Finite Group Databasebeta

← Group #10590742

Character table — Group #10590742

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222222224444444444444444444444444444999912121212121212121818181818182424242424242424
order122233446666668888366612121212121212122424242424242424242424242424242444442244444444888866121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111
χ511111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-111-1-1
χ611111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1-1-1-1-111-1-111
χ711111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-111
χ811111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-11111-1-1
χ911-1-111-11-1-11-1-11ii−i−i1-1-111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iii−i−i1-11-1i−ii−ii−i11-1-11-1i−ii−i1-1
χ1011-1-111-11-1-11-1-11ii−i−i1-1-111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iii−i−i-11-11−ii−iii−i11-1-1-11−ii−ii-11
χ1111-1-111-11-1-11-1-11ii−i−i1-1-111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−iii1-1-11i−i−ii−ii-1-1111-1i−i−ii-11
χ1211-1-111-11-1-11-1-11ii−i−i1-1-111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−iii-111-1−iii−i−ii-1-111-11−iii−i1-1
χ1311-1-111-11-1-11-1-11−i−iii1-1-111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiii−i−i1-1-11−iii−ii−i-1-1111-1−iii−i-11
χ1411-1-111-11-1-11-1-11−i−iii1-1-111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiii−i−i-111-1i−i−iii−i-1-111-11i−i−ii1-1
χ1511-1-111-11-1-11-1-11−i−iii1-1-111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−iii1-11-1−ii−ii−ii11-1-11-1−ii−ii1-1
χ1611-1-111-11-1-11-1-11−i−iii1-1-111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−iii-11-11i−ii−i−ii11-1-1-11i−ii−i-11
χ17222222-2-222222200002222-2-2-2-2-2-2-2-20000000000000000222200000000-2-2000000000000
χ18222222-2-222222200002222-2-2-2-2-2-2-2-20000000000000000-2-2-2-20000000022000000000000
χ1922222-1222-1-12-122222-1-1-1-1-12-1-1-12-1-122-1-1-1-1-1-122-1-1-1-1-1-1000022002200000000-1-1-1-10000
χ2022222-1222-1-12-122222-1-1-1-1-12-1-1-12-1-122-1-1-1-1-1-122-1-1-1-1-1-10000-2-200-2-20000000011110000
χ2122222-1222-1-12-12-2-2-2-2-1-1-1-1-12-1-1-12-1-1-2-2111111-2-211111100002200-2-200000000-1-1110000
χ2222222-1222-1-12-12-2-2-2-2-1-1-1-1-12-1-1-12-1-1-2-2111111-2-21111110000-2-200220000000011-1-10000
χ232222-1222-122-12-12222-1-1-1-12-1-1-12-1-1-1-1-122-1-1-1-1-1-122-1-1-1-10000002200220000000000-1-1-1-1
χ242222-1222-122-12-12222-1-1-1-12-1-1-12-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1000000-2-200-2-200000000001111
χ252222-1222-122-12-1-2-2-2-2-1-1-1-12-1-1-12-1-1-111-2-2111111-2-211110000002200-2-2000000000011-1-1
χ262222-1222-122-12-1-2-2-2-2-1-1-1-12-1-1-12-1-1-111-2-2111111-2-21111000000-2-200220000000000-1-111
χ2722-2-2222-2-2-22-2-2200002-2-22-2-2-2-2222200000000000000002i2i−2i−2i00000000−2i2i000000000000
χ2822-2-2222-2-2-22-2-2200002-2-22-2-2-2-222220000000000000000−2i−2i2i2i000000002i−2i000000000000
χ2922-2-22-1-22-21-1-2122i2i−2i−2i-111-1-12-1-11-2112i2i−i−i−i−i−i−i−2i−2iiiiiii00002-2002i−2i00000000-11−ii0000
χ3022-2-22-1-22-21-1-2122i2i−2i−2i-111-1-12-1-11-2112i2i−i−i−i−i−i−i−2i−2iiiiiii0000-2200−2i2i000000001-1i−i0000
χ3122-2-22-1-22-21-1-212−2i−2i2i2i-111-1-12-1-11-211−2i−2iiiiiii2i2i−i−i−i−i−i−i00002-200−2i2i00000000-11i−i0000
χ3222-2-22-1-22-21-1-212−2i−2i2i2i-111-1-12-1-11-211−2i−2iiiiiii2i2i−i−i−i−i−i−i0000-22002i−2i000000001-1−ii0000
χ3322-2-2-12-221-221-2-12i2i−2i−2i-111-12-1-1-1-2111−i−i2i2i−i−i−i−iii−2i−2iiiii0000002-2002i−2i0000000000−ii-11
χ3422-2-2-12-221-221-2-12i2i−2i−2i-111-12-1-1-1-2111−i−i2i2i−i−i−i−iii−2i−2iiiii000000-2200−2i2i0000000000i−i1-1
χ3522-2-2-12-221-221-2-1−2i−2i2i2i-111-12-1-1-1-2111ii−2i−2iiiii−i−i2i2i−i−i−i−i0000002-200−2i2i0000000000i−i-11
χ3622-2-2-12-221-221-2-1−2i−2i2i2i-111-12-1-1-1-2111ii−2i−2iiiii−i−i2i2i−i−i−i−i000000-22002i−2i0000000000−ii1-1
χ372-22-222002-2-2-22-22−22−222-2-2000000002−22−222−2−22−22−222−2−22i−2i2i−2i0000000000i2−i2i2−i200000000
χ382-22-222002-2-2-22-22−22−222-2-2000000002−22−222−2−22−22−222−2−2−2i2i−2i2i0000000000−i2i2−i2i200000000
χ392-22-222002-2-2-22-2−22−2222-2-200000000−22−22−2−222−22−22−2−2222i−2i2i−2i0000000000−i2i2−i2i200000000
χ402-22-222002-2-2-22-2−22−2222-2-200000000−22−22−2−222−22−22−2−222−2i2i−2i2i0000000000i2−i2i2−i200000000
χ412-2-222200-22-22-2-2i2−i2−i2i22-22-200000000i2−i2i2−i2i2i2−i2−i2−i2i2−i2i2−i2−i2i2i22-2-220000000000−i2i2i2−i200000000
χ422-2-222200-22-22-2-2i2−i2−i2i22-22-200000000i2−i2i2−i2i2i2−i2−i2−i2i2−i2i2−i2−i2i2i2-222-20000000000i2−i2−i2i200000000
χ432-2-222200-22-22-2-2−i2i2i2−i22-22-200000000−i2i2−i2i2−i2−i2i2i2i2−i2i2−i2i2i2−i2−i22-2-220000000000i2−i2−i2i200000000
χ442-2-222200-22-22-2-2−i2i2i2−i22-22-200000000−i2i2−i2i2−i2−i2i2i2i2−i2i2−i2i2i2−i2−i2-222-20000000000−i2i2i2−i200000000
χ4544444-2-4-44-2-24-240000-2-2-2-22-4222-422000000000000000000000000000000000000000000
χ464444-24-4-4-244-24-20000-2-2-2-2-4222-4222000000000000000000000000000000000000000000
χ474444-2-244-2-2-2-2-2-244441111-2-211-2-211-2-2-2-21111-2-2-2-2111100000000000000000000000000
χ484444-2-244-2-2-2-2-2-2-4-4-4-41111-2-211-2-2112222-1-1-1-12222-1-1-1-100000000000000000000000000
χ494444-2-2-4-4-2-2-2-2-2-20000111122-1-122-1-100003i−3i3i−3i00003i−3i3i−3i00000000000000000000000000
χ504444-2-2-4-4-2-2-2-2-2-20000111122-1-122-1-10000−3i3i−3i3i0000−3i3i−3i3i00000000000000000000000000
χ5144-4-44-24-4-42-2-4240000-222-22-422-24-2-2000000000000000000000000000000000000000000
χ5244-4-4-244-42-442-4-20000-222-2-42224-2-2-2000000000000000000000000000000000000000000
χ5344-4-4-2-24-422-222-200001-1-1122-1-1-2-21100003-33-30000-33-3300000000000000000000000000
χ5444-4-4-2-24-422-222-200001-1-1122-1-1-2-2110000-33-3300003-33-300000000000000000000000000
χ5544-4-4-2-2-4422-222-24i4i−4i−4i1-1-11-2-21122-1-1−2i−2i−2i−2iiiii2i2i2i2i−i−i−i−i00000000000000000000000000
χ5644-4-4-2-2-4422-222-2−4i−4i4i4i1-1-11-2-21122-1-12i2i2i2i−i−i−i−i−2i−2i−2i−2iiiii00000000000000000000000000
χ574-44-44-200422-4-2-422−2222−22-2-2220000000022−22−22−2−22222−22−22−2−22200000000000000000000000000
χ584-44-44-200422-4-2-4−2222−2222-2-22200000000−22222−222−2−2−22222−222−2−200000000000000000000000000
χ594-44-4-2400-2-4-424222−2222−22-2-22200000000−2222−22−2−222−2222−22−2−22200000000000000000000000000
χ604-44-4-2400-2-4-4242−2222−2222-2-222000000002−2−222222−2−22−2−222222−2−200000000000000000000000000
χ614-44-4-2-200-2222-2222−2222−2211-1-1003i−3i003i−3i−22−222ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ3−22−222ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ300000000000000000000000000
χ624-44-4-2-200-2222-2222−2222−2211-1-100−3i3i00−3i3i−22−22−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ3−22−22−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ300000000000000000000000000
χ634-44-4-2-200-2222-22−2222−222211-1-1003i−3i003i−3i2−22−2−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ32−22−2−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ300000000000000000000000000
χ644-44-4-2-200-2222-22−2222−222211-1-100−3i3i00−3i3i2−22−2ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ32−22−2ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ300000000000000000000000000
χ654-4-444-200-4-2242-42i2−2i2−2i22i2-22-22000000002i2−2i2−i2i2−i2−i2i2i2−2i22i2i2−i2i2i2−i2−i200000000000000000000000000
χ664-4-444-200-4-2242-4−2i22i22i2−2i2-22-2200000000−2i22i2i2−i2i2i2−i2−i22i2−2i2−i2i2−i2−i2i2i200000000000000000000000000
χ674-4-44-240024-4-2-422i2−2i2−2i22i2-22-2200000000−i2i22i2−2i2−i2−i2i2i2i2−i2−2i22i2i2i2−i2−i200000000000000000000000000
χ684-4-44-240024-4-2-42−2i22i22i2−2i2-22-2200000000i2−i2−2i22i2i2i2−i2−i2−i2i22i2−2i2−i2−i2i2i200000000000000000000000000
χ694-4-44-2-2002-22-2222i2−2i2−2i22i21-11-1003i−3i00−3i3i−i2i2−i2i2−ζ+2ζ32ζ−ζ3ζ−2ζ3−2ζ+ζ3i2−i2i2−i2ζ−2ζ3−2ζ+ζ3−ζ+2ζ32ζ−ζ300000000000000000000000000
χ704-4-44-2-2002-22-2222i2−2i2−2i22i21-11-100−3i3i003i−3i−i2i2−i2i22ζ−ζ3−ζ+2ζ3−2ζ+ζ3ζ−2ζ3i2−i2i2−i2−2ζ+ζ3ζ−2ζ32ζ−ζ3−ζ+2ζ300000000000000000000000000
χ714-4-44-2-2002-22-222−2i22i22i2−2i21-11-1003i−3i00−3i3ii2−i2i2−i2ζ−2ζ3−2ζ+ζ3−ζ+2ζ32ζ−ζ3−i2i2−i2i2−ζ+2ζ32ζ−ζ3ζ−2ζ3−2ζ+ζ300000000000000000000000000
χ724-4-44-2-2002-22-222−2i22i22i2−2i21-11-100−3i3i003i−3ii2−i2i2−i2−2ζ+ζ3ζ−2ζ32ζ−ζ3−ζ+2ζ3−i2i2−i2i22ζ−ζ3−ζ+2ζ3−2ζ+ζ3ζ−2ζ300000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.