Finite Group Databasebeta

← Group #11771626

Character table — Group #11771626

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size111122444444444488888888888888161616161616161618181818181818183636363636363636727272727272
order1222443366666688441212121224242424242424241212121212121212444488881616161616161616448888
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
χ911-1-11-111-1-1-1-1111-11-1-1-1111111-1-1-1-11111-1-1-1-1i−ii−iii−i−iζζ−ζ−ζζ3ζ3−ζ3−ζ3i−iζ−ζζ3−ζ3
χ1011-1-11-111-1-1-1-1111-11-1-1-1111111-1-1-1-11111-1-1-1-1i−ii−iii−i−i−ζ−ζζζ−ζ3−ζ3ζ3ζ3i−i−ζζ−ζ3ζ3
χ1111-1-11-111-1-1-1-1111-11-1-1-1111111-1-1-1-11111-1-1-1-1−ii−ii−i−iiiζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−iiζ3−ζ3ζ−ζ
χ1211-1-11-111-1-1-1-1111-11-1-1-1111111-1-1-1-11111-1-1-1-1−ii−ii−i−iii−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ii−ζ3ζ3−ζζ
χ1311-1-11-111-1-1-1-1111-1-11-1-1111111-1-1-1-1-1-1-1-11111i−ii−iii−i−iζζ−ζ−ζζ3ζ3−ζ3−ζ3−ii−ζζ−ζ3ζ3
χ1411-1-11-111-1-1-1-1111-1-11-1-1111111-1-1-1-1-1-1-1-11111i−ii−iii−i−i−ζ−ζζζ−ζ3−ζ3ζ3ζ3−iiζ−ζζ3−ζ3
χ1511-1-11-111-1-1-1-1111-1-11-1-1111111-1-1-1-1-1-1-1-11111−ii−ii−i−iiiζ3ζ3−ζ3−ζ3ζζ−ζ−ζi−i−ζ3ζ3−ζζ
χ1611-1-11-111-1-1-1-1111-1-11-1-1111111-1-1-1-1-1-1-1-11111−ii−ii−i−iii−ζ3−ζ3ζ3ζ3−ζ−ζζζi−iζ3−ζ3ζ−ζ
χ1722222222222222-2-2002222-2-2-2-2-2-2-2-2000000002222-2-2-2-200000000000000
χ1822222222222222-2-2002222-2-2-2-2-2-2-2-200000000-2-2-2-2222200000000000000
χ192222-2-2222222220000-2-2-2-2000000000000000022-2-20000i2−i2i2−i2i2−i2i2−i2000000
χ202222-2-2222222220000-2-2-2-2000000000000000022-2-20000−i2i2−i2i2−i2i2−i2i2000000
χ212222-2-2222222220000-2-2-2-20000000000000000-2-22200002−22−2−22−22000000
χ222222-2-2222222220000-2-2-2-20000000000000000-2-2220000−22−222−22−2000000
χ2322-2-22-222-2-2-2-222-2200-2-222-2-2-2-22222000000002i−2i2i−2i−2i−2i2i2i00000000000000
χ2422-2-22-222-2-2-2-222-2200-2-222-2-2-2-2222200000000−2i2i−2i2i2i2i−2i−2i00000000000000
χ2522-2-2-2222-2-2-2-222000022-2-200000000000000002i−2i−2i2i00001−i−1+i−1+i1−i1+i−1−i−1−i1+i000000
χ2622-2-2-2222-2-2-2-222000022-2-200000000000000002i−2i−2i2i0000−1+i1−i1−i−1+i−1−i1+i1+i−1−i000000
χ2722-2-2-2222-2-2-2-222000022-2-20000000000000000−2i2i2i−2i00001+i−1−i−1−i1+i1−i−1+i−1+i1−i000000
χ2822-2-2-2222-2-2-2-222000022-2-20000000000000000−2i2i2i−2i0000−1−i1+i1+i−1−i−1+i1−i1−i−1+i000000
χ294444441-211-2-21-244441-21-211-2-211-2-211-2-211-2-20000000000000000000000
χ304444441-211-2-21-244-4-41-21-211-2-211-2-2-1-122-1-1220000000000000000000000
χ314444441-211-2-21-2-4-4001-21-2-1-122-1-1223-3003-3000000000000000000000000
χ324444441-211-2-21-2-4-4001-21-2-1-122-1-122-3300-33000000000000000000000000
χ33444444-21-2-211-214444-21-21-2-211-2-211-2-211-2-2110000000000000000000000
χ34444444-21-2-211-2144-4-4-21-21-2-211-2-21122-1-122-1-10000000000000000000000
χ35444444-21-2-211-21-4-400-21-2122-1-122-1-1003-3003-30000000000000000000000
χ36444444-21-2-211-21-4-400-21-2122-1-122-1-100-3300-330000000000000000000000
χ3744-4-44-41-2-1-1221-24-44-4-121-211-2-2-1-12211-2-2-1-1220000000000000000000000
χ3844-4-44-41-2-1-1221-24-4-44-121-211-2-2-1-122-1-12211-2-20000000000000000000000
χ3944-4-44-41-2-1-1221-2-4400-121-2-1-12211-2-23-300-33000000000000000000000000
χ4044-4-44-41-2-1-1221-2-4400-121-2-1-12211-2-2-33003-3000000000000000000000000
χ4144-4-44-4-2122-1-1-214-44-42-1-21-2-21122-1-1-2-21122-1-10000000000000000000000
χ4244-4-44-4-2122-1-1-214-4-442-1-21-2-21122-1-122-1-1-2-2110000000000000000000000
χ4344-4-44-4-2122-1-1-21-44002-1-2122-1-1-2-211003-300-330000000000000000000000
χ4444-4-44-4-2122-1-1-21-44002-1-2122-1-1-2-21100-33003-30000000000000000000000
χ454-44-400444-44-4-4-4000000000000000000000000000022−2222−2200000000000000
χ464-44-400444-44-4-4-40000000000000000000000000000−2222−222200000000000000
χ474-4-440044-44-44-4-400000000000000000000000000002i2−2i2−2i22i200000000000000
χ484-4-440044-44-44-4-40000000000000000000000000000−2i22i22i2−2i200000000000000
χ498888-8-82-422-4-42-40000-24-2400000000000000000000000000000000000000
χ508888-8-8-42-4-422-4200004-24-200000000000000000000000000000000000000
χ5188-8-8-882-4-2-2442-400002-4-2400000000000000000000000000000000000000
χ5288-8-8-88-4244-2-2-420000-424-200000000000000000000000000000000000000
χ538-88-8002-42-2-44-240000000032−320032−3200000000000000000000000000000000
χ548-88-8002-42-2-44-2400000000−323200−323200000000000000000000000000000000
χ558-88-800-42-442-24-2000000000032−320032−32000000000000000000000000000000
χ568-88-800-42-442-24-20000000000−323200−3232000000000000000000000000000000
χ578-8-88002-4-224-4-240000000032−3200−323200000000000000000000000000000000
χ588-8-88002-4-224-4-2400000000−32320032−3200000000000000000000000000000000
χ598-8-8800-424-4-224-2000000000032−3200−3232000000000000000000000000000000
χ608-8-8800-424-4-224-20000000000−32320032−32000000000000000000000000000000

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