Finite Group Databasebeta

← Group #10590943

Character table — Group #10590943

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size1111222222222244444444444444444444444444444412121212181824242424242424242424363636
order1222334466666636668812121212121212122424242424242424242424242424242422222244666612121212488
χ1111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11-111-1-111-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-111-1-1-11-1-111-1-111-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111
χ5111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-11-1-1
χ6111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1111-1-1-1-111-111
χ7111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-1-11111-1-1-111
χ8111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1
χ9222222-2-2222222222200-2-2-2-2-2-2-2-200000000000000000000220000000000-200
χ10222222-2-2222222222200-2-2-2-2-2-2-2-200000000000000000000-2-20000000000200
χ1122222-12222-1-1-12-1-1-1-122-12-1-1-12-1-12222-1-1-1-1-1-1-1-1-1-1-1-122000020-1-100-1-100000
χ1222222-12222-1-1-12-1-1-1-122-12-1-1-12-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-20000-2011001100000
χ1322222-12222-1-1-12-1-1-1-1-2-2-12-1-1-12-1-1-2-2-2-2111111111111220000-20-1-1001100000
χ1422222-12222-1-1-12-1-1-1-1-2-2-12-1-1-12-1-1-2-2-2-2111111111111-2-20000201100-1-100000
χ152222-1222-1-1222-1-1-1-1-1222-1-1-12-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10022000200-1-100-1-1000
χ162222-1222-1-1222-1-1-1-1-1222-1-1-12-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100-2-2000-200110011000
χ172222-1222-1-1222-1-1-1-1-1-2-22-1-1-12-1-1-11111-2-2-2-2111111110022000-200-1-10011000
χ182222-1222-1-1222-1-1-1-1-1-2-22-1-1-12-1-1-11111-2-2-2-21111111100-2-20002001100-1-1000
χ1922-2-222002-22-2-2-222-2-2−i2i200000000−i2−i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2i2i200002-200000000000−i2i2
χ2022-2-222002-22-2-2-222-2-2−i2i200000000−i2−i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2i2i20000-2200000000000i2−i2
χ2122-2-222002-22-2-2-222-2-2i2−i200000000i2i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2−i2−i200002-200000000000i2−i2
χ2222-2-222002-22-2-2-222-2-2i2−i200000000i2i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2−i2−i20000-2200000000000−i2i2
χ232-2-22222-2-2-2-22-222-2-2200-2-2-2-222220000000000000000002-20000002-20000000
χ242-2-22222-2-2-2-22-222-2-2200-2-2-2-22222000000000000000000-22000000-220000000
χ252-2-2222-22-2-2-22-222-2-22002222-2-2-2-200000000000000002-20000002-2000000000
χ262-2-2222-22-2-2-22-222-2-22002222-2-2-2-20000000000000000-22000000-22000000000
χ272-2-222-1-22-2-21-112-111-100-12-1-11-21100003−33−333−3−333−3−32-2000000-11003−300000
χ282-2-222-1-22-2-21-112-111-100-12-1-11-21100003−33−333−3−333−3−3-220000001-100−3300000
χ292-2-222-1-22-2-21-112-111-100-12-1-11-2110000−33−33−3−333−3−3332-2000000-1100−3300000
χ302-2-222-1-22-2-21-112-111-100-12-1-11-2110000−33−33−3−333−3−333-220000001-1003−300000
χ312-2-22-122-211-22-2-1-111-100-21112-1-1-1−i3i3−i3i30000−i3i3−i3i3−i3i3−i3i3002-2000000-1100−i3i3000
χ322-2-22-122-211-22-2-1-111-100-21112-1-1-1−i3i3−i3i30000−i3i3−i3i3−i3i3−i3i300-220000001-100i3−i3000
χ332-2-22-122-211-22-2-1-111-100-21112-1-1-1i3−i3i3−i30000i3−i3i3−i3i3−i3i3−i3002-2000000-1100i3−i3000
χ342-2-22-122-211-22-2-1-111-100-21112-1-1-1i3−i3i3−i30000i3−i3i3−i3i3−i3i3−i300-220000001-100−i3i3000
χ3544444-2-4-444-2-2-24-2-2-2-2002-4222-42200000000000000000000000000000000000
χ364444-24-4-4-2-2444-2-2-2-2-200-4222-422200000000000000000000000000000000000
χ374444-2-244-2-2-2-2-2-2111144-2-211-2-211-2-2-2-2-2-2-2-2111111110000000000000000000
χ384444-2-244-2-2-2-2-2-21111-4-4-2-211-2-21122222222-1-1-1-1-1-1-1-10000000000000000000
χ394444-2-2-4-4-2-2-2-2-2-211110022-1-122-1-1000000003i−3i−3i3i3i−3i−3i3i0000000000000000000
χ404444-2-2-4-4-2-2-2-2-2-211110022-1-122-1-100000000−3i3i3i−3i−3i3i3i−3i0000000000000000000
χ4144-4-44-2004-4-222-4-2-222−2i22i200000000−2i2−2i22i22i2i2i2−i2−i2i2i2i2i2−i2−i2−i2−i20000000000000000000
χ4244-4-44-2004-4-222-4-2-2222i2−2i2000000002i22i2−2i2−2i2−i2−i2i2i2−i2−i2−i2−i2i2i2i2i20000000000000000000
χ4344-4-4-2400-224-4-42-2-222−2i22i200000000i2i2−i2−i2−2i2−2i22i22i2i2i2i2i2−i2−i2−i2−i20000000000000000000
χ4444-4-4-2400-224-4-42-2-2222i2−2i200000000−i2−i2i2i22i22i2−2i2−2i2−i2−i2−i2−i2i2i2i2i20000000000000000000
χ4544-4-4-2-200-22-222211-1-1−2i22i2003i−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−ζ230000000000000000000
χ4644-4-4-2-200-22-222211-1-1−2i22i200−3i3i00−3i3ii2i2−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+2ζ230000000000000000000
χ4744-4-4-2-200-22-222211-1-12i2−2i2003i−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+ζ230000000000000000000
χ4844-4-4-2-200-22-222211-1-12i2−2i200−3i3i00−3i3i−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+ζ13−2ζ230000000000000000000
χ494-44-44400-44-4-44-44-44-4000000000000000000000000000000000000000000000
χ504-44-44-200-4422-2-4-22-2200000000000000i6−i6−i6i6i6i6−i6−i6−i6−i6i6i60000000000000000000
χ514-44-44-200-4422-2-4-22-2200000000000000−i6i6i6−i6−i6−i6i6i6i6i6−i6−i60000000000000000000
χ524-44-4-24002-2-4-442-22-2200000000006−6−6600006−66−6−66−660000000000000000000
χ534-44-4-24002-2-4-442-22-220000000000−666−60000−66−666−66−60000000000000000000
χ544-44-4-2-2002-222-221-11-100003i−3i00−3i3i6−6−66i6−i6−i6i6−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ130000000000000000000
χ554-44-4-2-2002-222-221-11-100003i−3i00−3i3i−666−6−i6i6i6−i6ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ130000000000000000000
χ564-44-4-2-2002-222-221-11-10000−3i3i003i−3i6−6−66−i6i6i6−i6ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ230000000000000000000
χ574-44-4-2-2002-222-221-11-10000−3i3i003i−3i−666−6i6−i6−i6i6−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ230000000000000000000
χ584-4-444-24-4-4-42-224-222-2002-422-24-2-200000000000000000000000000000000000
χ594-4-44-24-4422-44-4-2-222-2004-2-2-2-422200000000000000000000000000000000000
χ604-4-44-2-24-4222-22-21-1-110022-1-1-2-211−2i32i3−2i32i30000i3−i3i3−i3i3−i3i3−i30000000000000000000
χ614-4-44-2-24-4222-22-21-1-110022-1-1-2-2112i3−2i32i3−2i30000−i3i3−i3i3−i3i3−i3i30000000000000000000
χ624-4-44-2-2-44222-22-21-1-1100-2-21122-1-1000023−2323−23−3−333−3−3330000000000000000000
χ634-4-44-2-2-44222-22-21-1-1100-2-21122-1-10000−2323−232333−3−333−3−30000000000000000000

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