Finite Group Databasebeta

← Group #11777960

Character table — Group #11777960

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size11112244444444448888888888888899991616161616161616181836363636363636363636727272727272
order1222443366666688241212121224242424242424244444666612121212448888888888248888
χ1111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1
χ3111111111111111111111111111111-1-1-1-111111111-1-1-1-1ii−i−iii−i−i-1-1ii−i−i
χ4111111111111111111111111111111-1-1-1-111111111-1-1-1-1−i−iii−i−iii-1-1−i−iii
χ51111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ61111111111111111-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−i11−i−iii
χ81111111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii11ii−i−i
χ911111111111111-1-11-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-1-111-11-1
χ1011111111111111-1-11-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11111-11-11-11
χ1111111111111111-1-11-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111ii−i−i−i−iii1-1i−i−ii
χ1211111111111111-1-11-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111−i−iiiii−i−i1-1−iii−i
χ1311111111111111-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-11-1-11-11
χ1411111111111111-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111111-11-11-1
χ1511111111111111-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111ii−i−i−i−iii-11−iii−i
χ1611111111111111-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111−i−iiiii−i−i-11i−i−ii
χ172222-2-2222222220000-2-2-2-200000000222200000000-2-2002-22-20000000000
χ182222-2-2222222220000-2-2-2-200000000222200000000-2-200-22-220000000000
χ192222-2-2222222220000-2-2-2-200000000-2-2-2-20000000022002i−2i−2i2i0000000000
χ202222-2-2222222220000-2-2-2-200000000-2-2-2-2000000002200−2i2i2i−2i0000000000
χ2122-2-22-222-2-222-2-20000-2-222000000002i2i−2i−2i000000002i−2i0000002ζ−2ζ2ζ3−2ζ3000000
χ2222-2-22-222-2-222-2-20000-2-222000000002i2i−2i−2i000000002i−2i000000−2ζ2ζ−2ζ32ζ3000000
χ2322-2-22-222-2-222-2-20000-2-22200000000−2i−2i2i2i00000000−2i2i0000002ζ3−2ζ32ζ−2ζ000000
χ2422-2-22-222-2-222-2-20000-2-22200000000−2i−2i2i2i00000000−2i2i000000−2ζ32ζ3−2ζ2ζ000000
χ2522-2-2-2222-2-222-2-22i−2i0022-2-22i2i2i2i−2i−2i−2i−2i2i2i−2i−2i00000000−2i2i2-200000000000000
χ2622-2-2-2222-2-222-2-22i−2i0022-2-22i2i2i2i−2i−2i−2i−2i−2i−2i2i2i000000002i−2i-2200000000000000
χ2722-2-2-2222-2-222-2-2−2i2i0022-2-2−2i−2i−2i−2i2i2i2i2i2i2i−2i−2i00000000−2i2i-2200000000000000
χ2822-2-2-2222-2-222-2-2−2i2i0022-2-2−2i−2i−2i−2i2i2i2i2i−2i−2i2i2i000000002i−2i2-200000000000000
χ294444441-21-21-21-244441-21-211-2-211-2-2000011-2-211-2-2000000000000000000
χ304444441-21-21-21-244-4-41-21-211-2-211-2-20000-1-122-1-122000000000000000000
χ314444441-21-21-21-2-4-44-41-21-2-1-122-1-122000011-2-2-1-122000000000000000000
χ324444441-21-21-21-2-4-4-441-21-2-1-122-1-1220000-1-12211-2-2000000000000000000
χ33444444-21-21-21-214444-21-21-2-211-2-2110000-2-211-2-211000000000000000000
χ34444444-21-21-21-2144-4-4-21-21-2-211-2-211000022-1-122-1-1000000000000000000
χ35444444-21-21-21-21-4-44-4-21-2122-1-122-1-10000-2-21122-1-1000000000000000000
χ36444444-21-21-21-21-4-4-44-21-2122-1-122-1-1000022-1-1-2-211000000000000000000
χ3744-4-4-441-2-121-2-124i−4i001-2-12ii−2i−2i−i−i2i2i00003-3003i−3i00000000000000000000
χ3844-4-4-441-2-121-2-124i−4i001-2-12ii−2i−2i−i−i2i2i0000-3300−3i3i00000000000000000000
χ3944-4-4-441-2-121-2-12−4i4i001-2-12−i−i2i2iii−2i−2i00003-300−3i3i00000000000000000000
χ4044-4-4-441-2-121-2-12−4i4i001-2-12−i−i2i2iii−2i−2i0000-33003i−3i00000000000000000000
χ4144-4-4-44-212-1-212-14i−4i00-212-1−2i−2iii2i2i−i−i0000003-3003i−3i000000000000000000
χ4244-4-4-44-212-1-212-14i−4i00-212-1−2i−2iii2i2i−i−i000000-3300−3i3i000000000000000000
χ4344-4-4-44-212-1-212-1−4i4i00-212-12i2i−i−i−2i−2iii0000003-300−3i3i000000000000000000
χ4444-4-4-44-212-1-212-1−4i4i00-212-12i2i−i−i−2i−2iii000000-33003i−3i000000000000000000
χ454-44-4004444-4-4-4-400000000000000004i−4i4i−4i00000000000000000000000000
χ464-44-4004444-4-4-4-40000000000000000−4i4i−4i4i00000000000000000000000000
χ474-4-440044-4-4-4-44400000000000000004-4-4400000000000000000000000000
χ484-4-440044-4-4-4-4440000000000000000-444-400000000000000000000000000
χ498888-8-82-42-42-42-40000-24-2400000000000000000000000000000000000000
χ508888-8-8-42-42-42-4200004-24-200000000000000000000000000000000000000
χ5188-8-88-82-4-242-4-240000-242-400000000000000000000000000000000000000
χ5288-8-88-8-424-2-424-200004-2-4200000000000000000000000000000000000000
χ538-88-8002-42-4-24-24000000003i2−3i2003i2−3i200000000000000000000000000000000
χ548-88-8002-42-4-24-2400000000−3i23i200−3i23i200000000000000000000000000000000
χ558-88-800-42-424-24-200000000003i2−3i2003i2−3i2000000000000000000000000000000
χ568-88-800-42-424-24-20000000000−3i23i200−3i23i2000000000000000000000000000000
χ578-8-88002-4-24-242-40000000032−3200−323200000000000000000000000000000000
χ588-8-88002-4-24-242-400000000−32320032−3200000000000000000000000000000000
χ598-8-8800-424-24-2-42000000000032−3200−3232000000000000000000000000000000
χ608-8-8800-424-24-2-420000000000−32320032−32000000000000000000000000000000

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