Finite Group Databasebeta

← Group #13138867

Character table — Group #13138867

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83
size111122222222224444446666666612121212121212121212121212121212121212121212121212121212181836363636363636363636363636363672727272727272727272
order1222344666121212128824242424336666663666121212121212121224242424242424242424242424242424442244488121212122424242424666612121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-11-1-11111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111
χ511111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-11111-1-1-1-1-1-111-1-111-1-1
χ611111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-1-1-11111-1-1-1-111-1-111-1-111
χ711111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-1-1-11111-1111-1-1-1-111
χ811111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-11111-1-1
χ9222222222222222222222-12-1-1-122-1-1-1-1-12-1-1-12-1-12222-1-1-1-1-1-1-1-1-1-1-1-10022000000000000020-1-1-1-10000
χ10222222222222222222222-12-1-1-122-1-1-1-1-12-1-1-12-1-12222-1-1-1-1-1-1-1-1-1-1-1-100-2-20000000000000-2011110000
χ1122222222222222222222-12-1222-1-1-1-1-1-12-1-1-12-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000220000000000020000-1-1-1-1
χ1222222222222222222222-12-1222-1-1-1-1-1-12-1-1-12-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000-2-200000000000-200001111
χ1322222222222222-2-2-2-2-2-22-12-1-1-122-1-1-1-1-12-1-1-12-1-1-2-2-2-211111111111100220000000000000-20-1-1110000
χ1422222222222222-2-2-2-2-2-22-12-1-1-122-1-1-1-1-12-1-1-12-1-1-2-2-2-211111111111100-2-200000000000002011-1-10000
χ1522222222222222-2-2-2-2-2-2-12-1222-1-1-1-1-1-12-1-1-12-1-1-11111-2-2-2-211111111000002200000000000-20000-1-111
χ1622222222222222-2-2-2-2-2-2-12-1222-1-1-1-1-1-12-1-1-12-1-1-11111-2-2-2-21111111100000-2-2000000000002000011-1-1
χ1722222-2-2222-2-2-2-2000000222222222222-2-2-2-2-2-2-2-200000000000000002200-2000022-2-200000000000000
χ1822222-2-2222-2-2-2-2000000222222222222-2-2-2-2-2-2-2-20000000000000000-2-20020000-2-22200000000000000
χ1922-2-2200-22-200002−222−2−22222-2-2-2-222-2-20000000022−2−222−2−22222−2−2−2−22i−2i00000−i2i22i−2i00−i2−i2i2i20000000000
χ2022-2-2200-22-200002−222−2−22222-2-2-2-222-2-20000000022−2−222−2−22222−2−2−2−2−2i2i00000i2−i2−2i2i00i2i2−i2−i20000000000
χ2122-2-2200-22-20000−22−2−2222222-2-2-2-222-2-200000000−2−222−2−222−2−2−2−222222i−2i00000i2−i22i−2i00i2i2−i2−i20000000000
χ2222-2-2200-22-20000−22−2−2222222-2-2-2-222-2-200000000−2−222−2−222−2−2−2−22222−2i2i00000−i2i2−2i2i00−i2−i2i2i20000000000
χ232-22-222-22-2-222-2-200000022-2-2-22-222-2-222222-2-2-2-20000000000000000000002i−2i00000000000000002i−2i00
χ242-22-222-22-2-222-2-200000022-2-2-22-222-2-222222-2-2-2-2000000000000000000000−2i2i0000000000000000−2i2i00
χ252-22-222-22-2-222-2-2000000-121-2-221-1-111-12-1-1-1-21113−33−3000033−3−333−3−3000002i−2i0000000000000000−ii−i3i3
χ262-22-222-22-2-222-2-2000000-121-2-221-1-111-12-1-1-1-21113−33−3000033−3−333−3−300000−2i2i0000000000000000i−ii3−i3
χ272-22-222-22-2-222-2-2000000-121-2-221-1-111-12-1-1-1-2111−33−330000−3−333−3−333000002i−2i0000000000000000−iii3−i3
χ282-22-222-22-2-222-2-2000000-121-2-221-1-111-12-1-1-1-2111−33−330000−3−333−3−33300000−2i2i0000000000000000i−i−i3i3
χ292-22-22-222-2-2-2-22200000022-2-2-22-222-2-22-2-2-2-222220000000000000000002-20000000000000002-2000000
χ302-22-22-222-2-2-2-22200000022-2-2-22-222-2-22-2-2-2-22222000000000000000000-22000000000000000-22000000
χ312-22-22-222-2-2-2-2220000002-1-211-1-22-111-11-211-12-1-10000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3002-2000000000000000-11−i3i30000
χ322-22-22-222-2-2-2-2220000002-1-211-1-22-111-11-211-12-1-10000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i300-220000000000000001-1i3−i30000
χ332-22-22-222-2-2-2-2220000002-1-211-1-22-111-11-211-12-1-10000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3002-2000000000000000-11i3−i30000
χ342-22-22-222-2-2-2-2220000002-1-211-1-22-111-11-211-12-1-10000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i300-220000000000000001-1−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
χ3744444-4-4444-4-4-4-40000004-24-2-2-244-2-2-2-22-4222-4220000000000000000000000000000000000000000000
χ3844444-4-4444-4-4-4-4000000-24-2444-2-2-2-2-2-2-4222-42220000000000000000000000000000000000000000000
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
χ4144-4-4400-44-4000022−222222−22−224-24-222-4-4-2-222000000002222−22−22−2−222−2−2−2−22222000000000000000000000000000
χ4244-4-4400-44-4000022−222222−22−22-24-24-4-422-2-22200000000−2−2222222−22−22−2−2−2−22222000000000000000000000000000
χ4344-4-4400-44-4000022−222222−22−22-2-2-2-2222211-1-1003i−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
χ4444-4-4400-44-4000022−222222−22−22-2-2-2-2222211-1-100−3i3i00−3i3i−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
χ4544-4-4400-44-40000−2222−22−2222224-24-222-4-4-2-22200000000−22−22222222−2−22222−2−2−2−2000000000000000000000000000
χ4644-4-4400-44-40000−2222−22−222222-24-24-4-422-2-2220000000022−2−2−22−2222222222−2−2−2−2000000000000000000000000000
χ4744-4-4400-44-40000−2222−22−222222-2-2-2-2222211-1-1003i−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
χ4844-4-4400-44-40000−2222−22−222222-2-2-2-2222211-1-100−3i3i00−3i3i22−2−222−2−2−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
χ494-44-444-44-4-444-4-40000004-2-422-2-44-222-2-24-2-22-4220000000000000000000000000000000000000000000
χ504-44-444-44-4-444-4-4000000-2-2222-22-21-1-11-2-21122-1-123−2323−230000−3−333−3−333000000000000000000000000000
χ514-44-444-44-4-444-4-4000000-2-2222-22-21-1-11-2-21122-1-1−2323−2323000033−3−333−3−3000000000000000000000000000
χ524-44-44-444-4-4-4-444000000-242-4-442-2-222-2-42224-2-2-20000000000000000000000000000000000000000000
χ534-44-44-444-4-4-4-444000000-2-2222-22-21-1-1122-1-1-2-2110000−2i32i3−2i32i3i3−i3i3−i3i3−i3i3−i3000000000000000000000000000
χ544-44-44-444-4-4-4-444000000-2-2222-22-21-1-1122-1-1-2-21100002i3−2i32i3−2i3−i3i3−i3i3−i3i3−i3i3000000000000000000000000000
χ554-4-44400-4-44000000000044-4-44-44-44-44-4000000000000000000000000000000000000000000000000000
χ564-4-44400-4-4400000000004-2-42-224-4-22-22000000000000i6−i6−i6i6i6−i6i6−i6−i6i6−i6i6000000000000000000000000000
χ574-4-44400-4-4400000000004-2-42-224-4-22-22000000000000−i6i6i6−i6−i6i6−i6i6i6−i6i6−i6000000000000000000000000000
χ584-4-44400-4-440000000000-242-44-4-22-22-22000000006−6−66000066−6−6−6−666000000000000000000000000000
χ594-4-44400-4-440000000000-242-44-4-22-22-2200000000−666−60000−6−66666−6−6000000000000000000000000000
χ604-4-44400-4-440000000000-2-222-22-221-11-1003i−3i00−3i3i6−6−66i6−i6−i6i6−ζ5+ζ13ζ7−ζ23−ζ7+ζ23ζ5−ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23−ζ5+ζ13000000000000000000000000000
χ614-4-44400-4-440000000000-2-222-22-221-11-1003i−3i00−3i3i−666−6−i6i6i6−i6ζ5−ζ13−ζ7+ζ23ζ7−ζ23−ζ5+ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23ζ5−ζ13000000000000000000000000000
χ624-4-44400-4-440000000000-2-222-22-221-11-100−3i3i003i−3i6−6−66−i6i6i6−i6ζ7−ζ23−ζ5+ζ13ζ5−ζ13−ζ7+ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13ζ7−ζ23000000000000000000000000000
χ634-4-44400-4-440000000000-2-222-22-221-11-100−3i3i003i−3i−666−6i6−i6−i6i6−ζ7+ζ23ζ5−ζ13−ζ5+ζ13ζ7−ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13−ζ7+ζ23000000000000000000000000000
χ646666-366-3-3-3-3-3-3-366-3-3-3-3000000000000000000000000000000000000220020022-1-1-1-1-1-1-1-10000000000
χ656666-366-3-3-3-3-3-3-366-3-3-3-3000000000000000000000000000000000000-2-200-200-2-2111111110000000000
χ666666-366-3-3-3-3-3-3-3-6-633330000000000000000000000000000000000002200200-2-2-1-1-1-111110000000000
χ676666-366-3-3-3-3-3-3-3-6-63333000000000000000000000000000000000000-2-200-200221111-1-1-1-10000000000
χ686666-3-6-6-3-3-333330033−3333−330000000000000000000000000000000000002200-20000-1-1113−33−30000000000
χ696666-3-6-6-3-3-333330033−3333−33000000000000000000000000000000000000-2-2002000011-1-1−33−330000000000
χ706666-3-6-6-3-3-3333300−3333−33330000000000000000000000000000000000002200-20000-1-111−33−330000000000
χ716666-3-6-6-3-3-3333300−3333−3333000000000000000000000000000000000000-2-2002000011-1-13−33−30000000000
χ7266-6-6-3003-3333−3333−3332−323ζ5−3ζ73ζ13−3ζ23−3ζ5+3ζ7−3ζ13+3ζ230000000000000000000000000000000000002i−2i00000−i2i2−ii−i3i3ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ70000000000
χ7366-6-6-3003-3333−3333−3332−323ζ5−3ζ73ζ13−3ζ23−3ζ5+3ζ7−3ζ13+3ζ23000000000000000000000000000000000000−2i2i00000i2−i2i−ii3−i3−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ70000000000
χ7466-6-6-3003-3333−3333−33−3232−3ζ5+3ζ7−3ζ13+3ζ233ζ5−3ζ73ζ13−3ζ230000000000000000000000000000000000002i−2i00000i2−i2−ii−i3i3−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ70000000000
χ7566-6-6-3003-3333−3333−33−3232−3ζ5+3ζ7−3ζ13+3ζ233ζ5−3ζ73ζ13−3ζ23000000000000000000000000000000000000−2i2i00000−i2i2i−ii3−i3ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ70000000000
χ7666-6-6-3003-33−3333−333332−323ζ13−3ζ233ζ5−3ζ7−3ζ13+3ζ23−3ζ5+3ζ70000000000000000000000000000000000002i−2i00000−i2i2−iii3−i3ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ230000000000
χ7766-6-6-3003-33−3333−333332−323ζ13−3ζ233ζ5−3ζ7−3ζ13+3ζ23−3ζ5+3ζ7000000000000000000000000000000000000−2i2i00000i2−i2i−i−i3i3−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ230000000000
χ7866-6-6-3003-33−3333−3333−3232−3ζ13+3ζ23−3ζ5+3ζ73ζ13−3ζ233ζ5−3ζ70000000000000000000000000000000000002i−2i00000i2−i2−iii3−i3−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ230000000000
χ7966-6-6-3003-33−3333−3333−3232−3ζ13+3ζ23−3ζ5+3ζ73ζ13−3ζ233ζ5−3ζ7000000000000000000000000000000000000−2i2i00000−i2i2i−i−i3i3ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ230000000000
χ8012-1212-12-612-12-666-6-666000000000000000000000000000000000000000000000000000000000000000000000
χ8112-1212-12-6-1212-66666-6-6000000000000000000000000000000000000000000000000000000000000000000000
χ8212-12-1212-60066-663−63−6363000000000000000000000000000000000000000000000000000000000000000000000
χ8312-12-1212-60066-6−636363−63000000000000000000000000000000000000000000000000000000000000000000000

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