Finite Group Databasebeta

← Group #11771663

Character table — Group #11771663

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size111122444444444488888888888888161616161616161618181818181818183636363636363636727272727272
order1244243366881212121224661212242424242424242466661212121244448888888888888816161616
χ1111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-1ii−i−i
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii-1-1−i−iii
χ51111111111111111-1-1111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1
χ61111111111111111-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i11−i−iii
χ81111111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii11ii−i−i
χ911-1-1-1111111-1-1-1-1-11-1-1-1111111-1-1-1-11111-1-1-1-1ii−i−ii−ii−iζζ−ζ−ζζ3ζ3−ζ3−ζ3i−iζ−ζζ3−ζ3
χ1011-1-1-1111111-1-1-1-1-11-1-1-1111111-1-1-1-11111-1-1-1-1ii−i−ii−ii−i−ζ−ζζζ−ζ3−ζ3ζ3ζ3i−i−ζζ−ζ3ζ3
χ1111-1-1-1111111-1-1-1-1-11-1-1-1111111-1-1-1-11111-1-1-1-1−i−iii−ii−iiζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−iiζ3−ζ3ζ−ζ
χ1211-1-1-1111111-1-1-1-1-11-1-1-1111111-1-1-1-11111-1-1-1-1−i−iii−ii−ii−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ii−ζ3ζ3−ζζ
χ1311-1-1-1111111-1-1-1-1-1-11-1-1111111-1-1-1-1-1-1-1-11111ii−i−ii−ii−iζζ−ζ−ζζ3ζ3−ζ3−ζ3−ii−ζζ−ζ3ζ3
χ1411-1-1-1111111-1-1-1-1-1-11-1-1111111-1-1-1-1-1-1-1-11111ii−i−ii−ii−i−ζ−ζζζ−ζ3−ζ3ζ3ζ3−iiζ−ζζ3−ζ3
χ1511-1-1-1111111-1-1-1-1-1-11-1-1111111-1-1-1-1-1-1-1-11111−i−iii−ii−iiζ3ζ3−ζ3−ζ3ζζ−ζ−ζi−i−ζ3ζ3−ζζ
χ1611-1-1-1111111-1-1-1-1-1-11-1-1111111-1-1-1-1-1-1-1-11111−i−iii−ii−ii−ζ3−ζ3ζ3ζ3−ζ−ζζζi−iζ3−ζ3ζ−ζ
χ172222222222-2-22222002222-2-2-2-2-2-2-2-2000000002222-2-2-2-200000000000000
χ182222222222-2-22222002222-2-2-2-2-2-2-2-200000000-2-2-2-2222200000000000000
χ192222-2-2222200222200-2-2-2-20000000000000000000022-2-2i2−i2i2−i2i2−i2i2−i2000000
χ202222-2-2222200222200-2-2-2-20000000000000000000022-2-2−i2i2−i2i2−i2i2−i2i2000000
χ212222-2-2222200222200-2-2-2-200000000000000000000-2-2222−22−2−22−22000000
χ222222-2-2222200222200-2-2-2-200000000000000000000-2-222−22−222−22−2000000
χ2322-2-22-2222200-2-2-2-20022-2-2000000000000000000002i−2i−2i2i1−i−1+i−1+i1−i1+i−1−i−1−i1+i000000
χ2422-2-22-2222200-2-2-2-20022-2-2000000000000000000002i−2i−2i2i−1+i1−i1−i−1+i−1−i1+i1+i−1−i000000
χ2522-2-22-2222200-2-2-2-20022-2-200000000000000000000−2i2i2i−2i1+i−1−i−1−i1+i1−i−1+i−1+i1−i000000
χ2622-2-22-2222200-2-2-2-20022-2-200000000000000000000−2i2i2i−2i−1−i1+i1+i−1−i−1+i1−i1−i−1+i000000
χ2722-2-2-222222-22-2-2-2-200-2-222-2-2-2-22222000000002i2i−2i−2i−2i2i−2i2i00000000000000
χ2822-2-2-222222-22-2-2-2-200-2-222-2-2-2-2222200000000−2i−2i2i2i2i−2i2i−2i00000000000000
χ294444441-21-24411-2-2441-21-211-2-211-2-211-2-211-2-20000000000000000000000
χ304444441-21-24411-2-2-4-41-21-211-2-211-2-2-1-122-1-1220000000000000000000000
χ314444441-21-2-4-411-2-2001-21-2-1-122-1-1223-3003-3000000000000000000000000
χ324444441-21-2-4-411-2-2001-21-2-1-122-1-122-3300-33000000000000000000000000
χ33444444-21-2144-2-21144-21-21-2-211-2-211-2-211-2-2110000000000000000000000
χ34444444-21-2144-2-211-4-4-21-21-2-211-2-21122-1-122-1-10000000000000000000000
χ35444444-21-21-4-4-2-21100-21-2122-1-122-1-1003-3003-30000000000000000000000
χ36444444-21-21-4-4-2-21100-21-2122-1-122-1-100-3300-330000000000000000000000
χ3744-4-4-441-21-24-4-1-1224-4-121-211-2-2-1-12211-2-2-1-1220000000000000000000000
χ3844-4-4-441-21-24-4-1-122-44-121-211-2-2-1-122-1-12211-2-20000000000000000000000
χ3944-4-4-441-21-2-44-1-12200-121-2-1-12211-2-23-300-33000000000000000000000000
χ4044-4-4-441-21-2-44-1-12200-121-2-1-12211-2-2-33003-3000000000000000000000000
χ4144-4-4-44-21-214-422-1-14-42-1-21-2-21122-1-1-2-21122-1-10000000000000000000000
χ4244-4-4-44-21-214-422-1-1-442-1-21-2-21122-1-122-1-1-2-2110000000000000000000000
χ4344-4-4-44-21-21-4422-1-1002-1-2122-1-1-2-211003-300-330000000000000000000000
χ4444-4-4-44-21-21-4422-1-1002-1-2122-1-1-2-21100-33003-30000000000000000000000
χ454-44i−4i0044-4-4004i−4i4i−4i00000000000000000000002+2i−2−2i2−2i−2+2i000000000000000000
χ464-44i−4i0044-4-4004i−4i4i−4i0000000000000000000000−2−2i2+2i−2+2i2−2i000000000000000000
χ474-4−4i4i0044-4-400−4i4i−4i4i00000000000000000000002−2i−2+2i2+2i−2−2i000000000000000000
χ484-4−4i4i0044-4-400−4i4i−4i4i0000000000000000000000−2+2i2−2i−2−2i2+2i000000000000000000
χ498888-8-82-42-40022-4-400-24-2400000000000000000000000000000000000000
χ508888-8-8-42-4200-4-422004-24-200000000000000000000000000000000000000
χ5188-8-88-82-42-400-2-244002-4-2400000000000000000000000000000000000000
χ5288-8-88-8-42-420044-2-200-424-200000000000000000000000000000000000000
χ538-88i−8i002-4-24002i−2i−4i4i00000032−32003i2−3i200000000000000000000000000000000
χ548-88i−8i002-4-24002i−2i−4i4i000000−323200−3i23i200000000000000000000000000000000
χ558-88i−8i00-424-200−4i4i2i−2i0000000032−32003i2−3i2000000000000000000000000000000
χ568-88i−8i00-424-200−4i4i2i−2i00000000−323200−3i23i2000000000000000000000000000000
χ578-8−8i8i002-4-2400−2i2i4i−4i00000032−3200−3i23i200000000000000000000000000000000
χ588-8−8i8i002-4-2400−2i2i4i−4i000000−3232003i2−3i200000000000000000000000000000000
χ598-8−8i8i00-424-2004i−4i−2i2i0000000032−3200−3i23i2000000000000000000000000000000
χ608-8−8i8i00-424-2004i−4i−2i2i00000000−3232003i2−3i2000000000000000000000000000000

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