Finite Group Databasebeta

← Group #11790067

Character table — Group #11790067

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1111111144444444444444444444448888888888888888888888889999999936363636363636363636363636363636363636363636
order122222223344444466666666666666121212121212121212121212121212121212121212121212444444444444448888888888888888
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
χ5111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-111-1-1-1-1
χ6111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-11111
χ7111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−iii−i−i−i−i−i−iiiii
χ8111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−iii−i−iiiiiii−i−i−i−i
χ91111111111-1-111-1-111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-111-1-1-1-111-1-1
χ101111111111-1-111-1-111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-111-1-11111-1-111
χ111111111111-1-111-1-111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111ii−i−i−i−iii−i−iii−i−iii
χ121111111111-1-111-1-111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111−i−iiiii−i−iii−i−iii−i−i
χ131111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-111
χ141111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-11111-1-11111-1-1
χ151111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1ii−i−i−i−i−i−iiiiiii−i−i
χ161111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1−i−iiiiiii−i−i−i−i−i−iii
χ17222-22-2-2-222000000222222-2-2-2-2-2-2-2-200000000000000000000000022-2-222-2-20000002-22-2000000000000
χ18222-22-2-2-222000000222222-2-2-2-2-2-2-2-200000000000000000000000022-2-222-2-2000000-22-22000000000000
χ19222-22-2-2-222000000222222-2-2-2-2-2-2-2-2000000000000000000000000-2-222-2-2220000002i−2i−2i2i000000000000
χ20222-22-2-2-222000000222222-2-2-2-2-2-2-2-2000000000000000000000000-2-222-2-222000000−2i2i2i−2i000000000000
χ2122-22-2-22-22200000022-2-2-2-2-2-22222-2-20000000000000000000000002i−2i2i−2i2i−2i2i−2i000000000000002ζ3−2ζ300002ζ−2ζ
χ2222-22-2-22-22200000022-2-2-2-2-2-22222-2-20000000000000000000000002i−2i2i−2i2i−2i2i−2i00000000000000−2ζ32ζ30000−2ζ2ζ
χ2322-22-2-22-22200000022-2-2-2-2-2-22222-2-2000000000000000000000000−2i2i−2i2i−2i2i−2i2i000000000000002ζ−2ζ00002ζ3−2ζ3
χ2422-22-2-22-22200000022-2-2-2-2-2-22222-2-2000000000000000000000000−2i2i−2i2i−2i2i−2i2i00000000000000−2ζ2ζ0000−2ζ32ζ3
χ2522-2-2-22-222200002-222-2-2-2-222-2-2-2-22200000000000000002222-2-2-2-22i−2i−2i2i2i−2i−2i2i00002i−2i0000000000000000
χ2622-2-2-22-222200002-222-2-2-2-222-2-2-2-22200000000000000002222-2-2-2-2−2i2i2i−2i−2i2i2i−2i0000−2i2i0000000000000000
χ2722-2-2-22-22220000-2222-2-2-2-222-2-2-2-2220000000000000000-2-2-2-222222i−2i−2i2i2i−2i−2i2i0000−2i2i0000000000000000
χ2822-2-2-22-22220000-2222-2-2-2-222-2-2-2-2220000000000000000-2-2-2-22222−2i2i2i−2i−2i2i2i−2i00002i−2i0000000000000000
χ292-222-2-2-2222000000-2-222-2-2-2-222-2-2220000000000000000000000002i−2i2i−2i−2i2i−2i2i0000000000002ζ−2ζ00002ζ3−2ζ300
χ302-222-2-2-2222000000-2-222-2-2-2-222-2-2220000000000000000000000002i−2i2i−2i−2i2i−2i2i000000000000−2ζ2ζ0000−2ζ32ζ300
χ312-222-2-2-2222000000-2-222-2-2-2-222-2-222000000000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000002ζ3−2ζ300002ζ−2ζ00
χ322-222-2-2-2222000000-2-222-2-2-2-222-2-222000000000000000000000000−2i2i−2i2i2i−2i2i−2i000000000000−2ζ32ζ30000−2ζ2ζ00
χ332-22-2-222-222002-200-2-222-2-222-2-222-2-2000000002222-2-2-2-2000000002i−2i−2i2i−2i2i2i−2i002i−2i000000000000000000
χ342-22-2-222-222002-200-2-222-2-222-2-222-2-2000000002222-2-2-2-200000000−2i2i2i−2i2i−2i−2i2i00−2i2i000000000000000000
χ352-22-2-222-22200-2200-2-222-2-222-2-222-2-200000000-2-2-2-22222000000002i−2i−2i2i−2i2i2i−2i00−2i2i000000000000000000
χ362-22-2-222-22200-2200-2-222-2-222-2-222-2-200000000-2-2-2-2222200000000−2i2i2i−2i2i−2i−2i2i002i−2i000000000000000000
χ372-2-2222-2-2222-20000-2-2-2-2222222-2-2-2-22222-2-2-2-200000000000000002222-2-2-2-22-200000000000000000000
χ382-2-2222-2-2222-20000-2-2-2-2222222-2-2-2-22222-2-2-2-20000000000000000-2-2-2-22222-2200000000000000000000
χ392-2-2222-2-222-220000-2-2-2-2222222-2-2-2-2-2-2-2-2222200000000000000002222-2-2-2-2-2200000000000000000000
χ402-2-2222-2-222-220000-2-2-2-2222222-2-2-2-2-2-2-2-222220000000000000000-2-2-2-222222-200000000000000000000
χ412-2-2-22-22222000000-2-2-2-222-2-2-2-2222200000000000000000000000022-2-2-2-22200000000002-200002-20000
χ422-2-2-22-22222000000-2-2-2-222-2-2-2-2222200000000000000000000000022-2-2-2-2220000000000-220000-220000
χ432-2-2-22-22222000000-2-2-2-222-2-2-2-22222000000000000000000000000-2-22222-2-200000000002i−2i0000−2i2i0000
χ442-2-2-22-22222000000-2-2-2-222-2-2-2-22222000000000000000000000000-2-22222-2-20000000000−2i2i00002i−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
χ5344-4-4-44-441-200004-41-2-12-121-2-12-121-23i−3i003i−3i003i−3i003i−3i0011-2-2-1-122000000000000000000000000000000
χ5444-4-4-44-441-200004-41-2-12-121-2-12-121-2−3i3i00−3i3i00−3i3i00−3i3i0011-2-2-1-122000000000000000000000000000000
χ5544-4-4-44-441-20000-441-2-12-121-2-12-121-23i−3i003i−3i00−3i3i00−3i3i00-1-12211-2-2000000000000000000000000000000
χ5644-4-4-44-441-20000-441-2-12-121-2-12-121-2−3i3i00−3i3i003i−3i003i−3i00-1-12211-2-2000000000000000000000000000000
χ5744-4-4-44-44-2100004-4-212-12-1-212-12-1-21003i−3i003i−3i003i−3i003i−3i-2-21122-1-1000000000000000000000000000000
χ5844-4-4-44-44-2100004-4-212-12-1-212-12-1-2100−3i3i00−3i3i00−3i3i00−3i3i-2-21122-1-1000000000000000000000000000000
χ5944-4-4-44-44-210000-44-212-12-1-212-12-1-21003i−3i003i−3i00−3i3i00−3i3i22-1-1-2-211000000000000000000000000000000
χ6044-4-4-44-44-210000-44-212-12-1-212-12-1-2100−3i3i00−3i3i003i−3i003i−3i22-1-1-2-211000000000000000000000000000000
χ614-44-4-444-41-2004-400-121-2-121-2-121-2-123i−3i00−3i3i0011-2-2-1-1223i−3i003i−3i00000000000000000000000000000000
χ624-44-4-444-41-2004-400-121-2-121-2-121-2-12−3i3i003i−3i0011-2-2-1-122−3i3i00−3i3i00000000000000000000000000000000
χ634-44-4-444-41-200-4400-121-2-121-2-121-2-123i−3i00−3i3i00-1-12211-2-2−3i3i00−3i3i00000000000000000000000000000000
χ644-44-4-444-41-200-4400-121-2-121-2-121-2-12−3i3i003i−3i00-1-12211-2-23i−3i003i−3i00000000000000000000000000000000
χ654-44-4-444-4-21004-4002-1-212-1-212-1-212-1003i−3i00−3i3i-2-21122-1-1003i−3i003i−3i000000000000000000000000000000
χ664-44-4-444-4-21004-4002-1-212-1-212-1-212-100−3i3i003i−3i-2-21122-1-100−3i3i00−3i3i000000000000000000000000000000
χ674-44-4-444-4-2100-44002-1-212-1-212-1-212-1003i−3i00−3i3i22-1-1-2-21100−3i3i00−3i3i000000000000000000000000000000
χ684-44-4-444-4-2100-44002-1-212-1-212-1-212-100−3i3i003i−3i22-1-1-2-211003i−3i003i−3i000000000000000000000000000000
χ694-4-4444-4-41-24-40000-12-121-21-21-2-12-1211-2-2-1-1223i−3i00−3i3i00−3i3i003i−3i00000000000000000000000000000000
χ704-4-4444-4-41-24-40000-12-121-21-21-2-12-1211-2-2-1-122−3i3i003i−3i003i−3i00−3i3i00000000000000000000000000000000
χ714-4-4444-4-41-2-440000-12-121-21-21-2-12-12-1-12211-2-23i−3i00−3i3i003i−3i00−3i3i00000000000000000000000000000000
χ724-4-4444-4-41-2-440000-12-121-21-21-2-12-12-1-12211-2-2−3i3i003i−3i00−3i3i003i−3i00000000000000000000000000000000
χ734-4-4444-4-4-214-400002-12-1-21-21-212-12-1-2-21122-1-1003i−3i00−3i3i00−3i3i003i−3i000000000000000000000000000000
χ744-4-4444-4-4-214-400002-12-1-21-21-212-12-1-2-21122-1-100−3i3i003i−3i003i−3i00−3i3i000000000000000000000000000000
χ754-4-4444-4-4-21-4400002-12-1-21-21-212-12-122-1-1-2-211003i−3i00−3i3i003i−3i00−3i3i000000000000000000000000000000
χ764-4-4444-4-4-21-4400002-12-1-21-21-212-12-122-1-1-2-21100−3i3i003i−3i00−3i3i003i−3i000000000000000000000000000000
χ77888-88-8-8-82-40000002-42-42-4-24-24-24-24000000000000000000000000000000000000000000000000000000
χ78888-88-8-8-8-42000000-42-42-424-24-24-24-2000000000000000000000000000000000000000000000000000000
χ7988-88-8-88-82-40000002-4-24-24-242-42-4-24000000000000000000000000000000000000000000000000000000
χ8088-88-8-88-8-42000000-424-24-24-2-42-424-2000000000000000000000000000000000000000000000000000000
χ818-888-8-8-882-4000000-242-4-24-242-4-242-4000000000000000000000000000000000000000000000000000000
χ828-888-8-8-88-420000004-2-424-24-2-424-2-42000000000000000000000000000000000000000000000000000000
χ838-8-8-88-8882-4000000-24-242-4-24-242-42-4000000000000000000000000000000000000000000000000000000
χ848-8-8-88-888-420000004-24-2-424-24-2-42-42000000000000000000000000000000000000000000000000000000

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