Finite Group Databasebeta

← Group #13139034

Character table — Group #13139034

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83
size111122222222224444446666666612121212121212121212121212121212121212121212121212121212181836363636363636363636363636363672727272727272727272
order122234466612121212882424242433666666366612121212121212122424242424242424242424242424242422222246688121224242424246666661212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111
χ511111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111-1-1-1-1-1-11111-1-1-1-1
χ611111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111-1-111-1-1-1-111-1-1-1-11111
χ711111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111-1-11111-11-1-111-1-111
χ811111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-111111-111-1-111-1-1
χ9222222222222222222222-12-1-12-12-1-1-1-12-1-1-12-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1002200000000000002000-1-1-1-100
χ10222222222222222222222-12-1-12-12-1-1-1-12-1-1-12-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100-2-20000000000000-2000111100
χ1122222222222222222222-12-122-12-1-1-1-1-1-12-1-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000220000000000002-1-10000-1-1
χ1222222222222222222222-12-122-12-1-1-1-1-1-12-1-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000-2-2000000000000-211000011
χ1322222222222222-2-2-2-2-2-22-12-1-12-12-1-1-1-12-1-1-12-1-1-1-2-2-2-211111111111100220000000000000-2000-1-11100
χ1422222222222222-2-2-2-2-2-22-12-1-12-12-1-1-1-12-1-1-12-1-1-1-2-2-2-211111111111100-2-20000000000000200011-1-100
χ1522222222222222-2-2-2-2-2-2-12-122-12-1-1-1-1-1-12-1-1-12-1-11111-2-2-2-211111111000022000000000000-2-1-1000011
χ1622222222222222-2-2-2-2-2-2-12-122-12-1-1-1-1-1-12-1-1-12-1-11111-2-2-2-2111111110000-2-20000000000002110000-1-1
χ1722222-2-2222-2-2-2-2000000222222222222-2-2-2-2-2-2-2-20000000000000000220000-22200-2-200000000000000
χ1822222-2-2222-2-2-2-2000000222222222222-2-2-2-2-2-2-2-20000000000000000-2-200002-2-2002200000000000000
χ192-22-222-2-2-2222-2-200000022-2-2-222-22-2-22-2-2-2-222220000000000000000002-2000000000000000002-20000
χ202-22-222-2-2-2222-2-200000022-2-2-222-22-2-22-2-2-2-22222000000000000000000-2200000000000000000-220000
χ212-22-222-2-2-2222-2-20000002-1-2112-1-2-111-1-21112-1-1-10000−i3−i3i3i3−i3−i3−i3−i3i3i3i3i3002-200000000000000000-11−i3i300
χ222-22-222-2-2-2222-2-20000002-1-2112-1-2-111-1-21112-1-1-10000−i3−i3i3i3−i3−i3−i3−i3i3i3i3i300-22000000000000000001-1i3−i300
χ232-22-222-2-2-2222-2-20000002-1-2112-1-2-111-1-21112-1-1-10000i3i3−i3−i3i3i3i3i3−i3−i3−i3−i3002-200000000000000000-11i3−i300
χ242-22-222-2-2-2222-2-20000002-1-2112-1-2-111-1-21112-1-1-10000i3i3−i3−i3i3i3i3i3−i3−i3−i3−i300-22000000000000000001-1−i3i300
χ252-22-22-22-2-22-2-22200000022-2-2-222-22-2-222222-2-2-2-2000000000000000000002-200000000000002-2000000
χ262-22-22-22-2-22-2-22200000022-2-2-222-22-2-222222-2-2-2-200000000000000000000-220000000000000-22000000
χ272-22-22-22-2-22-2-222000000-121-2-2-121-111-1-12-1-11-21133−3−3000033−3−333−3−300002-20000000000000-1100003−3
χ282-22-22-22-2-22-2-222000000-121-2-2-121-111-1-12-1-11-21133−3−3000033−3−333−3−30000-2200000000000001-10000−33
χ292-22-22-22-2-22-2-222000000-121-2-2-121-111-1-12-1-11-211−3−3330000−3−333−3−33300002-20000000000000-110000−33
χ302-22-22-22-2-22-2-222000000-121-2-2-121-111-1-12-1-11-211−3−3330000−3−333−3−3330000-2200000000000001-100003−3
χ312-2-222002-2-200002−222−2−222-22-2-2-2222-2-2000000002−22−22−22−22−22−22−22−22-2000002-22−20022−2−20000000000
χ322-2-222002-2-200002−222−2−222-22-2-2-2222-2-2000000002−22−22−22−22−22−22−22−2-2200000-22−2200−2−2220000000000
χ332-2-222002-2-20000−22−2−22222-22-2-2-2222-2-200000000−22−22−22−22−22−22−22−222-2000002-2−2200−2−2220000000000
χ342-2-222002-2-20000−22−2−22222-22-2-2-2222-2-200000000−22−22−22−22−22−22−22−22-2200000-222−20022−2−20000000000
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
χ3744444-4-4444-4-4-4-40000004-24-2-24-24-2-2-2-2-4222-42220000000000000000000000000000000000000000000
χ3844444-4-4444-4-4-4-4000000-24-244-24-2-2-2-2-22-4222-4220000000000000000000000000000000000000000000
χ3944444-4-4444-4-4-4-4000000-2-2-2-2-2-2-2-2111122-1-122-1-1000000003i3i−3i−3i−3i−3i3i3i000000000000000000000000000
χ4044444-4-4444-4-4-4-4000000-2-2-2-2-2-2-2-2111122-1-122-1-100000000−3i−3i3i3i3i3i−3i−3i000000000000000000000000000
χ4144-4-4400-44-40000000000444-44-4-4-44-44-4000000000000000000000000000000000000000000000000000
χ4244-4-4400-44-400000000004-242-2-42-4-22-22000000000000i6−i6−i6i6i6−i6i6−i6−i6i6−i6i6000000000000000000000000000
χ4344-4-4400-44-400000000004-242-2-42-4-22-22000000000000−i6i6i6−i6−i6i6−i6i6i6−i6i6−i6000000000000000000000000000
χ4444-4-4400-44-40000000000-24-2-442-42-22-22000000006−6−6600006−6−666−6−66000000000000000000000000000
χ4544-4-4400-44-40000000000-24-2-442-42-22-2200000000−666−60000−666−6−666−6000000000000000000000000000
χ4644-4-4400-44-40000000000-2-2-22-22221-11-1003i−3i003i−3i6−6−66i6−i6−i6i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000000
χ4744-4-4400-44-40000000000-2-2-22-22221-11-1003i−3i003i−3i−666−6−i6i6i6−i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000000
χ4844-4-4400-44-40000000000-2-2-22-22221-11-100−3i3i00−3i3i6−6−66−i6i6i6−i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000000
χ4944-4-4400-44-40000000000-2-2-22-22221-11-100−3i3i00−3i3i−666−6i6−i6−i6i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000000
χ504-44-444-4-4-4444-4-4000000-242-4-4-242-222-22-422-24-2-20000000000000000000000000000000000000000000
χ514-44-444-4-4-4444-4-4000000-2-2222-2-221-1-1122-1-1-2-2110000−2i3−2i32i32i3i3i3i3i3−i3−i3−i3−i3000000000000000000000000000
χ524-44-444-4-4-4444-4-4000000-2-2222-2-221-1-1122-1-1-2-21100002i32i3−2i3−2i3−i3−i3−i3−i3i3i3i3i3000000000000000000000000000
χ534-44-44-44-4-44-4-4440000004-2-4224-2-4-222-24-2-2-2-42220000000000000000000000000000000000000000000
χ544-44-44-44-4-44-4-444000000-2-2222-2-221-1-11-2-21122-1-12323−23−230000−3−333−3−333000000000000000000000000000
χ554-44-44-44-4-44-4-444000000-2-2222-2-221-1-11-2-21122-1-1−23−232323000033−3−333−3−3000000000000000000000000000
χ564-4-444004-4-4000022−222222−22−224-2-4-22-424-2-2220000000022−2222−22−22−22−22−22−22−22000000000000000000000000000
χ574-4-444004-4-4000022−222222−22−22-2424-42-4-2-2-22200000000−22−2222−2222−22−22−22−22−22000000000000000000000000000
χ584-4-444004-4-4000022−222222−22−22-2-22-2222-211-1-1003i−3i00−3i3i−22−22−22−22−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23000000000000000000000000000
χ594-4-444004-4-4000022−222222−22−22-2-22-2222-211-1-100−3i3i003i−3i−22−22−22−22ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23000000000000000000000000000
χ604-4-444004-4-40000−2222−22−2222224-2-4-22-424-2-22200000000−2222−22222−22−22−22−22−22−2000000000000000000000000000
χ614-4-444004-4-40000−2222−22−222222-2424-42-4-2-2-222000000002−22−2−2222−22222−22−22−22−2000000000000000000000000000
χ624-4-444004-4-40000−2222−22−222222-2-22-2222-211-1-1003i−3i00−3i3i2−22−22−22−22ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23000000000000000000000000000
χ634-4-444004-4-40000−2222−22−222222-2-22-2222-211-1-100−3i3i003i−3i2−22−22−22−2−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ23000000000000000000000000000
χ646666-366-3-3-3-3-3-3-366-3-3-3-30000000000000000000000000000000000002200002-1-122-1-1-1-1-1-10000000000
χ656666-366-3-3-3-3-3-3-366-3-3-3-3000000000000000000000000000000000000-2-20000-211-2-21111110000000000
χ666666-366-3-3-3-3-3-3-3-6-633330000000000000000000000000000000000002200002-1-1-2-2-1-111110000000000
χ676666-366-3-3-3-3-3-3-3-6-63333000000000000000000000000000000000000-2-20000-2112211-1-1-1-10000000000
χ686666-3-6-6-3-3-333330033−3333−33000000000000000000000000000000000000220000-2-1-100113−33−30000000000
χ696666-3-6-6-3-3-333330033−3333−33000000000000000000000000000000000000-2-2000021100-1-1−33−330000000000
χ706666-3-6-6-3-3-3333300−3333−3333000000000000000000000000000000000000220000-2-1-10011−33−330000000000
χ716666-3-6-6-3-3-3333300−3333−3333000000000000000000000000000000000000-2-2000021100-1-13−33−30000000000
χ726-6-66-300-33333−3333−3332−323ζ5−3ζ73ζ13−3ζ23−3ζ5+3ζ7−3ζ13+3ζ230000000000000000000000000000000000002-200000-112−23−3ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ230000000000
χ736-6-66-300-33333−3333−3332−323ζ5−3ζ73ζ13−3ζ23−3ζ5+3ζ7−3ζ13+3ζ23000000000000000000000000000000000000-22000001-1−22−33−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ230000000000
χ746-6-66-300-33333−3333−33−3232−3ζ5+3ζ7−3ζ13+3ζ233ζ5−3ζ73ζ13−3ζ230000000000000000000000000000000000002-200000-11−223−3−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ230000000000
χ756-6-66-300-33333−3333−33−3232−3ζ5+3ζ7−3ζ13+3ζ233ζ5−3ζ73ζ13−3ζ23000000000000000000000000000000000000-22000001-12−2−33ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ230000000000
χ766-6-66-300-333−3333−333332−323ζ13−3ζ233ζ5−3ζ7−3ζ13+3ζ23−3ζ5+3ζ70000000000000000000000000000000000002-200000-112−2−33ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ70000000000
χ776-6-66-300-333−3333−333332−323ζ13−3ζ233ζ5−3ζ7−3ζ13+3ζ23−3ζ5+3ζ7000000000000000000000000000000000000-22000001-1−223−3−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ70000000000
χ786-6-66-300-333−3333−3333−3232−3ζ13+3ζ23−3ζ5+3ζ73ζ13−3ζ233ζ5−3ζ70000000000000000000000000000000000002-200000-11−22−33−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ70000000000
χ796-6-66-300-333−3333−3333−3232−3ζ13+3ζ23−3ζ5+3ζ73ζ13−3ζ233ζ5−3ζ7000000000000000000000000000000000000-22000001-12−23−3ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ70000000000
χ801212-12-12-6006-6663−63−6363000000000000000000000000000000000000000000000000000000000000000000000
χ811212-12-12-6006-66−636363−63000000000000000000000000000000000000000000000000000000000000000000000
χ8212-1212-12-612-1266-6-6-666000000000000000000000000000000000000000000000000000000000000000000000
χ8312-1212-12-6-121266-666-6-6000000000000000000000000000000000000000000000000000000000000000000000

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