Finite Group Databasebeta

← Group #11786428

Character table — Group #11786428

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111122224444444444444444444448888888888888888888888889999181818183636363636363636363636363672727272
order1222224433466666688881212121212121212666612121212242424242424242424242424242424242222224444444444488884444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-1-1-1i−ii−i
χ411111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1−i−i−i−iiiii-1-1-1-1−ii−ii
χ511111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1
χ611111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i1111−ii−ii
χ811111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii1111i−ii−i
χ91111-1-11111-111111111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-111-1-111-1-111-1-111-1-1
χ101111-1-11111-111111111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-111-1-11111-1-1-1-111
χ111111-1-11111-111111111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11ii−i−i−i−iii-1-111i−i−ii
χ121111-1-11111-111111111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11−i−iiiii−i−i-1-111−iii−i
χ131111-1-11111-1111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-111-1-111-1-1-1-111-1-111
χ141111-1-11111-1111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-111-1-111-1-11111-1-1
χ151111-1-11111-1111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11ii−i−i−i−iii11-1-1−iii−i
χ161111-1-11111-1111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11−i−iiiii−i−i11-1-1i−i−ii
χ17222222-2-222-22222220000-2-2-2-2-2-2-2-22222-2-2-2-20000000000000000222222-2-2-20000000000000000
χ18222222-2-222-22222220000-2-2-2-2-2-2-2-22222-2-2-2-20000000000000000-2-2-2-2-2-22220000000000000000
χ192222-2-2-2-22222222220000-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000002222-2-2-2-220000000000000000
χ202222-2-2-2-22222222220000-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000-2-2-2-22222-20000000000000000
χ2122-2-22-20022022-2-2-2-22−22−20000000022-2-200002222−2−2−2−22222−2−2−2−222-2-22-2000000000002−22−20000
χ2222-2-22-20022022-2-2-2-22−22−20000000022-2-200002222−2−2−2−22222−2−2−2−2-2-222-2200000000000−22−220000
χ2322-2-22-20022022-2-2-2-2−22−220000000022-2-20000−2−2−2−22222−2−2−2−2222222-2-22-200000000000−22−220000
χ2422-2-22-20022022-2-2-2-2−22−220000000022-2-20000−2−2−2−22222−2−2−2−22222-2-222-22000000000002−22−20000
χ2522-2-2-220022022-2-2-2-22−2−2200000000-2-22200002222−2−2−2−2−2−2−2−2222222-2-2-22000000000002−2−220000
χ2622-2-2-220022022-2-2-2-22−2−2200000000-2-22200002222−2−2−2−2−2−2−2−22222-2-2222-200000000000−222−20000
χ2722-2-2-220022022-2-2-2-2−222−200000000-2-2220000−2−2−2−222222222−2−2−2−222-2-2-2200000000000−222−20000
χ2822-2-2-220022022-2-2-2-2−222−200000000-2-2220000−2−2−2−222222222−2−2−2−2-2-2222-2000000000002−2−220000
χ292-2-22002-2220-2-2-2-22200002222-2-2-2-20000000000000000000000002-22-2002-20002i−2i002i−2i00000000
χ302-2-22002-2220-2-2-2-22200002222-2-2-2-20000000000000000000000002-22-2002-2000−2i2i00−2i2i00000000
χ312-2-22002-2220-2-2-2-22200002222-2-2-2-2000000000000000000000000-22-2200-220002-200-2200000000
χ322-2-22002-2220-2-2-2-22200002222-2-2-2-2000000000000000000000000-22-2200-22000-22002-200000000
χ332-2-2200-22220-2-2-2-2220000-2-2-2-222220000000000000000000000002-22-200-2202i−2i002i−2i0000000000
χ342-2-2200-22220-2-2-2-2220000-2-2-2-222220000000000000000000000002-22-200-220−2i2i00−2i2i0000000000
χ352-2-2200-22220-2-2-2-2220000-2-2-2-22222000000000000000000000000-22-22002-202-200-220000000000
χ362-2-2200-22220-2-2-2-2220000-2-2-2-22222000000000000000000000000-22-22002-20-22002-20000000000
χ37444444441-241-21-21-2444411-2-211-2-21-21-211-2-211-2-211-2-211-2-211-2-20000000000000000000000000
χ38444444441-241-21-21-2-4-4-4-411-2-211-2-21-21-211-2-2-1-122-1-122-1-122-1-1220000000000000000000000000
χ3944444444-214-21-21-214444-2-211-2-211-21-21-2-211-2-211-2-211-2-211-2-2110000000000000000000000000
χ4044444444-214-21-21-21-4-4-4-4-2-211-2-211-21-21-2-21122-1-122-1-122-1-122-1-10000000000000000000000000
χ41444444-4-41-2-41-21-21-20000-1-122-1-1221-21-2-1-1223i−3i003i−3i003i−3i003i−3i000000000000000000000000000
χ42444444-4-41-2-41-21-21-20000-1-122-1-1221-21-2-1-122−3i3i00−3i3i00−3i3i00−3i3i000000000000000000000000000
χ43444444-4-4-21-4-21-21-21000022-1-122-1-1-21-2122-1-1003i−3i003i−3i003i−3i003i−3i0000000000000000000000000
χ44444444-4-4-21-4-21-21-21000022-1-122-1-1-21-2122-1-100−3i3i00−3i3i00−3i3i00−3i3i0000000000000000000000000
χ454444-4-4441-2-41-21-21-244-4-411-2-211-2-2-12-12-1-12211-2-211-2-2-1-122-1-1220000000000000000000000000
χ464444-4-4441-2-41-21-21-2-4-44411-2-211-2-2-12-12-1-122-1-122-1-12211-2-211-2-20000000000000000000000000
χ474444-4-444-21-4-21-21-2144-4-4-2-211-2-2112-12-122-1-1-2-211-2-21122-1-122-1-10000000000000000000000000
χ484444-4-444-21-4-21-21-21-4-444-2-211-2-2112-12-122-1-122-1-122-1-1-2-211-2-2110000000000000000000000000
χ494444-4-4-4-41-241-21-21-20000-1-122-1-122-12-1211-2-23i−3i003i−3i00−3i3i00−3i3i000000000000000000000000000
χ504444-4-4-4-41-241-21-21-20000-1-122-1-122-12-1211-2-2−3i3i00−3i3i003i−3i003i−3i000000000000000000000000000
χ514444-4-4-4-4-214-21-21-21000022-1-122-1-12-12-1-2-211003i−3i003i−3i00−3i3i00−3i3i0000000000000000000000000
χ524444-4-4-4-4-214-21-21-21000022-1-122-1-12-12-1-2-21100−3i3i00−3i3i003i−3i003i−3i0000000000000000000000000
χ5344-4-44-4001-201-2-12-1222−2222−223i−3i003i−3i001-2-123i−3i002ζ+ζ3−ζ−2ζ3−2−2−2ζ−ζ3ζ+2ζ3222ζ+ζ3−ζ−2ζ3−2−2−2ζ−ζ3ζ+2ζ3220000000000000000000000000
χ5444-4-44-4001-201-2-12-1222−2222−22−3i3i00−3i3i001-2-12−3i3i00−ζ−2ζ32ζ+ζ3−2−2ζ+2ζ3−2ζ−ζ322−ζ−2ζ32ζ+ζ3−2−2ζ+2ζ3−2ζ−ζ3220000000000000000000000000
χ5544-4-44-4001-201-2-12-12−2222−22223i−3i003i−3i001-2-123i−3i00−2ζ−ζ3ζ+2ζ3222ζ+ζ3−ζ−2ζ3−2−2−2ζ−ζ3ζ+2ζ3222ζ+ζ3−ζ−2ζ3−2−20000000000000000000000000
χ5644-4-44-4001-201-2-12-12−2222−2222−3i3i00−3i3i001-2-12−3i3i00ζ+2ζ3−2ζ−ζ322−ζ−2ζ32ζ+ζ3−2−2ζ+2ζ3−2ζ−ζ322−ζ−2ζ32ζ+ζ3−2−20000000000000000000000000
χ5744-4-44-400-210-212-12-122−2222−22003i−3i003i−3i-212-1003i−3i−2−22ζ+ζ3−ζ−2ζ322−2ζ−ζ3ζ+2ζ3−2−22ζ+ζ3−ζ−2ζ322−2ζ−ζ3ζ+2ζ30000000000000000000000000
χ5844-4-44-400-210-212-12-122−2222−2200−3i3i00−3i3i-212-100−3i3i−2−2−ζ−2ζ32ζ+ζ322ζ+2ζ3−2ζ−ζ3−2−2−ζ−2ζ32ζ+ζ322ζ+2ζ3−2ζ−ζ30000000000000000000000000
χ5944-4-44-400-210-212-12-1−2222−2222003i−3i003i−3i-212-1003i−3i22−2ζ−ζ3ζ+2ζ3−2−22ζ+ζ3−ζ−2ζ322−2ζ−ζ3ζ+2ζ3−2−22ζ+ζ3−ζ−2ζ30000000000000000000000000
χ6044-4-44-400-210-212-12-1−2222−222200−3i3i00−3i3i-212-100−3i3i22ζ+2ζ3−2ζ−ζ3−2−2−ζ−2ζ32ζ+ζ322ζ+2ζ3−2ζ−ζ3−2−2−ζ−2ζ32ζ+ζ30000000000000000000000000
χ6144-4-4-44001-201-2-12-1222−22−22223i−3i003i−3i00-121-2−3i3i002ζ+ζ3−ζ−2ζ3−2−2−2ζ−ζ3ζ+2ζ322−2ζ−ζ3ζ+2ζ3222ζ+ζ3−ζ−2ζ3−2−20000000000000000000000000
χ6244-4-4-44001-201-2-12-1222−22−2222−3i3i00−3i3i00-121-23i−3i00−ζ−2ζ32ζ+ζ3−2−2ζ+2ζ3−2ζ−ζ322ζ+2ζ3−2ζ−ζ322−ζ−2ζ32ζ+ζ3−2−20000000000000000000000000
χ6344-4-4-44001-201-2-12-12−222222−223i−3i003i−3i00-121-2−3i3i00−2ζ−ζ3ζ+2ζ3222ζ+ζ3−ζ−2ζ3−2−22ζ+ζ3−ζ−2ζ3−2−2−2ζ−ζ3ζ+2ζ3220000000000000000000000000
χ6444-4-4-44001-201-2-12-12−222222−22−3i3i00−3i3i00-121-23i−3i00ζ+2ζ3−2ζ−ζ322−ζ−2ζ32ζ+ζ3−2−2−ζ−2ζ32ζ+ζ3−2−2ζ+2ζ3−2ζ−ζ3220000000000000000000000000
χ6544-4-4-4400-210-212-12-122−22−2222003i−3i003i−3i2-1-2100−3i3i−2−22ζ+ζ3−ζ−2ζ322−2ζ−ζ3ζ+2ζ322−2ζ−ζ3ζ+2ζ3−2−22ζ+ζ3−ζ−2ζ30000000000000000000000000
χ6644-4-4-4400-210-212-12-122−22−222200−3i3i00−3i3i2-1-21003i−3i−2−2−ζ−2ζ32ζ+ζ322ζ+2ζ3−2ζ−ζ322ζ+2ζ3−2ζ−ζ3−2−2−ζ−2ζ32ζ+ζ30000000000000000000000000
χ6744-4-4-4400-210-212-12-1−222222−22003i−3i003i−3i2-1-2100−3i3i22−2ζ−ζ3ζ+2ζ3−2−22ζ+ζ3−ζ−2ζ3−2−22ζ+ζ3−ζ−2ζ322−2ζ−ζ3ζ+2ζ30000000000000000000000000
χ6844-4-4-4400-210-212-12-1−222222−2200−3i3i00−3i3i2-1-21003i−3i22ζ+2ζ3−2ζ−ζ3−2−2−ζ−2ζ32ζ+ζ3−2−2−ζ−2ζ32ζ+ζ322ζ+2ζ3−2ζ−ζ30000000000000000000000000
χ694-44-40000440-4-444-4-40000000000000000000000000000000000004-4-44000000000000000000000
χ704-44-40000440-4-444-4-4000000000000000000000000000000000000-444-4000000000000000000000
χ718-88-800002-40-242-4-2400006i−6i00−6i6i000000000000000000000000000000000000000000000000000
χ728-88-800002-40-242-4-240000−6i6i006i−6i000000000000000000000000000000000000000000000000000
χ738-88-80000-4204-2-424-20000006i−6i00−6i6i0000000000000000000000000000000000000000000000000
χ748-88-80000-4204-2-424-2000000−6i6i006i−6i0000000000000000000000000000000000000000000000000
χ758-8-88008-82-40-24-242-4000022-4-4-2-2440000000000000000000000000000000000000000000000000
χ768-8-88008-8-4204-24-2-420000-4-42244-2-20000000000000000000000000000000000000000000000000
χ778-8-8800-882-40-24-242-40000-2-24422-4-40000000000000000000000000000000000000000000000000
χ788-8-8800-88-4204-24-2-42000044-2-2-4-4220000000000000000000000000000000000000000000000000

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