Finite Group Databasebeta

← Group #10590842

Character table — Group #10590842

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size1111222222222244444444444444444444444444444424242424242424242424242436363636
order122233446666663666881212121212121212242424242424242424242424242424242444661212121212122488
χ1111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-111-1-111-1-1
χ6111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-111-1-111
χ7111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11111-1-1-1-111
χ8111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-11111-1-1
χ9222222-2-2222222222200-2-2-2-2-2-2-2-200000000000000000000000000002-200
χ10222222-2-2222222222200-2-2-2-2-2-2-2-20000000000000000000000000000-2200
χ1122222-1222-1-12-12-1-1-1-122-12-1-1-12-1-12222-1-1-1-1-1-1-1-1-1-1-1-12200-1-1-1-100000000
χ1222222-1222-1-12-12-1-1-1-122-12-1-1-12-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-200111100000000
χ1322222-1222-1-12-12-1-1-1-1-2-2-12-1-1-12-1-1-2-2-2-21111111111112-200-1-11100000000
χ1422222-1222-1-12-12-1-1-1-1-2-2-12-1-1-12-1-1-2-2-2-2111111111111-220011-1-100000000
χ152222-1222-122-12-1-1-1-1-1222-1-1-12-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100220000-1-1-1-10000
χ162222-1222-122-12-1-1-1-1-1222-1-1-12-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100-2-2000011110000
χ172222-1222-122-12-1-1-1-1-1-2-22-1-1-12-1-1-11111-2-2-2-211111111002-20000-1-1110000
χ182222-1222-122-12-1-1-1-1-1-2-22-1-1-12-1-1-11111-2-2-2-21111111100-22000011-1-10000
χ192-2-22222-2-2-22-2-222-2-222i−2i2222-2-2-2-22i2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i−2i−2i0000000000000000
χ202-2-22222-2-2-22-2-222-2-22−2i2i2222-2-2-2-2−2i−2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i0000000000000000
χ212-2-2222-22-2-22-2-222-2-2200-2-2-2-222220000000000000000000000000000002-2
χ222-2-2222-22-2-22-2-222-2-2200-2-2-2-22222000000000000000000000000000000-22
χ232-2-222-12-2-21-1-212-111-12i−2i-12-1-11-2112i2i−2i−2i−i−iii−i−i−i−iiiii0000−i3i33−300000000
χ242-2-222-12-2-21-1-212-111-12i−2i-12-1-11-2112i2i−2i−2i−i−iii−i−i−i−iiiii0000i3−i3−3300000000
χ252-2-222-12-2-21-1-212-111-1−2i2i-12-1-11-211−2i−2i2i2iii−i−iiiii−i−i−i−i0000−i3i3−3300000000
χ262-2-222-12-2-21-1-212-111-1−2i2i-12-1-11-211−2i−2i2i2iii−i−iiiii−i−i−i−i0000i3−i33−300000000
χ272-2-22-122-21-221-2-1-111-12i−2i2-1-1-1-2111−i−iii2i2i−2i−2i−i−i−i−iiiii000000003−3−i3i30000
χ282-2-22-122-21-221-2-1-111-12i−2i2-1-1-1-2111−i−iii2i2i−2i−2i−i−i−i−iiiii00000000−33i3−i30000
χ292-2-22-122-21-221-2-1-111-1−2i2i2-1-1-1-2111ii−i−i−2i−2i2i2iiiii−i−i−i−i000000003−3i3−i30000
χ302-2-22-122-21-221-2-1-111-1−2i2i2-1-1-1-2111ii−i−i−2i−2i2i2iiiii−i−i−i−i00000000−33−i3i30000
χ3144444-2-4-44-2-24-24-2-2-2-2002-4222-42200000000000000000000000000000000
χ324444-24-4-4-244-24-2-2-2-2-200-4222-422200000000000000000000000000000000
χ334444-2-244-2-2-2-2-2-2111144-2-211-2-211-2-2-2-2-2-2-2-2111111110000000000000000
χ344444-2-244-2-2-2-2-2-21111-4-4-2-211-2-21122222222-1-1-1-1-1-1-1-10000000000000000
χ354444-2-2-4-4-2-2-2-2-2-211110022-1-122-1-1000000003i3i−3i−3i3i3i−3i−3i0000000000000000
χ364444-2-2-4-4-2-2-2-2-2-211110022-1-122-1-100000000−3i−3i3i3i−3i−3i3i3i0000000000000000
χ3744-4-4440044-4-4-4-444-4-4000000000000000000000000000000000000000000
χ3844-4-44-2004-22-42-4-2-222000000000000006−66−66−66−66−66−60000000000000000
χ3944-4-44-2004-22-42-4-2-22200000000000000−66−66−66−66−66−660000000000000000
χ4044-4-4-2400-24-42-42-2-2220000000000i6−i6i6−i60000i6−i6−i6i6i6−i6−i6i60000000000000000
χ4144-4-4-2400-24-42-42-2-2220000000000−i6i6−i6i60000−i6i6i6−i6−i6i6i6−i60000000000000000
χ4244-4-4-2-200-2-2222211-1-100003i−3i003i−3ii6−i6i6−i66−66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000000000
χ4344-4-4-2-200-2-2222211-1-100003i−3i003i−3i−i6i6−i6i6−66−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000000000
χ4444-4-4-2-200-2-2222211-1-10000−3i3i00−3i3ii6−i6i6−i6−66−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000000000
χ4544-4-4-2-200-2-2222211-1-10000−3i3i00−3i3i−i6i6−i6i66−66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000000000
χ464-44-44400-4-4-444-44-44-4000000000000000000000000000000000000000000
χ474-44-44-200-4224-2-4-22-2200000000000000i6−i6−i6i6i6−i6i6−i6−i6i6−i6i60000000000000000
χ484-44-44-200-4224-2-4-22-2200000000000000−i6i6i6−i6−i6i6−i6i6i6−i6i6−i60000000000000000
χ494-44-4-24002-4-4-242-22-2200000000006−6−6600006−6−66−666−60000000000000000
χ504-44-4-24002-4-4-242-22-220000000000−666−60000−666−66−6−660000000000000000
χ514-44-4-2-200222-2-221-11-100003i−3i00−3i3i6−6−66−i6i6i6−i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ130000000000000000
χ524-44-4-2-200222-2-221-11-100003i−3i00−3i3i−666−6i6−i6−i6i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ130000000000000000
χ534-44-4-2-200222-2-221-11-10000−3i3i003i−3i6−6−66i6−i6−i6i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ230000000000000000
χ544-44-4-2-200222-2-221-11-10000−3i3i003i−3i−666−6−i6i6i6−i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ230000000000000000
χ554-4-444-2-44-42-2-424-222-2002-422-24-2-200000000000000000000000000000000
χ564-4-44-24-442-442-4-2-222-200-42224-2-2-200000000000000000000000000000000
χ574-4-44-2-24-422-222-21-1-114i−4i-2-21122-1-1−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−i0000000000000000
χ584-4-44-2-24-422-222-21-1-11−4i4i-2-21122-1-12i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii0000000000000000
χ594-4-44-2-2-4422-222-21-1-110022-1-1-2-2110000000033-3-3-3-3330000000000000000
χ604-4-44-2-2-4422-222-21-1-110022-1-1-2-21100000000-3-33333-3-30000000000000000

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