Finite Group Databasebeta

← Group #13139033

Character table — Group #13139033

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83
size111122222222224444446666666612121212121212121212121212121212121212121212121212121212181836363636363636363636363636363672727272727272727272
order12223446661212121288242424243366666636661212121212121212242424242424242424242424242424242222224668812122424242444666612121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-111-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-111
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
χ711111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111-1-11111-1111-1-1-1-111
χ811111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-111111-1-1-11111-1-1
χ9222222222222222222222-122-1-1-12-1-1-1-1-12-1-1-12-1-12222-1-1-1-1-1-1-1-1-1-1-1-10022000000000000020-1-100-1-100
χ10222222222222222222222-122-1-1-12-1-1-1-1-12-1-1-12-1-12222-1-1-1-1-1-1-1-1-1-1-1-100-2-20000000000000-2011001100
χ1122222222222222222222-12-1-1222-1-1-1-1-12-1-1-12-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000022000000000000200-1-100-1-1
χ1222222222222222222222-12-1-1222-1-1-1-1-12-1-1-12-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000-2-2000000000000-200110011
χ1322222222222222-2-2-2-2-2-22-122-1-1-12-1-1-1-1-12-1-1-12-1-1-2-2-2-211111111111100220000000000000-20-1-1001100
χ1422222222222222-2-2-2-2-2-22-122-1-1-12-1-1-1-1-12-1-1-12-1-1-2-2-2-211111111111100-2-20000000000000201100-1-100
χ1522222222222222-2-2-2-2-2-2-12-1-1222-1-1-1-1-12-1-1-12-1-1-11111-2-2-2-211111111000022000000000000-200-1-10011
χ1622222222222222-2-2-2-2-2-2-12-1-1222-1-1-1-1-12-1-1-12-1-1-11111-2-2-2-2111111110000-2-20000000000002001100-1-1
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
χ1922-2-22002-2-20000−i2i2−i2−i2i2i2222-22-2-2-222-2-200000000−i2−i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2i2i22-2000002-2−i2i200−i2−i2i2i20000000000
χ2022-2-22002-2-20000−i2i2−i2−i2i2i2222-22-2-2-222-2-200000000−i2−i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2i2i2-2200000-22i2−i200i2i2−i2−i20000000000
χ2122-2-22002-2-20000i2−i2i2i2−i2−i2222-22-2-2-222-2-200000000i2i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2−i2−i22-2000002-2i2−i200i2i2−i2−i20000000000
χ2222-2-22002-2-20000i2−i2i2i2−i2−i2222-22-2-2-222-2-200000000i2i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2−i2−i2-2200000-22−i2i200−i2−i2i2i20000000000
χ232-2-2222-2-2-2222-2-200000022-2-2-22-222-2-22-2-2-2-22222000000000000000000002-20000000000000002-20000
χ242-2-2222-2-2-2222-2-200000022-2-2-22-222-2-22-2-2-2-2222200000000000000000000-22000000000000000-220000
χ252-2-2222-2-2-2222-2-2000000-1211-22-2-1-111-1-21112-1-1-1−i3i3−i3i30000−i3−i3i3i3−i3−i3i3i300002-2000000000000000-1100−i3i3
χ262-2-2222-2-2-2222-2-2000000-1211-22-2-1-111-1-21112-1-1-1−i3i3−i3i30000−i3−i3i3i3−i3−i3i3i30000-220000000000000001-100i3−i3
χ272-2-2222-2-2-2222-2-2000000-1211-22-2-1-111-1-21112-1-1-1i3−i3i3−i30000i3i3−i3−i3i3i3−i3−i300002-2000000000000000-1100i3−i3
χ282-2-2222-2-2-2222-2-2000000-1211-22-2-1-111-1-21112-1-1-1i3−i3i3−i30000i3i3−i3−i3i3i3−i3−i30000-220000000000000001-100−i3i3
χ292-2-222-22-2-22-2-22200000022-2-2-22-222-2-222222-2-2-2-20000000000000000002-20000000000000002-2000000
χ302-2-222-22-2-22-2-22200000022-2-2-22-222-2-222222-2-2-2-2000000000000000000-22000000000000000-22000000
χ312-2-222-22-2-22-2-2220000002-1-2-21-112-111-1-12-1-11-21100003−33−33−33−33−33−3002-2000000000000000-11003−300
χ322-2-222-22-2-22-2-2220000002-1-2-21-112-111-1-12-1-11-21100003−33−33−33−33−33−300-220000000000000001-100−3300
χ332-2-222-22-2-22-2-2220000002-1-2-21-112-111-1-12-1-11-2110000−33−33−33−33−33−33002-2000000000000000-1100−3300
χ342-2-222-22-2-22-2-2220000002-1-2-21-112-111-1-12-1-11-2110000−33−33−33−33−33−3300-220000000000000001-1003−300
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
χ3744444-4-4444-4-4-4-40000004-244-2-2-24-2-2-2-22-4222-4220000000000000000000000000000000000000000000
χ3844444-4-4444-4-4-4-4000000-24-2-2444-2-2-2-2-2-4222-42220000000000000000000000000000000000000000000
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
χ4144-4-44004-4-40000−2i22i2−2i2−2i22i22i24-24-4-222-4-2-22200000000−2i2−2i22i22i2i2i2−i2−i2i2i2i2i2−i2−i2−i2−i2000000000000000000000000000
χ4244-4-44004-4-40000−2i22i2−2i2−2i22i22i2-24-224-4-42-2-22200000000i2i2−i2−i2−2i2−2i22i22i2i2i2i2i2−i2−i2−i2−i2000000000000000000000000000
χ4344-4-44004-4-40000−2i22i2−2i2−2i22i22i2-2-2-22-222211-1-1003i−3i003i−3ii2i2−i2−i2i2i2−i2−i2−2ζ5+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
χ4444-4-44004-4-40000−2i22i2−2i2−2i22i22i2-2-2-22-222211-1-100−3i3i00−3i3ii2i2−i2−i2i2i2−i2−i2ζ5−2ζ7+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
χ4544-4-44004-4-400002i2−2i22i22i2−2i2−2i24-24-4-222-4-2-222000000002i22i2−2i2−2i2−i2−i2i2i2−i2−i2−i2−i2i2i2i2i2000000000000000000000000000
χ4644-4-44004-4-400002i2−2i22i22i2−2i2−2i2-24-224-4-42-2-22200000000−i2−i2i2i22i22i2−2i2−2i2−i2−i2−i2−i2i2i2i2i2000000000000000000000000000
χ4744-4-44004-4-400002i2−2i22i22i2−2i2−2i2-2-2-22-222211-1-1003i−3i003i−3i−i2−i2i2i2−i2−i2i2i22ζ5−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
χ4844-4-44004-4-400002i2−2i22i22i2−2i2−2i2-2-2-22-222211-1-100−3i3i00−3i3i−i2−i2i2i2−i2−i2i2i2−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
χ494-44-4400-44-4000000000044-44-4-44-44-44-4000000000000000000000000000000000000000000000000000
χ504-44-4400-44-400000000004-2-4422-2-4-22-22000000000000i6−i6−i6i6i6−i6i6−i6−i6i6−i6i6000000000000000000000000000
χ514-44-4400-44-400000000004-2-4422-2-4-22-22000000000000−i6i6i6−i6−i6i6−i6i6i6−i6i6−i6000000000000000000000000000
χ524-44-4400-44-40000000000-242-2-4-442-22-22000000006−6−66000066−6−6−6−666000000000000000000000000000
χ534-44-4400-44-40000000000-242-2-4-442-22-2200000000−666−60000−6−66666−6−6000000000000000000000000000
χ544-44-4400-44-40000000000-2-22-222-221-11-1003i−3i00−3i3i6−6−66i6−i6−i6i6−ζ5+ζ13ζ7−ζ23−ζ7+ζ23ζ5−ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23−ζ5+ζ13000000000000000000000000000
χ554-44-4400-44-40000000000-2-22-222-221-11-1003i−3i00−3i3i−666−6−i6i6i6−i6ζ5−ζ13−ζ7+ζ23ζ7−ζ23−ζ5+ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23ζ5−ζ13000000000000000000000000000
χ564-44-4400-44-40000000000-2-22-222-221-11-100−3i3i003i−3i6−6−66−i6i6i6−i6ζ7−ζ23−ζ5+ζ13ζ5−ζ13−ζ7+ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13ζ7−ζ23000000000000000000000000000
χ574-44-4400-44-40000000000-2-22-222-221-11-100−3i3i003i−3i−666−6i6−i6−i6i6−ζ7+ζ23ζ5−ζ13−ζ5+ζ13ζ7−ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13−ζ7+ζ23000000000000000000000000000
χ584-4-4444-4-4-4444-4-40000004-2-4-42-224-222-22-422-24-2-20000000000000000000000000000000000000000000
χ594-4-4444-4-4-4444-4-4000000-2-2222-22-21-1-1122-1-1-2-211−2i32i3−2i32i30000i3i3−i3−i3i3i3−i3−i3000000000000000000000000000
χ604-4-4444-4-4-4444-4-4000000-2-2222-22-21-1-1122-1-1-2-2112i3−2i32i3−2i30000−i3−i3i3i3−i3−i3i3i3000000000000000000000000000
χ614-4-444-44-4-44-4-444000000-2422-44-4-2-222-24-2-2-2-42220000000000000000000000000000000000000000000
χ624-4-444-44-4-44-4-444000000-2-2222-22-21-1-11-2-21122-1-1000023−2323−23−33−33−33−33000000000000000000000000000
χ634-4-444-44-4-44-4-444000000-2-2222-22-21-1-11-2-21122-1-10000−2323−23233−33−33−33−3000000000000000000000000000
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
χ7266-6-6-300-33333−3333−33−3i23i23ζ5+3ζ73ζ13+3ζ23−3ζ5−3ζ7−3ζ13−3ζ230000000000000000000000000000000000002-200000-11−i2i23−3ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ230000000000
χ7366-6-6-300-33333−3333−33−3i23i23ζ5+3ζ73ζ13+3ζ23−3ζ5−3ζ7−3ζ13−3ζ23000000000000000000000000000000000000-22000001-1i2−i2−33−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ230000000000
χ7466-6-6-300-33333−3333−333i2−3i2−3ζ5−3ζ7−3ζ13−3ζ233ζ5+3ζ73ζ13+3ζ230000000000000000000000000000000000002-200000-11i2−i23−3−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ230000000000
χ7566-6-6-300-33333−3333−333i2−3i2−3ζ5−3ζ7−3ζ13−3ζ233ζ5+3ζ73ζ13+3ζ23000000000000000000000000000000000000-22000001-1−i2i2−33ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ230000000000
χ7666-6-6-300-333−3333−3333−3i23i23ζ13+3ζ233ζ5+3ζ7−3ζ13−3ζ23−3ζ5−3ζ70000000000000000000000000000000000002-200000-11−i2i2−33ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ70000000000
χ7766-6-6-300-333−3333−3333−3i23i23ζ13+3ζ233ζ5+3ζ7−3ζ13−3ζ23−3ζ5−3ζ7000000000000000000000000000000000000-22000001-1i2−i23−3−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ70000000000
χ7866-6-6-300-333−3333−33333i2−3i2−3ζ13−3ζ23−3ζ5−3ζ73ζ13+3ζ233ζ5+3ζ70000000000000000000000000000000000002-200000-11i2−i2−33−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ70000000000
χ7966-6-6-300-333−3333−33333i2−3i2−3ζ13−3ζ23−3ζ5−3ζ73ζ13+3ζ233ζ5+3ζ7000000000000000000000000000000000000-22000001-1−i2i23−3ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ70000000000
χ8012-1212-12-6006-6663−63−6363000000000000000000000000000000000000000000000000000000000000000000000
χ8112-1212-12-6006-66−636363−63000000000000000000000000000000000000000000000000000000000000000000000
χ8212-12-1212-612-1266-6-6-666000000000000000000000000000000000000000000000000000000000000000000000
χ8312-12-1212-6-121266-666-6-6000000000000000000000000000000000000000000000000000000000000000000000

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