Finite Group Databasebeta

← Group #11786502

Character table — Group #11786502

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111122224444444444444444444448888888888888888888888889999181818183636363636363636363636363672727272
order1222444423366666688881212121212121212666612121212242424242424242424242424242424242222444424444444488884444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1ii−i−iii−i−i-1-1-1-1i−ii−i
χ411111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1−i−iii−i−iii-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
χ711111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−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−iii−i−iii1111i−ii−i
χ91111-1-111-11111111111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-11111-1-1-1-111-1-111-1-1
χ101111-1-111-11111111111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1111111-1-1-1-111
χ111111-1-111-11111111111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111ii−i−i−i−iii-1-111i−i−ii
χ121111-1-111-11111111111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111−i−iiiii−i−i-1-111−iii−i
χ131111-1-111-111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-11111-1-1-1-1-1-111-1-111
χ141111-1-111-111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-11111-1-11111-1-1
χ151111-1-111-111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111ii−i−i−i−iii11-1-1−iii−i
χ161111-1-111-111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111−i−iiiii−i−i11-1-1i−i−ii
χ17222222-2-2-2222222220000-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000002222-2-222-20000000000000000
χ18222222-2-2-2222222220000-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000-2-2-2-222-2-220000000000000000
χ192222-2-2-2-22222222220000-2-2-2-2-2-2-2-22222-2-2-2-200000000000000002222-2-2-2-220000000000000000
χ202222-2-2-2-22222222220000-2-2-2-2-2-2-2-22222-2-2-2-20000000000000000-2-2-2-22222-20000000000000000
χ2122-2-22i−2i0002222-2-2-2-22−2i2−i20000000000002i2i−2i−2i2222−2−2−2−2i2i2i2i2−i2−i2−i2−i22-2-22002i−2i0000000002−2i2−i20000
χ2222-2-22i−2i0002222-2-2-2-22−2i2−i20000000000002i2i−2i−2i2222−2−2−2−2i2i2i2i2−i2−i2−i2−i2-222-200−2i2i000000000−22−i2i20000
χ2322-2-22i−2i0002222-2-2-2-2−22−i2i20000000000002i2i−2i−2i−2−2−2−22222−i2−i2−i2−i2i2i2i2i22-2-22002i−2i000000000−22−i2i20000
χ2422-2-22i−2i0002222-2-2-2-2−22−i2i20000000000002i2i−2i−2i−2−2−2−22222−i2−i2−i2−i2i2i2i2i2-222-200−2i2i0000000002−2i2−i20000
χ2522-2-2−2i2i0002222-2-2-2-22−2−i2i2000000000000−2i−2i2i2i2222−2−2−2−2−i2−i2−i2−i2i2i2i2i22-2-2200−2i2i0000000002−2−i2i20000
χ2622-2-2−2i2i0002222-2-2-2-22−2−i2i2000000000000−2i−2i2i2i2222−2−2−2−2−i2−i2−i2−i2i2i2i2i2-222-2002i−2i000000000−22i2−i20000
χ2722-2-2−2i2i0002222-2-2-2-2−22i2−i2000000000000−2i−2i2i2i−2−2−2−22222i2i2i2i2−i2−i2−i2−i22-2-2200−2i2i000000000−22i2−i20000
χ2822-2-2−2i2i0002222-2-2-2-2−22i2−i2000000000000−2i−2i2i2i−2−2−2−22222i2i2i2i2−i2−i2−i2−i2-222-2002i−2i0000000002−2−i2i20000
χ292-2-22002-2022-2-2-2-22200002222-2-2-2-200000000000000000000000022-2-22-200000002i−2i2i−2i00000000
χ302-2-22002-2022-2-2-2-22200002222-2-2-2-200000000000000000000000022-2-22-20000000−2i2i−2i2i00000000
χ312-2-22002-2022-2-2-2-22200002222-2-2-2-2000000000000000000000000-2-222-2200000002-2-2200000000
χ322-2-22002-2022-2-2-2-22200002222-2-2-2-2000000000000000000000000-2-222-220000000-222-200000000
χ332-2-2200-22022-2-2-2-2220000-2-2-2-2222200000000000000000000000022-2-2-220002i−2i2i−2i000000000000
χ342-2-2200-22022-2-2-2-2220000-2-2-2-2222200000000000000000000000022-2-2-22000−2i2i−2i2i000000000000
χ352-2-2200-22022-2-2-2-2220000-2-2-2-22222000000000000000000000000-2-2222-20002-2-22000000000000
χ362-2-2200-22022-2-2-2-2220000-2-2-2-22222000000000000000000000000-2-2222-2000-222-2000000000000
χ374444444441-21-21-21-2444411-2-211-2-211-2-21-21-211-2-211-2-211-2-211-2-20000000000000000000000000
χ384444444441-21-21-21-2-4-4-4-411-2-211-2-211-2-21-21-2-1-122-1-122-1-122-1-1220000000000000000000000000
χ39444444444-21-21-21-214444-2-211-2-211-2-211-21-21-2-211-2-211-2-211-2-2110000000000000000000000000
χ40444444444-21-21-21-21-4-4-4-4-2-211-2-211-2-211-21-2122-1-122-1-122-1-122-1-10000000000000000000000000
χ41444444-4-4-41-21-21-21-20000-1-122-1-122-1-1221-21-23i−3i003i−3i003i−3i003i−3i000000000000000000000000000
χ42444444-4-4-41-21-21-21-20000-1-122-1-122-1-1221-21-2−3i3i00−3i3i00−3i3i00−3i3i000000000000000000000000000
χ43444444-4-4-4-21-21-21-21000022-1-122-1-122-1-1-21-21003i−3i003i−3i003i−3i003i−3i0000000000000000000000000
χ44444444-4-4-4-21-21-21-21000022-1-122-1-122-1-1-21-2100−3i3i00−3i3i00−3i3i00−3i3i0000000000000000000000000
χ454444-4-444-41-21-21-21-244-4-411-2-211-2-2-1-122-12-1211-2-211-2-2-1-122-1-1220000000000000000000000000
χ464444-4-444-41-21-21-21-2-4-44411-2-211-2-2-1-122-12-12-1-122-1-12211-2-211-2-20000000000000000000000000
χ474444-4-444-4-21-21-21-2144-4-4-2-211-2-21122-1-12-12-1-2-211-2-21122-1-122-1-10000000000000000000000000
χ484444-4-444-4-21-21-21-21-4-444-2-211-2-21122-1-12-12-122-1-122-1-1-2-211-2-2110000000000000000000000000
χ494444-4-4-4-441-21-21-21-20000-1-122-1-12211-2-2-12-123i−3i003i−3i00−3i3i00−3i3i000000000000000000000000000
χ504444-4-4-4-441-21-21-21-20000-1-122-1-12211-2-2-12-12−3i3i00−3i3i003i−3i003i−3i000000000000000000000000000
χ514444-4-4-4-44-21-21-21-21000022-1-122-1-1-2-2112-12-1003i−3i003i−3i00−3i3i00−3i3i0000000000000000000000000
χ524444-4-4-4-44-21-21-21-21000022-1-122-1-1-2-2112-12-100−3i3i00−3i3i003i−3i003i−3i0000000000000000000000000
χ5344-4-44i−4i0001-21-2-12-1222−222i2−2i23i−3i003i−3i003-300i−2i−i2i2ζ+ζ3−ζ−2ζ3−2−2−2ζ−ζ3ζ+2ζ322−ζ+2ζ32ζ−ζ3−i2−i2ζ−2ζ3−2ζ+ζ3i2i20000000000000000000000000
χ5444-4-44i−4i0001-21-2-12-1222−222i2−2i2−3i3i00−3i3i00-3300i−2i−i2i−ζ−2ζ32ζ+ζ3−2−2ζ+2ζ3−2ζ−ζ3222ζ−ζ3−ζ+2ζ3−i2−i2−2ζ+ζ3ζ−2ζ3i2i20000000000000000000000000
χ5544-4-44i−4i0001-21-2-12-12−2222−2i22i23i−3i003i−3i003-300i−2i−i2i−2ζ−ζ3ζ+2ζ3222ζ+ζ3−ζ−2ζ3−2−2ζ−2ζ3−2ζ+ζ3i2i2−ζ+2ζ32ζ−ζ3−i2−i20000000000000000000000000
χ5644-4-44i−4i0001-21-2-12-12−2222−2i22i2−3i3i00−3i3i00-3300i−2i−i2iζ+2ζ3−2ζ−ζ322−ζ−2ζ32ζ+ζ3−2−2−2ζ+ζ3ζ−2ζ3i2i22ζ−ζ3−ζ+2ζ3−i2−i20000000000000000000000000
χ5744-4-44i−4i000-21-212-12-122−222i2−2i2003i−3i003i−3i003-3−2ii2i−i−2−22ζ+ζ3−ζ−2ζ322−2ζ−ζ3ζ+2ζ3−i2−i2−ζ+2ζ32ζ−ζ3i2i2ζ−2ζ3−2ζ+ζ30000000000000000000000000
χ5844-4-44i−4i000-21-212-12-122−222i2−2i200−3i3i00−3i3i00-33−2ii2i−i−2−2−ζ−2ζ32ζ+ζ322ζ+2ζ3−2ζ−ζ3−i2−i22ζ−ζ3−ζ+2ζ3i2i2−2ζ+ζ3ζ−2ζ30000000000000000000000000
χ5944-4-44i−4i000-21-212-12-1−2222−2i22i2003i−3i003i−3i003-3−2ii2i−i22−2ζ−ζ3ζ+2ζ3−2−22ζ+ζ3−ζ−2ζ3i2i2ζ−2ζ3−2ζ+ζ3−i2−i2−ζ+2ζ32ζ−ζ30000000000000000000000000
χ6044-4-44i−4i000-21-212-12-1−2222−2i22i200−3i3i00−3i3i00-33−2ii2i−i22ζ+2ζ3−2ζ−ζ3−2−2−ζ−2ζ32ζ+ζ3i2i2−2ζ+ζ3ζ−2ζ3−i2−i22ζ−ζ3−ζ+2ζ30000000000000000000000000
χ6144-4-4−4i4i0001-21-2-12-1222−22−2i22i23i−3i003i−3i00-3300−i2ii−2i2ζ+ζ3−ζ−2ζ3−2−2−2ζ−ζ3ζ+2ζ322ζ−2ζ3−2ζ+ζ3i2i2−ζ+2ζ32ζ−ζ3−i2−i20000000000000000000000000
χ6244-4-4−4i4i0001-21-2-12-1222−22−2i22i2−3i3i00−3i3i003-300−i2ii−2i−ζ−2ζ32ζ+ζ3−2−2ζ+2ζ3−2ζ−ζ322−2ζ+ζ3ζ−2ζ3i2i22ζ−ζ3−ζ+2ζ3−i2−i20000000000000000000000000
χ6344-4-4−4i4i0001-21-2-12-12−22222i2−2i23i−3i003i−3i00-3300−i2ii−2i−2ζ−ζ3ζ+2ζ3222ζ+ζ3−ζ−2ζ3−2−2−ζ+2ζ32ζ−ζ3−i2−i2ζ−2ζ3−2ζ+ζ3i2i20000000000000000000000000
χ6444-4-4−4i4i0001-21-2-12-12−22222i2−2i2−3i3i00−3i3i003-300−i2ii−2iζ+2ζ3−2ζ−ζ322−ζ−2ζ32ζ+ζ3−2−22ζ−ζ3−ζ+2ζ3−i2−i2−2ζ+ζ3ζ−2ζ3i2i20000000000000000000000000
χ6544-4-4−4i4i000-21-212-12-122−22−2i22i2003i−3i003i−3i00-332i−i−2ii−2−22ζ+ζ3−ζ−2ζ322−2ζ−ζ3ζ+2ζ3i2i2ζ−2ζ3−2ζ+ζ3−i2−i2−ζ+2ζ32ζ−ζ30000000000000000000000000
χ6644-4-4−4i4i000-21-212-12-122−22−2i22i200−3i3i00−3i3i003-32i−i−2ii−2−2−ζ−2ζ32ζ+ζ322ζ+2ζ3−2ζ−ζ3i2i2−2ζ+ζ3ζ−2ζ3−i2−i22ζ−ζ3−ζ+2ζ30000000000000000000000000
χ6744-4-4−4i4i000-21-212-12-1−22222i2−2i2003i−3i003i−3i00-332i−i−2ii22−2ζ−ζ3ζ+2ζ3−2−22ζ+ζ3−ζ−2ζ3−i2−i2−ζ+2ζ32ζ−ζ3i2i2ζ−2ζ3−2ζ+ζ30000000000000000000000000
χ6844-4-4−4i4i000-21-212-12-1−22222i2−2i200−3i3i00−3i3i003-32i−i−2ii22ζ+2ζ3−2ζ−ζ3−2−2−ζ−2ζ32ζ+ζ3−i2−i22ζ−ζ3−ζ+2ζ3i2i2−2ζ+ζ3ζ−2ζ30000000000000000000000000
χ694-44-40000044-4-444-4-40000000000000000000000000000000000004-44-4000000000000000000000
χ704-44-40000044-4-444-4-4000000000000000000000000000000000000-44-44000000000000000000000
χ718-88-8000002-4-242-4-2400006i−6i00−6i6i000000000000000000000000000000000000000000000000000
χ728-88-8000002-4-242-4-240000−6i6i006i−6i000000000000000000000000000000000000000000000000000
χ738-88-800000-424-2-424-20000006i−6i00−6i6i0000000000000000000000000000000000000000000000000
χ748-88-800000-424-2-424-2000000−6i6i006i−6i0000000000000000000000000000000000000000000000000
χ758-8-88008-802-4-24-242-4000022-4-4-2-2440000000000000000000000000000000000000000000000000
χ768-8-88008-80-424-24-2-420000-4-42244-2-20000000000000000000000000000000000000000000000000
χ778-8-8800-8802-4-24-242-40000-2-24422-4-40000000000000000000000000000000000000000000000000
χ788-8-8800-880-424-24-2-42000044-2-2-4-4220000000000000000000000000000000000000000000000000

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