Finite Group Databasebeta

← Group #11786395

Character table — Group #11786395

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1111111144444444444444444444448888888888888888888888889999999936363636363636363636363636363636363636363636
order122222223344444466666666666666121212121212121212121212121212121212121212121212444444442244448888888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iiiiiii−i−i−i−i−i−i
χ4111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−i−i−i−i−iiiiiii
χ5111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-111-1-1-1-1
χ6111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111-1-11111
χ7111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111ii−i−iii−i−i−i−i−i−iiiii
χ8111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111−i−iii−i−iiiiiii−i−i−i−i
χ91111111111-1-111-1-111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-111-1-1-1-111-1-1
χ101111111111-1-111-1-111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-1-11111-1-111
χ111111111111-1-111-1-111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1ii−i−i−i−iii−i−iii−i−iii
χ121111111111-1-111-1-111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1−i−iiiii−i−iii−i−iii−i−i
χ131111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-111
χ141111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ151111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111ii−i−i−i−i−i−iiiiiii−i−i
χ161111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111−i−iiiiiii−i−i−i−i−i−iii
χ17222-2-2-2-222200002-22222-2-2-2-222-2-2-2-200000000000000002222-2-2-2-22222-2-2-2-22-200000000000000000000
χ18222-2-2-2-222200002-22222-2-2-2-222-2-2-2-200000000000000002222-2-2-2-2-2-2-2-22222-2200000000000000000000
χ19222-2-2-2-22220000-222222-2-2-2-222-2-2-2-20000000000000000-2-2-2-222222222-2-2-2-2-2200000000000000000000
χ20222-2-2-2-22220000-222222-2-2-2-222-2-2-2-20000000000000000-2-2-2-22222-2-2-2-222222-200000000000000000000
χ2122-222-2-2-22200000022-2-2-2-2-2-2-2-222220000000000000000000000002i2i−2i−2i2i−2i2i−2i0000002ζ−2ζ2ζ3−2ζ3000000000000
χ2222-222-2-2-22200000022-2-2-2-2-2-2-2-222220000000000000000000000002i2i−2i−2i2i−2i2i−2i000000−2ζ2ζ−2ζ32ζ3000000000000
χ2322-222-2-2-22200000022-2-2-2-2-2-2-2-22222000000000000000000000000−2i−2i2i2i−2i2i−2i2i0000002ζ3−2ζ32ζ−2ζ000000000000
χ2422-222-2-2-22200000022-2-2-2-2-2-2-2-22222000000000000000000000000−2i−2i2i2i−2i2i−2i2i000000−2ζ32ζ3−2ζ2ζ000000000000
χ2522-2-2-222-22200000022-2-22222-2-2-2-2-2-20000000000000000000000002i2i−2i−2i−2i2i−2i2i000000000000002ζ−2ζ00002ζ3−2ζ3
χ2622-2-2-222-22200000022-2-22222-2-2-2-2-2-20000000000000000000000002i2i−2i−2i−2i2i−2i2i00000000000000−2ζ2ζ0000−2ζ32ζ3
χ2722-2-2-222-22200000022-2-22222-2-2-2-2-2-2000000000000000000000000−2i−2i2i2i2i−2i2i−2i000000000000002ζ3−2ζ300002ζ−2ζ
χ2822-2-2-222-22200000022-2-22222-2-2-2-2-2-2000000000000000000000000−2i−2i2i2i2i−2i2i−2i00000000000000−2ζ32ζ30000−2ζ2ζ
χ292-222-22-2-222002i−2i00-2-22222-2-2-2-222-2-2000000002i2i2i2i−2i−2i−2i−2i000000002i−2i2i−2i2i−2i−2i2i00002-20000000000000000
χ302-222-22-2-222002i−2i00-2-22222-2-2-2-222-2-2000000002i2i2i2i−2i−2i−2i−2i00000000−2i2i−2i2i−2i2i2i−2i0000-220000000000000000
χ312-222-22-2-22200−2i2i00-2-22222-2-2-2-222-2-200000000−2i−2i−2i−2i2i2i2i2i000000002i−2i2i−2i2i−2i−2i2i0000-220000000000000000
χ322-222-22-2-22200−2i2i00-2-22222-2-2-2-222-2-200000000−2i−2i−2i−2i2i2i2i2i00000000−2i2i−2i2i−2i2i2i−2i00002-20000000000000000
χ332-22-22-22-2222i−2i0000-2-222-2-222-2-2-2-2222i2i2i2i−2i−2i−2i−2i00000000000000002i−2i2i−2i−2i2i2i−2i002-2000000000000000000
χ342-22-22-22-2222i−2i0000-2-222-2-222-2-2-2-2222i2i2i2i−2i−2i−2i−2i0000000000000000−2i2i−2i2i2i−2i−2i2i00-22000000000000000000
χ352-22-22-22-222−2i2i0000-2-222-2-222-2-2-2-222−2i−2i−2i−2i2i2i2i2i00000000000000002i−2i2i−2i−2i2i2i−2i00-22000000000000000000
χ362-22-22-22-222−2i2i0000-2-222-2-222-2-2-2-222−2i−2i−2i−2i2i2i2i2i0000000000000000−2i2i−2i2i2i−2i−2i2i002-2000000000000000000
χ372-2-22-2-22222000000-2-2-2-2-2-2222222-2-20000000000000000000000002-2-2222-2-20000000000002i−2i00002i−2i00
χ382-2-22-2-22222000000-2-2-2-2-2-2222222-2-20000000000000000000000002-2-2222-2-2000000000000−2i2i0000−2i2i00
χ392-2-22-2-22222000000-2-2-2-2-2-2222222-2-2000000000000000000000000-222-2-2-2220000000000002-20000-2200
χ402-2-22-2-22222000000-2-2-2-2-2-2222222-2-2000000000000000000000000-222-2-2-222000000000000-2200002-200
χ412-2-2-222-2222000000-2-2-2-222-2-222-2-2220000000000000000000000002-2-22-2-22200000000002-200002-20000
χ422-2-2-222-2222000000-2-2-2-222-2-222-2-2220000000000000000000000002-2-22-2-2220000000000-220000-220000
χ432-2-2-222-2222000000-2-2-2-222-2-222-2-222000000000000000000000000-222-222-2-200000000002i−2i0000−2i2i0000
χ442-2-2-222-2222000000-2-2-2-222-2-222-2-222000000000000000000000000-222-222-2-20000000000−2i2i00002i−2i0000
χ45444444441-24444441-21-21-21-21-21-21-211-2-211-2-211-2-211-2-211-2-211-2-2000000000000000000000000000000
χ46444444441-244-4-4-4-41-21-21-21-21-21-21-211-2-211-2-2-1-122-1-122-1-122-1-122000000000000000000000000000000
χ47444444441-2-4-444-4-41-21-21-21-21-21-21-2-1-122-1-12211-2-211-2-2-1-122-1-122000000000000000000000000000000
χ48444444441-2-4-4-4-4441-21-21-21-21-21-21-2-1-122-1-122-1-122-1-12211-2-211-2-2000000000000000000000000000000
χ4944444444-21444444-21-21-21-21-21-21-21-2-211-2-211-2-211-2-211-2-211-2-211000000000000000000000000000000
χ5044444444-2144-4-4-4-4-21-21-21-21-21-21-21-2-211-2-21122-1-122-1-122-1-122-1-1000000000000000000000000000000
χ5144444444-21-4-444-4-4-21-21-21-21-21-21-2122-1-122-1-1-2-211-2-21122-1-122-1-1000000000000000000000000000000
χ5244444444-21-4-4-4-444-21-21-21-21-21-21-2122-1-122-1-122-1-122-1-1-2-211-2-211000000000000000000000000000000
χ53444-4-4-4-441-200004-41-21-2-12-121-2-12-123i−3i003i−3i003i−3i003i−3i0011-2-2-1-122000000000000000000000000000000
χ54444-4-4-4-441-200004-41-21-2-12-121-2-12-12−3i3i00−3i3i00−3i3i00−3i3i0011-2-2-1-122000000000000000000000000000000
χ55444-4-4-4-441-20000-441-21-2-12-121-2-12-123i−3i003i−3i00−3i3i00−3i3i00-1-12211-2-2000000000000000000000000000000
χ56444-4-4-4-441-20000-441-21-2-12-121-2-12-12−3i3i00−3i3i003i−3i003i−3i00-1-12211-2-2000000000000000000000000000000
χ57444-4-4-4-44-2100004-4-21-212-12-1-212-12-1003i−3i003i−3i003i−3i003i−3i-2-21122-1-1000000000000000000000000000000
χ58444-4-4-4-44-2100004-4-21-212-12-1-212-12-100−3i3i00−3i3i00−3i3i00−3i3i-2-21122-1-1000000000000000000000000000000
χ59444-4-4-4-44-210000-44-21-212-12-1-212-12-1003i−3i003i−3i00−3i3i00−3i3i22-1-1-2-211000000000000000000000000000000
χ60444-4-4-4-44-210000-44-21-212-12-1-212-12-100−3i3i00−3i3i003i−3i003i−3i22-1-1-2-211000000000000000000000000000000
χ614-444-44-4-41-2004i−4i00-121-21-2-12-121-2-123-300-3300ii−2i−2i−i−i2i2i3i−3i003i−3i00000000000000000000000000000000
χ624-444-44-4-41-2004i−4i00-121-21-2-12-121-2-12-33003-300ii−2i−2i−i−i2i2i−3i3i00−3i3i00000000000000000000000000000000
χ634-444-44-4-41-200−4i4i00-121-21-2-12-121-2-123-300-3300−i−i2i2iii−2i−2i−3i3i00−3i3i00000000000000000000000000000000
χ644-444-44-4-41-200−4i4i00-121-21-2-12-121-2-12-33003-300−i−i2i2iii−2i−2i3i−3i003i−3i00000000000000000000000000000000
χ654-444-44-4-4-21004i−4i002-1-21-212-12-1-212-1003-300-33−2i−2iii2i2i−i−i003i−3i003i−3i000000000000000000000000000000
χ664-444-44-4-4-21004i−4i002-1-21-212-12-1-212-100-33003-3−2i−2iii2i2i−i−i00−3i3i00−3i3i000000000000000000000000000000
χ674-444-44-4-4-2100−4i4i002-1-21-212-12-1-212-1003-300-332i2i−i−i−2i−2iii00−3i3i00−3i3i000000000000000000000000000000
χ684-444-44-4-4-2100−4i4i002-1-21-212-12-1-212-100-33003-32i2i−i−i−2i−2iii003i−3i003i−3i000000000000000000000000000000
χ694-44-44-44-41-24i−4i0000-121-2-121-2-12-121-2ii−2i−2i−i−i2i2i3-300-3300−3i3i003i−3i00000000000000000000000000000000
χ704-44-44-44-41-24i−4i0000-121-2-121-2-12-121-2ii−2i−2i−i−i2i2i-33003-3003i−3i00−3i3i00000000000000000000000000000000
χ714-44-44-44-41-2−4i4i0000-121-2-121-2-12-121-2−i−i2i2iii−2i−2i3-300-33003i−3i00−3i3i00000000000000000000000000000000
χ724-44-44-44-41-2−4i4i0000-121-2-121-2-12-121-2−i−i2i2iii−2i−2i-33003-300−3i3i003i−3i00000000000000000000000000000000
χ734-44-44-44-4-214i−4i00002-1-212-1-212-12-1-21−2i−2iii2i2i−i−i003-300-3300−3i3i003i−3i000000000000000000000000000000
χ744-44-44-44-4-214i−4i00002-1-212-1-212-12-1-21−2i−2iii2i2i−i−i00-33003-3003i−3i00−3i3i000000000000000000000000000000
χ754-44-44-44-4-21−4i4i00002-1-212-1-212-12-1-212i2i−i−i−2i−2iii003-300-33003i−3i00−3i3i000000000000000000000000000000
χ764-44-44-44-4-21−4i4i00002-1-212-1-212-12-1-212i2i−i−i−2i−2iii00-33003-300−3i3i003i−3i000000000000000000000000000000
χ7788-888-8-8-82-40000002-4-24-24-24-242-42-4000000000000000000000000000000000000000000000000000000
χ7888-888-8-8-8-42000000-424-24-24-24-2-42-42000000000000000000000000000000000000000000000000000000
χ7988-8-8-888-82-40000002-4-242-42-4-24-24-24000000000000000000000000000000000000000000000000000000
χ8088-8-8-888-8-42000000-424-2-42-424-24-24-2000000000000000000000000000000000000000000000000000000
χ818-8-88-8-8882-4000000-24-24-242-42-42-4-24000000000000000000000000000000000000000000000000000000
χ828-8-88-8-888-420000004-24-24-2-42-42-424-2000000000000000000000000000000000000000000000000000000
χ838-8-8-888-882-4000000-24-242-4-242-4-242-4000000000000000000000000000000000000000000000000000000
χ848-8-8-888-88-420000004-24-2-424-2-424-2-42000000000000000000000000000000000000000000000000000000

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