Finite Group Databasebeta

← Group #11777578

Character table — Group #11777578

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size1111224444444444448888888888888999916161616161616161818181818183636363636363636363636363636727272
order1222442233666666884121212122424242424242424444466661212121244888844888888888888488
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-1-1-1-1i−iii−i−iii−i−i-1i−i
χ41111111111111111111111111111111-1-1-1-111111111-1-1−i−iii-1-1-1-1−ii−i−iii−i−iii-1−ii
χ51111111111111111-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1
χ61111111111111111-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-111
χ71111111111111111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1ii−i−i-1-111i−iii−i−i−i−iii1−ii
χ81111111111111111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1−i−iii-1-111−ii−i−iiiii−i−i1i−i
χ9111111-1-11111111111-11111111111111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-11111-1-1-1
χ10111111-1-11111111111-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-11111-1-1-1-1-111
χ11111111-1-11111111111-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i11-1-1i−i−i−iiiii−i−i1−ii
χ12111111-1-11111111111-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii11-1-1−iiii−i−i−i−iii1i−i
χ13111111-1-111111111-1-111111-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1111
χ14111111-1-111111111-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111111-1-1
χ15111111-1-111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1ii−i−i1111i−i−i−iii−i−iii-1i−i
χ16111111-1-111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1−i−iii1111−iiii−i−iii−i−i-1−ii
χ172222-2-20022222222000-2-2-2-200000000222200000000-2-222220000-2-200000000000
χ182222-2-20022222222000-2-2-2-200000000222200000000-2-2-2-2-2-200002200000000000
χ192222-2-20022222222000-2-2-2-200000000-2-2-2-200000000222i2i−2i−2i0000−2i2i00000000000
χ202222-2-20022222222000-2-2-2-200000000-2-2-2-20000000022−2i−2i2i2i00002i−2i00000000000
χ2122-2-22-22-222-2-2-2-222000-2-222000000002i−2i2i−2i22-2-200002i−2i00002i−2i000000000000000
χ2222-2-22-22-222-2-2-2-222000-2-22200000000−2i2i−2i2i22-2-20000−2i2i0000−2i2i000000000000000
χ2322-2-22-2-2222-2-2-2-222000-2-222000000002i−2i2i−2i-2-22200002i−2i0000−2i2i000000000000000
χ2422-2-22-2-2222-2-2-2-222000-2-22200000000−2i2i−2i2i-2-2220000−2i2i00002i−2i000000000000000
χ2522-2-2-220022-2-2-2-22200022-2-2000000002i−2i2i−2i00000000−2i2i00000000002ζ−2ζ2ζ3−2ζ30000000
χ2622-2-2-220022-2-2-2-22200022-2-2000000002i−2i2i−2i00000000−2i2i0000000000−2ζ2ζ−2ζ32ζ30000000
χ2722-2-2-220022-2-2-2-22200022-2-200000000−2i2i−2i2i000000002i−2i00000000002ζ3−2ζ32ζ−2ζ0000000
χ2822-2-2-220022-2-2-2-22200022-2-200000000−2i2i−2i2i000000002i−2i0000000000−2ζ32ζ3−2ζ2ζ0000000
χ292-22-200002222-2-2-2-2i2−i200000i2i2i2i2−i2−i2−i2−i22i−2i−2i2i00000000002ζ3−2ζ32ζ−2ζ002−20000001+i−1−i1−i−1+i000
χ302-22-200002222-2-2-2-2i2−i200000i2i2i2i2−i2−i2−i2−i22i−2i−2i2i0000000000−2ζ32ζ3−2ζ2ζ002−2000000−1−i1+i−1+i1−i000
χ312-22-200002222-2-2-2-2i2−i200000i2i2i2i2−i2−i2−i2−i2−2i2i2i−2i00000000002ζ−2ζ2ζ3−2ζ300−220000001−i−1+i1+i−1−i000
χ322-22-200002222-2-2-2-2i2−i200000i2i2i2i2−i2−i2−i2−i2−2i2i2i−2i0000000000−2ζ2ζ−2ζ32ζ300−22000000−1+i1−i−1−i1+i000
χ332-22-200002222-2-2-2-2−i2i200000−i2−i2−i2−i2i2i2i2i22i−2i−2i2i00000000002ζ3−2ζ32ζ−2ζ00−22000000−1−i1+i−1+i1−i000
χ342-22-200002222-2-2-2-2−i2i200000−i2−i2−i2−i2i2i2i2i22i−2i−2i2i0000000000−2ζ32ζ3−2ζ2ζ00−220000001+i−1−i1−i−1+i000
χ352-22-200002222-2-2-2-2−i2i200000−i2−i2−i2−i2i2i2i2i2−2i2i2i−2i00000000002ζ−2ζ2ζ3−2ζ3002−2000000−1+i1−i−1−i1+i000
χ362-22-200002222-2-2-2-2−i2i200000−i2−i2−i2−i2i2i2i2i2−2i2i2i−2i0000000000−2ζ2ζ−2ζ32ζ3002−20000001−i−1+i1+i−1−i000
χ37444444441-21-21-21-24441-21-211-2-211-2-200001-21-211-2-200000000000000000000000
χ38444444441-21-21-21-2-4-4-41-21-2-1-122-1-12200001-21-2-1-12200000000000000000000000
χ3944444444-21-21-21-21444-21-21-2-211-2-2110000-21-21-2-21100000000000000000000000
χ4044444444-21-21-21-21-4-4-4-21-2122-1-122-1-10000-21-2122-1-100000000000000000000000
χ41444444-4-41-21-21-21-244-41-21-211-2-211-2-20000-12-12-1-12200000000000000000000000
χ42444444-4-41-21-21-21-2-4-441-21-2-1-122-1-1220000-12-1211-2-200000000000000000000000
χ43444444-4-4-21-21-21-2144-4-21-21-2-211-2-21100002-12-122-1-100000000000000000000000
χ44444444-4-4-21-21-21-21-4-44-21-2122-1-122-1-100002-12-1-2-21100000000000000000000000
χ4544-4-44-44-41-2-12-121-2000-121-23-3003-30000001-2-123-30000000000000000000000000
χ4644-4-44-44-41-2-12-121-2000-121-2-3300-330000001-2-12-330000000000000000000000000
χ4744-4-44-44-4-212-12-1-210002-1-21003-3003-30000-212-1003-300000000000000000000000
χ4844-4-44-44-4-212-12-1-210002-1-2100-3300-330000-212-100-3300000000000000000000000
χ4944-4-44-4-441-2-12-121-2000-121-23-3003-3000000-121-2-330000000000000000000000000
χ5044-4-44-4-441-2-12-121-2000-121-2-3300-33000000-121-23-30000000000000000000000000
χ5144-4-44-4-44-212-12-1-210002-1-21003-3003-300002-1-2100-3300000000000000000000000
χ5244-4-44-4-44-212-12-1-210002-1-2100-3300-3300002-1-21003-300000000000000000000000
χ534-4-44000044-4-444-4-400000000000000044-4-40000000000000000000000000000000
χ544-4-44000044-4-444-4-4000000000000000-4-4440000000000000000000000000000000
χ558888-8-8002-42-42-42-4000-24-240000000000000000000000000000000000000000000
χ568888-8-800-42-42-42-420004-24-20000000000000000000000000000000000000000000
χ5788-8-8-88002-4-24-242-40002-4-240000000000000000000000000000000000000000000
χ5888-8-8-8800-424-24-2-42000-424-20000000000000000000000000000000000000000000
χ598-88-800002-42-4-24-244i2−4i200000i2i2−2i2−2i2−i2−i22i22i200000000000000000000000000000000000
χ608-88-800002-42-4-24-24−4i24i200000−i2−i22i22i2i2i2−2i2−2i200000000000000000000000000000000000
χ618-88-80000-42-424-24-24i2−4i200000−2i2−2i2i2i22i22i2−i2−i200000000000000000000000000000000000
χ628-88-80000-42-424-24-2−4i24i2000002i22i2−i2−i2−2i2−2i2i2i200000000000000000000000000000000000
χ638-8-8800002-4-242-4-2400000003i2−3i200−3i23i20000000000000000000000000000000000000
χ648-8-8800002-4-242-4-240000000−3i23i2003i2−3i20000000000000000000000000000000000000
χ658-8-880000-424-2-424-20000000003i2−3i200−3i23i200000000000000000000000000000000000
χ668-8-880000-424-2-424-2000000000−3i23i2003i2−3i200000000000000000000000000000000000

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