Finite Group Databasebeta

← Group #11777628

Character table — Group #11777628

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size1111224444444444448888888888888999916161616161616161818181818183636363636363636363636363636727272
order1222443344666666882121212122424242424242424444466661212121244888822888888888888488
χ1111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-1
χ31111111111111111111111111111111-1-1-1-111111111-1-1ii−i−i-1-1-1-1iii−i−i−iii−i−i-1i−i
χ41111111111111111111111111111111-1-1-1-111111111-1-1−i−iii-1-1-1-1−i−i−iiii−i−iii-1−ii
χ51111111111111111-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1111111-1-1-1-1-1-1-1
χ61111111111111111-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111-111
χ71111111111111111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1ii−i−i-1-111iii−i−i−i−i−iii1−ii
χ81111111111111111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1−i−iii-1-111−i−i−iiiiii−i−i1i−i
χ911111111-1-111111111-11111111111111111-1-1-1-1-1-1-1-1111111-1-1111-1-11-1-11111-1-1-1
χ1011111111-1-111111111-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-111-111-1-1-1-1-111
χ1111111111-1-111111111-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i11-1-1i−i−i−iiiii−i−i1−ii
χ1211111111-1-111111111-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii11-1-1−iiii−i−i−i−iii1i−i
χ1311111111-1-1111111-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-11-1-11-1-1-1-1-1-1111
χ1411111111-1-1111111-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-111-11111111-1-1
χ1511111111-1-1111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1ii−i−i1111i−i−i−iii−i−iii-1i−i
χ1611111111-1-1111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1−i−iii1111−iiii−i−iii−i−i-1−ii
χ172222-2-22200222222000-2-2-2-200000000222200000000-2-222220000-200-2000000000
χ182222-2-22200222222000-2-2-2-200000000222200000000-2-2-2-2-2-200002002000000000
χ192222-2-22200222222000-2-2-2-200000000-2-2-2-200000000222i2i−2i−2i0000−2i002i000000000
χ202222-2-22200222222000-2-2-2-200000000-2-2-2-20000000022−2i−2i2i2i00002i00−2i000000000
χ2122-2-22-22200-2-222-2-2000-2-222000000002i2i−2i−2i000000002i−2i0000000002ζ3−2ζ302ζ−2ζ0000000
χ2222-2-22-22200-2-222-2-2000-2-222000000002i2i−2i−2i000000002i−2i000000000−2ζ32ζ30−2ζ2ζ0000000
χ2322-2-22-22200-2-222-2-2000-2-22200000000−2i−2i2i2i00000000−2i2i0000000002ζ−2ζ02ζ3−2ζ30000000
χ2422-2-22-22200-2-222-2-2000-2-22200000000−2i−2i2i2i00000000−2i2i000000000−2ζ2ζ0−2ζ32ζ30000000
χ2522-2-2-22222i−2i-2-222-2-200022-2-2000000002i2i−2i−2i00002i2i−2i−2i−2i2i00002-2000000000000000
χ2622-2-2-22222i−2i-2-222-2-200022-2-200000000−2i−2i2i2i00002i2i−2i−2i2i−2i0000-22000000000000000
χ2722-2-2-2222−2i2i-2-222-2-200022-2-2000000002i2i−2i−2i0000−2i−2i2i2i−2i2i0000-22000000000000000
χ2822-2-2-2222−2i2i-2-222-2-200022-2-200000000−2i−2i2i2i0000−2i−2i2i2i2i−2i00002-2000000000000000
χ292-22-200220022-2-2-2-2i2−i200000i2i2i2i2−i2−i2−i2−i22i−2i2i−2i00000000002ζ−2ζ2ζ3−2ζ3002−20000001−i−1+i1+i−1−i000
χ302-22-200220022-2-2-2-2i2−i200000i2i2i2i2−i2−i2−i2−i22i−2i2i−2i0000000000−2ζ2ζ−2ζ32ζ3002−2000000−1+i1−i−1−i1+i000
χ312-22-200220022-2-2-2-2i2−i200000i2i2i2i2−i2−i2−i2−i2−2i2i−2i2i00000000002ζ3−2ζ32ζ−2ζ00−220000001+i−1−i1−i−1+i000
χ322-22-200220022-2-2-2-2i2−i200000i2i2i2i2−i2−i2−i2−i2−2i2i−2i2i0000000000−2ζ32ζ3−2ζ2ζ00−22000000−1−i1+i−1+i1−i000
χ332-22-200220022-2-2-2-2−i2i200000−i2−i2−i2−i2i2i2i2i22i−2i2i−2i00000000002ζ−2ζ2ζ3−2ζ300−22000000−1+i1−i−1−i1+i000
χ342-22-200220022-2-2-2-2−i2i200000−i2−i2−i2−i2i2i2i2i22i−2i2i−2i0000000000−2ζ2ζ−2ζ32ζ300−220000001−i−1+i1+i−1−i000
χ352-22-200220022-2-2-2-2−i2i200000−i2−i2−i2−i2i2i2i2i2−2i2i−2i2i00000000002ζ3−2ζ32ζ−2ζ002−2000000−1−i1+i−1+i1−i000
χ362-22-200220022-2-2-2-2−i2i200000−i2−i2−i2−i2i2i2i2i2−2i2i−2i2i0000000000−2ζ32ζ3−2ζ2ζ002−20000001+i−1−i1−i−1+i000
χ374444441-2441-21-21-24441-21-211-2-211-2-2000011-2-21-21-200000000000000000000000
χ384444441-2441-21-21-2-4-4-41-21-2-1-122-1-1220000-1-1221-21-200000000000000000000000
χ394444441-2-4-41-21-21-244-41-21-211-2-211-2-20000-1-122-12-1200000000000000000000000
χ404444441-2-4-41-21-21-2-4-441-21-2-1-122-1-122000011-2-2-12-1200000000000000000000000
χ41444444-2144-21-21-21444-21-21-2-211-2-2110000-2-211-21-2100000000000000000000000
χ42444444-2144-21-21-21-4-4-4-21-2122-1-122-1-1000022-1-1-21-2100000000000000000000000
χ43444444-21-4-4-21-21-2144-4-21-21-2-211-2-211000022-1-12-12-100000000000000000000000
χ44444444-21-4-4-21-21-21-4-44-21-2122-1-122-1-10000-2-2112-12-100000000000000000000000
χ4544-4-4-441-24i−4i-121-2-120001-2-123i−3i003i−3i0000003-300i−2i−i2i00000000000000000000000
χ4644-4-4-441-24i−4i-121-2-120001-2-12−3i3i00−3i3i000000-3300i−2i−i2i00000000000000000000000
χ4744-4-4-441-2−4i4i-121-2-120001-2-123i−3i003i−3i000000-3300−i2ii−2i00000000000000000000000
χ4844-4-4-441-2−4i4i-121-2-120001-2-12−3i3i00−3i3i0000003-300−i2ii−2i00000000000000000000000
χ4944-4-4-44-214i−4i2-1-212-1000-212-1003i−3i003i−3i0000003-3−2ii2i−i00000000000000000000000
χ5044-4-4-44-214i−4i2-1-212-1000-212-100−3i3i00−3i3i000000-33−2ii2i−i00000000000000000000000
χ5144-4-4-44-21−4i4i2-1-212-1000-212-1003i−3i003i−3i000000-332i−i−2ii00000000000000000000000
χ5244-4-4-44-21−4i4i2-1-212-1000-212-100−3i3i00−3i3i0000003-32i−i−2ii00000000000000000000000
χ534-4-44004400-4-4-4-4440000000000000004-4-440000000000000000000000000000000
χ544-4-44004400-4-4-4-444000000000000000-444-40000000000000000000000000000000
χ558888-8-82-4002-42-42-4000-24-240000000000000000000000000000000000000000000
χ568888-8-8-4200-42-42-420004-24-20000000000000000000000000000000000000000000
χ5788-8-88-82-400-242-4-24000-242-40000000000000000000000000000000000000000000
χ5888-8-88-8-42004-2-424-20004-2-420000000000000000000000000000000000000000000
χ598-88-8002-4002-4-24-244i2−4i200000i2i2−2i2−2i2−i2−i22i22i200000000000000000000000000000000000
χ608-88-8002-4002-4-24-24−4i24i200000−i2−i22i22i2i2i2−2i2−2i200000000000000000000000000000000000
χ618-88-800-4200-424-24-24i2−4i200000−2i2−2i2i2i22i22i2−i2−i200000000000000000000000000000000000
χ628-88-800-4200-424-24-2−4i24i2000002i22i2−i2−i2−2i2−2i2i2i200000000000000000000000000000000000
χ638-8-88002-400-24-242-4000000032−3200−32320000000000000000000000000000000000000
χ648-8-88002-400-24-242-40000000−32320032−320000000000000000000000000000000000000
χ658-8-8800-42004-24-2-4200000000032−3200−323200000000000000000000000000000000000
χ668-8-8800-42004-24-2-42000000000−32320032−3200000000000000000000000000000000000

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