Finite Group Databasebeta

← Group #13138871

Character table — Group #13138871

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111122222222224444446666666612121212121212121212121212121212121212121212121212121212363636363636363636363636727272727272727272727272
order1222344666121212128824242424336666663666121212121212121224242424242424242424242424242424246688121224242424244466121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-11111
χ511111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11-1-1111-1-111-1-1
χ611111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-111-1-1-111-1-111
χ711111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-111-1-1-1-111
χ811111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-11111-1-1
χ9222222222222222222222-12-1-12-12-1-1-1-1-12-1-1-12-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000000000002020-1-1-1-10000
χ10222222222222222222222-12-1-12-12-1-1-1-1-12-1-1-12-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000000-20-2011110000
χ1122222222222222222222-12-122-12-1-1-1-1-12-1-1-12-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000000002020000-1-1-1-1
χ1222222222222222222222-12-122-12-1-1-1-1-12-1-1-12-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000-20-200001111
χ1322222222222222-2-2-2-2-2-22-12-1-12-12-1-1-1-1-12-1-1-12-1-1-2-2-2-211111111111100000000000020-20-1-1110000
χ1422222222222222-2-2-2-2-2-22-12-1-12-12-1-1-1-1-12-1-1-12-1-1-2-2-2-2111111111111000000000000-202011-1-10000
χ1522222222222222-2-2-2-2-2-2-12-122-12-1-1-1-1-12-1-1-12-1-1-11111-2-2-2-211111111000000000000020-2000011-1-1
χ1622222222222222-2-2-2-2-2-2-12-122-12-1-1-1-1-12-1-1-12-1-1-11111-2-2-2-2111111110000000000000-2020000-1-111
χ1722222-2-2222-2-2-2-2000000222222222222-2-2-2-2-2-2-2-200000000000000002-22200-2-20000000000000000
χ1822222-2-2222-2-2-2-2000000222222222222-2-2-2-2-2-2-2-20000000000000000-22-2-200220000000000000000
χ192-22-222-2-2-2222-2-22i−2i2i2i−2i−2i22-2-22-2-222-2-222222-2-2-2-22i2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i−2i−2i000000000000000000000000
χ202-22-222-2-2-2222-2-22i−2i2i2i−2i−2i2-1-21-1-212-111-1-12-1-11-2112i2i−2i−2i−i−iii−i−i−i−iiiii0000000000000000−i3i33−30000
χ212-22-222-2-2-2222-2-22i−2i2i2i−2i−2i2-1-21-1-212-111-1-12-1-11-2112i2i−2i−2i−i−iii−i−i−i−iiiii0000000000000000i3−i3−330000
χ222-22-222-2-2-2222-2-22i−2i2i2i−2i−2i-121-221-2-1-111-12-1-1-1-2111−i−iii2i2i−2i−2i−i−i−i−iiiii000000000000000000003−3−i3i3
χ232-22-222-2-2-2222-2-22i−2i2i2i−2i−2i-121-221-2-1-111-12-1-1-1-2111−i−iii2i2i−2i−2i−i−i−i−iiiii00000000000000000000−33i3−i3
χ242-22-222-2-2-2222-2-2−2i2i−2i−2i2i2i22-2-22-2-222-2-222222-2-2-2-2−2i−2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i000000000000000000000000
χ252-22-222-2-2-2222-2-2−2i2i−2i−2i2i2i2-1-21-1-212-111-1-12-1-11-211−2i−2i2i2iii−i−iiiii−i−i−i−i0000000000000000−i3i3−330000
χ262-22-222-2-2-2222-2-2−2i2i−2i−2i2i2i2-1-21-1-212-111-1-12-1-11-211−2i−2i2i2iii−i−iiiii−i−i−i−i0000000000000000i3−i33−30000
χ272-22-222-2-2-2222-2-2−2i2i−2i−2i2i2i-121-221-2-1-111-12-1-1-1-2111ii−i−i−2i−2i2i2iiiii−i−i−i−i000000000000000000003−3i3−i3
χ282-22-222-2-2-2222-2-2−2i2i−2i−2i2i2i-121-221-2-1-111-12-1-1-1-2111ii−i−i−2i−2i2i2iiiii−i−i−i−i00000000000000000000−33−i3i3
χ292-22-22-22-2-22-2-22200000022-2-22-2-222-2-22-2-2-2-22222000000000000000000002-20022-2-2000000000000
χ302-22-22-22-2-22-2-22200000022-2-22-2-222-2-22-2-2-2-2222200000000000000000000-2200-2-222000000000000
χ3144444444444444444444-2-2-2-2-2-2-2-21111-2-211-2-211-2-2-2-2-2-2-2-211111111000000000000000000000000
χ3244444444444444-4-4-4-4-4-4-2-2-2-2-2-2-2-21111-2-211-2-21122222222-1-1-1-1-1-1-1-1000000000000000000000000
χ3344444-4-4444-4-4-4-40000004-24-2-24-24-2-2-2-22-4222-4220000000000000000000000000000000000000000
χ3444444-4-4444-4-4-4-4000000-24-244-24-2-2-2-2-2-4222-42220000000000000000000000000000000000000000
χ3544444-4-4444-4-4-4-4000000-2-2-2-2-2-2-2-2111122-1-122-1-1000000003i3i−3i−3i3i3i−3i−3i000000000000000000000000
χ3644444-4-4444-4-4-4-4000000-2-2-2-2-2-2-2-2111122-1-122-1-100000000−3i−3i3i3i−3i−3i3i3i000000000000000000000000
χ3744-4-44004-4-400000000004444-4-4-4-444-4-4000000000000000000000000000000000000000000000000
χ3844-4-44004-4-400000000004-24-22-42-4-2-2220000000000006−66−66−66−66−66−6000000000000000000000000
χ3944-4-44004-4-400000000004-24-22-42-4-2-222000000000000−66−66−66−66−66−66000000000000000000000000
χ4044-4-44004-4-40000000000-24-24-42-42-2-22200000000i6−i6i6−i60000i6−i6−i6i6i6−i6−i6i6000000000000000000000000
χ4144-4-44004-4-40000000000-24-24-42-42-2-22200000000−i6i6−i6i60000−i6i6i6−i6−i6i6i6−i6000000000000000000000000
χ4244-4-44004-4-40000000000-2-2-2-2222211-1-1003i−3i003i−3ii6−i6i6−i66−66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000
χ4344-4-44004-4-40000000000-2-2-2-2222211-1-1003i−3i003i−3i−i6i6−i6i6−66−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000
χ4444-4-44004-4-40000000000-2-2-2-2222211-1-100−3i3i00−3i3ii6−i6i6−i6−66−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000
χ4544-4-44004-4-40000000000-2-2-2-2222211-1-100−3i3i00−3i3i−i6i6−i6i66−66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000
χ464-44-444-4-4-4444-4-44i−4i4i4i−4i−4i-2-222-222-21-1-11-2-21122-1-1−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−i000000000000000000000000
χ474-44-444-4-4-4444-4-4−4i4i−4i−4i4i4i-2-222-222-21-1-11-2-21122-1-12i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii000000000000000000000000
χ484-44-44-44-4-44-4-4440000004-2-42-2-424-222-22-422-24-2-20000000000000000000000000000000000000000
χ494-44-44-44-4-44-4-444000000-242-442-4-2-222-2-42224-2-2-20000000000000000000000000000000000000000
χ504-44-44-44-4-44-4-444000000-2-222-222-21-1-1122-1-1-2-2110000000033-3-3-3-333000000000000000000000000
χ514-44-44-44-4-44-4-444000000-2-222-222-21-1-1122-1-1-2-21100000000-3-33333-3-3000000000000000000000000
χ524-4-44400-44-4000000000044-4-4-444-44-44-4000000000000000000000000000000000000000000000000
χ534-4-44400-44-400000000004-2-4224-2-4-22-22000000000000i6−i6−i6i6i6−i6i6−i6−i6i6−i6i6000000000000000000000000
χ544-4-44400-44-400000000004-2-4224-2-4-22-22000000000000−i6i6i6−i6−i6i6−i6i6i6−i6i6−i6000000000000000000000000
χ554-4-44400-44-40000000000-242-4-4-242-22-22000000006−6−6600006−6−66−666−6000000000000000000000000
χ564-4-44400-44-40000000000-242-4-4-242-22-2200000000−666−60000−666−66−6−66000000000000000000000000
χ574-4-44400-44-40000000000-2-2222-2-221-11-1003i−3i00−3i3i6−6−66−i6i6i6−i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000
χ584-4-44400-44-40000000000-2-2222-2-221-11-1003i−3i00−3i3i−666−6i6−i6−i6i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000
χ594-4-44400-44-40000000000-2-2222-2-221-11-100−3i3i003i−3i6−6−66i6−i6−i6i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000
χ604-4-44400-44-40000000000-2-2222-2-221-11-100−3i3i003i−3i−666−6−i6i6i6−i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000
χ616666-366-3-3-3-3-3-3-366-3-3-3-300000000000000000000000000000000000022-1-122-1-1-1-1-1-1000000000000
χ626666-366-3-3-3-3-3-3-366-3-3-3-3000000000000000000000000000000000000-2-211-2-2111111000000000000
χ636666-366-3-3-3-3-3-3-3-6-6333300000000000000000000000000000000000022-1-1-2-2-1-11111000000000000
χ646666-366-3-3-3-3-3-3-3-6-63333000000000000000000000000000000000000-2-2112211-1-1-1-1000000000000
χ656666-3-6-6-3-3-333330033−3333−330000000000000000000000000000000000002-2-1-100113−33−3000000000000
χ666666-3-6-6-3-3-333330033−3333−33000000000000000000000000000000000000-221100-1-1−33−33000000000000
χ676666-3-6-6-3-3-3333300−3333−33330000000000000000000000000000000000002-2-1-10011−33−33000000000000
χ686666-3-6-6-3-3-3333300−3333−3333000000000000000000000000000000000000-221100-1-13−33−3000000000000
χ696-66-6-36-633-3-3-3336i−6i−3i−3i3i3i00000000000000000000000000000000000000−i3i300−i3i33−3−33000000000000
χ706-66-6-36-633-3-3-3336i−6i−3i−3i3i3i00000000000000000000000000000000000000i3−i300i3−i3−333−3000000000000
χ716-66-6-36-633-3-3-333−6i6i3i3i−3i−3i00000000000000000000000000000000000000−i3i300−i3i3−333−3000000000000
χ726-66-6-36-633-3-3-333−6i6i3i3i−3i−3i00000000000000000000000000000000000000i3−i300i3−i33−3−33000000000000
χ736-66-6-3-6633-333-3-300−3i33i33i3−3i300000000000000000000000000000000000000−i3i32-2i3−i3-1-111000000000000
χ746-66-6-3-6633-333-3-300−3i33i33i3−3i300000000000000000000000000000000000000i3−i3-22−i3i311-1-1000000000000
χ756-66-6-3-6633-333-3-3003i3−3i3−3i33i300000000000000000000000000000000000000−i3i3-22i3−i311-1-1000000000000
χ766-66-6-3-6633-333-3-3003i3−3i3−3i33i300000000000000000000000000000000000000i3−i32-2−i3i3-1-111000000000000
χ771212-12-12-600-66663−6363−63000000000000000000000000000000000000000000000000000000000000000000
χ781212-12-12-600-666−6363−6363000000000000000000000000000000000000000000000000000000000000000000
χ7912-12-1212-6006-6663−63−6363000000000000000000000000000000000000000000000000000000000000000000
χ8012-12-1212-6006-66−636363−63000000000000000000000000000000000000000000000000000000000000000000

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