Finite Group Databasebeta

← Group #10590888

Character table — Group #10590888

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size1111222222222244444444444444444444444444444424242424242424242424242436363636
order1222334466666636668812121212121212122424242424242424242424242424242422446666121212124488
χ1111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-11-111-1-111-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-11-11-1-111-1-111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1
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
χ8111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1
χ9222222-2-2222222222200-2-2-2-2-2-2-2-200000000000000000000000000002-200
χ10222222-2-2222222222200-2-2-2-2-2-2-2-20000000000000000000000000000-2200
χ1122222-1222-12-12-1-1-1-1-1222-1-1-12-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1020200-1-100-1-10000
χ1222222-1222-12-12-1-1-1-1-1222-1-1-12-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10-20-2001100110000
χ1322222-1222-12-12-1-1-1-1-1-2-22-1-1-12-1-1-1-2-2-2-2111111111111020-200-1-100110000
χ1422222-1222-12-12-1-1-1-1-1-2-22-1-1-12-1-1-1-2-2-2-21111111111110-202001100-1-10000
χ152222-1222-12-12-12-1-1-1-122-12-1-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-12020-1-100-1-1000000
χ162222-1222-12-12-12-1-1-1-122-12-1-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-20-20110011000000
χ172222-1222-12-12-12-1-1-1-1-2-2-12-1-1-12-1-11111-2-2-2-21111111120-20-1-10011000000
χ182222-1222-12-12-12-1-1-1-1-2-2-12-1-1-12-1-11111-2-2-2-211111111-20201100-1-1000000
χ1922-2-2222-2-2-222-2-22-2-2200-2-2-2-222220000000000000000000000000000002i−2i
χ2022-2-2222-2-2-222-2-22-2-2200-2-2-2-22222000000000000000000000000000000−2i2i
χ2122-2-222-22-2-222-2-22-2-222i−2i2222-2-2-2-22i2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i−2i−2i0000000000000000
χ2222-2-222-22-2-222-2-22-2-22−2i2i2222-2-2-2-2−2i−2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i0000000000000000
χ2322-2-22-1-22-212-1-21-111-12i−2i2-1-1-1-21112i2i−2i−2i−i−iii−i−i−i−iiiii000000−i3i3003−30000
χ2422-2-22-1-22-212-1-21-111-12i−2i2-1-1-1-21112i2i−2i−2i−i−iii−i−i−i−iiiii000000i3−i300−330000
χ2522-2-22-1-22-212-1-21-111-1−2i2i2-1-1-1-2111−2i−2i2i2iii−i−iiiii−i−i−i−i000000−i3i300−330000
χ2622-2-22-1-22-212-1-21-111-1−2i2i2-1-1-1-2111−2i−2i2i2iii−i−iiiii−i−i−i−i000000i3−i3003−30000
χ2722-2-2-12-221-2-121-2-111-12i−2i-12-1-11-211−i−iii2i2i−2i−2i−i−i−i−iiiii0000−i3i3003−3000000
χ2822-2-2-12-221-2-121-2-111-12i−2i-12-1-11-211−i−iii2i2i−2i−2i−i−i−i−iiiii0000i3−i300−33000000
χ2922-2-2-12-221-2-121-2-111-1−2i2i-12-1-11-211ii−i−i−2i−2i2i2iiiii−i−i−i−i0000−i3i300−33000000
χ3022-2-2-12-221-2-121-2-111-1−2i2i-12-1-11-211ii−i−i−2i−2i2i2iiiii−i−i−i−i0000i3−i3003−3000000
χ3144444-2-4-44-24-24-2-2-2-2-200-4222-422200000000000000000000000000000000
χ324444-24-4-4-24-24-24-2-2-2-2002-4222-42200000000000000000000000000000000
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
χ3744-4-44-24-4-424-2-42-222-200-42224-2-2-200000000000000000000000000000000
χ3844-4-4-244-42-4-242-4-222-2002-422-24-2-200000000000000000000000000000000
χ3944-4-4-2-24-422-2-2221-1-110022-1-1-2-2110000000033-3-3-3-3330000000000000000
χ4044-4-4-2-24-422-2-2221-1-110022-1-1-2-21100000000-3-33333-3-30000000000000000
χ4144-4-4-2-2-4422-2-2221-1-114i−4i-2-21122-1-1−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−i0000000000000000
χ4244-4-4-2-2-4422-2-2221-1-11−4i4i-2-21122-1-12i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii0000000000000000
χ434-44-444004-4-4-4-4444-4-4000000000000000000000000000000000000000000
χ444-44-44-20042-42-4-2-2-22200000000000000i6−i6i6−i6i6−i6i6−i6i6−i6i6−i60000000000000000
χ454-44-44-20042-42-4-2-2-22200000000000000−i6i6−i6i6−i6i6−i6i6−i6i6−i6i60000000000000000
χ464-44-4-2400-2-42-424-2-22200000000006−66−600006−6−666−6−660000000000000000
χ474-44-4-2400-2-42-424-2-2220000000000−66−660000−666−6−666−60000000000000000
χ484-44-4-2-200-22222-211-1-100003i−3i003i−3i6−66−6i6−i6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ230000000000000000
χ494-44-4-2-200-22222-211-1-100003i−3i003i−3i−66−66−i6i6−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ230000000000000000
χ504-44-4-2-200-22222-211-1-10000−3i3i00−3i3i6−66−6−i6i6−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ130000000000000000
χ514-44-4-2-200-22222-211-1-10000−3i3i00−3i3i−66−66i6−i6i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ130000000000000000
χ524-4-444400-44-4-44-44-44-4000000000000000000000000000000000000000000
χ534-4-444-200-4-2-4242-22-22000000000000006−6−666−66−6−66−660000000000000000
χ544-4-444-200-4-2-4242-22-2200000000000000−666−6−66−666−66−60000000000000000
χ554-4-44-2400242-4-2-4-22-220000000000i6−i6−i6i60000i6−i6−i6i6−i6i6i6−i60000000000000000
χ564-4-44-2400242-4-2-4-22-220000000000−i6i6i6−i60000−i6i6i6−i6i6−i6−i6i60000000000000000
χ574-4-44-2-2002-222-221-11-100003i−3i00−3i3ii6−i6−i6i6−666−6−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000000000
χ584-4-44-2-2002-222-221-11-100003i−3i00−3i3i−i6i6i6−i66−6−66ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000000000
χ594-4-44-2-2002-222-221-11-10000−3i3i003i−3ii6−i6−i6i66−6−66−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000000000
χ604-4-44-2-2002-222-221-11-10000−3i3i003i−3i−i6i6i6−i6−666−6ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000000000

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