000000000002000011-1-1
χ1722222-2-2222-2-2-2-2000000222222222222-2-2-2-2-2-2-2-2000000000000000022-200002200-2-200000000000000
χ1822222-2-2222-2-2-2-2000000222222222222-2-2-2-2-2-2-2-20000000000000000-2-220000-2-2002200000000000000
χ1922-2-22002-2-200002−222−2−22222-2-2-2-222-2-20000000022−2−222−2−22222−2−2−2−22-2000002-22−20022−2−20000000000
χ2022-2-22002-2-200002−222−2−22222-2-2-2-222-2-20000000022−2−222−2−22222−2−2−2−2-2200000-22−2200−2−2220000000000
χ2122-2-22002-2-20000−22−2−2222222-2-2-2-222-2-200000000−2−222−2−222−2−2−2−222222-2000002-2−2200−2−2220000000000
χ2222-2-22002-2-20000−22−2−2222222-2-2-2-222-2-200000000−2−222−2−222−2−2−2−22222-2200000-222−20022−2−20000000000
χ232-22-222-2-2-2222-2-200000022-2-22-22-22-2-22-2-2-2-222220000000000000000000002i−2i00000000000000002i−2i00
χ242-22-222-2-2-2222-2-200000022-2-22-22-22-2-22-2-2-2-22222000000000000000000000−2i2i0000000000000000−2i2i00
χ252-22-222-2-2-2222-2-2000000-121-2-1-221-111-11-211-12-1-1−i3i3−i3i30000−i3−i3i3i3−i3−i3i3i3000002i−2i0000000000000000−ii3−3
χ262-22-222-2-2-2222-2-2000000-121-2-1-221-111-11-211-12-1-1−i3i3−i3i30000−i3−i3i3i3−i3−i3i3i300000−2i2i0000000000000000i−i−33
χ272-22-222-2-2-2222-2-2000000-121-2-1-221-111-11-211-12-1-1i3−i3i3−i30000i3i3−i3−i3i3i3−i3−i3000002i−2i0000000000000000−ii−33
χ282-22-222-2-2-2222-2-2000000-121-2-1-221-111-11-211-12-1-1i3−i3i3−i30000i3i3−i3−i3i3i3−i3−i300000−2i2i0000000000000000i−i3−3
χ292-22-22-22-2-22-2-22200000022-2-22-22-22-2-222222-2-2-2-200000000000000000002i−2i000000000000002i−2i000000
χ302-22-22-22-2-22-2-22200000022-2-22-22-22-2-222222-2-2-2-20000000000000000000−2i2i00000000000000−2i2i000000
χ312-22-22-22-2-22-2-2220000002-1-2121-1-2-111-12-1-1-1-211100003−33−33−33−33−33−30002i−2i00000000000000−ii−i3i30000
χ322-22-22-22-2-22-2-2220000002-1-2121-1-2-111-12-1-1-1-211100003−33−33−33−33−33−3000−2i2i00000000000000i−ii3−i30000
χ332-22-22-22-2-22-2-2220000002-1-2121-1-2-111-12-1-1-1-21110000−33−33−33−33−33−330002i−2i00000000000000−iii3−i30000
χ342-22-22-22-2-22-2-2220000002-1-2121-1-2-111-12-1-1-1-21110000−33−33−33−33−33−33000−2i2i00000000000000i−i−i3i30000
χ3544444444444444444444-2-2-2-2-2-2-2-21111-2-211-2-211-2-2-2-2-2-2-2-211111111000000000000000000000000000
χ3644444444444444-4-4-4-4-4-4-2-2-2-2-2-2-2-21111-2-211-2-21122222222-1-1-1-1-1-1-1-1000000000000000000000000000
χ3744444-4-4444-4-4-4-40000004-24-24-2-24-2-2-2-2-4222-42220000000000000000000000000000000000000000000
χ3844444-4-4444-4-4-4-4000000-24-24-244-2-2-2-2-22-4222-4220000000000000000000000000000000000000000000
χ3944444-4-4444-4-4-4-4000000-2-2-2-2-2-2-2-2111122-1-122-1-1000000003i−3i−3i3i3i−3i−3i3i000000000000000000000000000
χ4044444-4-4444-4-4-4-4000000-2-2-2-2-2-2-2-2111122-1-122-1-100000000−3i3i3i−3i−3i3i3i−3i000000000000000000000000000
χ4144-4-44004-4-4000022−222222−22−224-24-2-422-4-2-222000000002222−22−22−2−222−2−2−2−22222000000000000000000000000000
χ4244-4-44004-4-4000022−222222−22−22-24-242-4-42-2-22200000000−2−2222222−22−22−2−2−2−22222000000000000000000000000000
χ4344-4-44004-4-4000022−222222−22−22-2-2-2-2222211-1-1003i−3i003i−3i−2−222−2−222−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ23ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ23−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ23000000000000000000000000000
χ4444-4-44004-4-4000022−222222−22−22-2-2-2-2222211-1-100−3i3i00−3i3i−2−222−2−222ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ23−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ232ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ23000000000000000000000000000
χ4544-4-44004-4-40000−2222−22−2222224-24-2-422-4-2-22200000000−22−22222222−2−22222−2−2−2−2000000000000000000000000000
χ4644-4-44004-4-40000−2222−22−222222-24-242-4-42-2-2220000000022−2−2−22−2222222222−2−2−2−2000000000000000000000000000
χ4744-4-44004-4-40000−2222−22−222222-2-2-2-2222211-1-1003i−3i003i−3i22−2−222−2−22ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ23−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ23ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ23000000000000000000000000000
χ4844-4-44004-4-40000−2222−22−222222-2-2-2-2222211-1-100−3i3i00−3i3i22−2−222−2−2−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ232ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ23−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ23000000000000000000000000000
χ494-44-444-4-4-4444-4-40000004-2-4242-2-4-222-2-42224-2-2-20000000000000000000000000000000000000000000
χ504-44-444-4-4-4444-4-4000000-2-222-22-221-1-1122-1-1-2-211−2i32i3−2i32i30000i3i3−i3−i3i3i3−i3−i3000000000000000000000000000
χ514-44-444-4-4-4444-4-4000000-2-222-22-221-1-1122-1-1-2-2112i3−2i32i3−2i30000−i3−i3i3i3−i3−i3i3i3000000000000000000000000000
χ524-44-44-44-4-44-4-444000000-242-4-2-442-222-2-24-2-22-4220000000000000000000000000000000000000000000
χ534-44-44-44-4-44-4-444000000-2-222-22-221-1-11-2-21122-1-1000023−2323−23−33−33−33−33000000000000000000000000000
χ544-44-44-44-4-44-4-444000000-2-222-22-221-1-11-2-21122-1-10000−2323−23233−33−33−33−3000000000000000000000000000
χ554-4-44400-44-4000000000044-4-4-44-444-44-4000000000000000000000000000000000000000000000000000
χ564-4-44400-44-400000000004-2-42-4-224-22-220000000000006−6−666−66−6−66−66000000000000000000000000000
χ574-4-44400-44-400000000004-2-42-4-224-22-22000000000000−666−6−66−666−66−6000000000000000000000000000
χ584-4-44400-44-40000000000-242-424-4-2-22-2200000000i6−i6−i6i60000i6i6−i6−i6−i6−i6i6i6000000000000000000000000000
χ594-4-44400-44-40000000000-242-424-4-2-22-2200000000−i6i6i6−i60000−i6−i6i6i6i6i6−i6−i6000000000000000000000000000
χ604-4-44400-44-40000000000-2-2222-22-21-11-1003i−3i00−3i3ii6−i6−i6i66−6−66−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13000000000000000000000000000
χ614-4-44400-44-40000000000-2-2222-22-21-11-1003i−3i00−3i3i−i6i6i6−i6−666−6ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13000000000000000000000000000
χ624-4-44400-44-40000000000-2-2222-22-21-11-100−3i3i003i−3ii6−i6−i6i6−666−6−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23000000000000000000000000000
χ634-4-44400-44-40000000000-2-2222-22-21-11-100−3i3i003i−3i−i6i6i6−i66−6−66ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23000000000000000000000000000
χ646666-366-3-3-3-3-3-3-366-3-3-3-30000000000000000000000000000000000002220000-1-122-1-1-1-1-1-10000000000
χ656666-366-3-3-3-3-3-3-366-3-3-3-3000000000000000000000000000000000000-2-2-2000011-2-21111110000000000
χ666666-366-3-3-3-3-3-3-3-6-633330000000000000000000000000000000000002220000-1-1-2-2-1-111110000000000
χ676666-366-3-3-3-3-3-3-3-6-63333000000000000000000000000000000000000-2-2-20000112211-1-1-1-10000000000
χ686666-3-6-6-3-3-333330033−3333−3300000000000000000000000000000000000022-20000-1-100113−33−30000000000
χ696666-3-6-6-3-3-333330033−3333−33000000000000000000000000000000000000-2-2200001100-1-1−33−330000000000
χ706666-3-6-6-3-3-3333300−3333−333300000000000000000000000000000000000022-20000-1-10011−33−330000000000
χ716666-3-6-6-3-3-3333300−3333−3333000000000000000000000000000000000000-2-2200001100-1-13−33−30000000000
χ7266-6-6-300-33333−3333−3332−323ζ5−3ζ73ζ13−3ζ23−3ζ5+3ζ7−3ζ13+3ζ230000000000000000000000000000000000002-200000-112−23−3ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ230000000000
χ7366-6-6-300-33333−3333−3332−323ζ5−3ζ73ζ13−3ζ23−3ζ5+3ζ7−3ζ13+3ζ23000000000000000000000000000000000000-22000001-1−22−33−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ230000000000
χ7466-6-6-300-33333−3333−33−3232−3ζ5+3ζ7−3ζ13+3ζ233ζ5−3ζ73ζ13−3ζ230000000000000000000000000000000000002-200000-11−223−3−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ230000000000
χ7566-6-6-300-33333−3333−33−3232−3ζ5+3ζ7−3ζ13+3ζ233ζ5−3ζ73ζ13−3ζ23000000000000000000000000000000000000-22000001-12−2−33ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ230000000000
χ7666-6-6-300-333−3333−333332−323ζ13−3ζ233ζ5−3ζ7−3ζ13+3ζ23−3ζ5+3ζ70000000000000000000000000000000000002-200000-112−2−33ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ70000000000
χ7766-6-6-300-333−3333−333332−323ζ13−3ζ233ζ5−3ζ7−3ζ13+3ζ23−3ζ5+3ζ7000000000000000000000000000000000000-22000001-1−223−3−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ70000000000
χ7866-6-6-300-333−3333−3333−3232−3ζ13+3ζ23−3ζ5+3ζ73ζ13−3ζ233ζ5−3ζ70000000000000000000000000000000000002-200000-11−22−33−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ70000000000
χ7966-6-6-300-333−3333−3333−3232−3ζ13+3ζ23−3ζ5+3ζ73ζ13−3ζ233ζ5−3ζ7000000000000000000000000000000000000-22000001-12−23−3ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ70000000000
χ8012-1212-12-612-1266-6-6-666000000000000000000000000000000000000000000000000000000000000000000000
χ8112-1212-12-6-121266-666-6-6000000000000000000000000000000000000000000000000000000000000000000000
χ8212-12-1212-6006-6663−63−6363000000000000000000000000000000000000000000000000000000000000000000000
χ8312-12-1212-6006-66−636363−63000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.