Finite Group Databasebeta

← Group #11788695

Character table — Group #11788695

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size11222444444446666888888888991212121212121212121216161818182424242424242424242436364848484872727272
order12244336688121288886612121224242424222244882424242424242444466881212242488121224244488
χ1111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-111-1-1111111-1-1-1-1-1-1-1-1
χ31111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-11111111-1-111-1-1-1-1111111-1-1-1-1
χ41111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ5111111111-1-111111111111-1-1-1-111-1-1-1-1111111-1-111111-1-1-1-1-1-111-1-111-1-111-1-1
χ6111111111-1-111111111111-1-1-1-111-1-1-1-1111111-1-1111-1-1-1-111-1-111-1-1-1-111-1-111
χ7111111111-1-111-1-1-1-111111-1-1-1-1111111-1-1-1-1-1-1-1-11111111-1-111-1-1-1-111-1-1-1-111
χ8111111111-1-111-1-1-1-111111-1-1-1-1111111-1-1-1-1-1-1-1-1111-1-1111111-1-1-1-1-1-11111-1-1
χ9111-1-11111i−i-1-1ii−i−i11-1-1-1ii−i−i-1-11-11-1i−iii−i−ii−i-1111-11-1i−i1-1i−ii−i1-1i−ii−i1-1
χ10111-1-11111i−i-1-1ii−i−i11-1-1-1ii−i−i-1-11-11-1i−iii−i−ii−i-111-111-1−ii1-1i−ii−i-11−ii−ii-11
χ11111-1-11111i−i-1-1−i−iii11-1-1-1ii−i−i-1-1-11-11−ii−i−iiii−i-1111-1-11i−i-11−iii−i1-1i−i−ii-11
χ12111-1-11111i−i-1-1−i−iii11-1-1-1ii−i−i-1-1-11-11−ii−i−iiii−i-111-11-11−ii-11−iii−i-11−iii−i1-1
χ13111-1-11111−ii-1-1ii−i−i11-1-1-1−i−iii-1-1-11-11i−iii−i−i−ii-1111-1-11−ii-11i−i−ii1-1−iii−i-11
χ14111-1-11111−ii-1-1ii−i−i11-1-1-1−i−iii-1-1-11-11i−iii−i−i−ii-111-11-11i−i-11i−i−ii-11i−i−ii1-1
χ15111-1-11111−ii-1-1−i−iii11-1-1-1−i−iii-1-11-11-1−ii−i−iii−ii-1111-11-1−ii1-1−ii−ii1-1−ii−ii1-1
χ16111-1-11111−ii-1-1−i−iii11-1-1-1−i−iii-1-11-11-1−ii−i−iii−ii-111-111-1i−i1-1−ii−ii-11i−ii−i-11
χ1722222222222220000222222222-2-2000000000022-2-2-20000000000-2-200000000
χ18222222222-2-222000022222-2-2-2-2-2-20000000000-2-2-2-2-200000000002200000000
χ19222-2-222222i−2i-2-2000022-2-2-22i2i−2i−2i2200000000002i−2i2-2-20000000000−2i2i00000000
χ20222-2-22222−2i2i-2-2000022-2-2-2−2i−2i2i2i220000000000−2i2i2-2-200000000002i−2i00000000
χ2122-22-2222200-2-20000-2-22-2200002222-2-200000000-2-22002200-2-2000000000000
χ2222-22-2222200-2-20000-2-22-22000022-2-22200000000-2-2200-2-20022000000000000
χ2322-22-2222200-2-22i2i−2i−2i-2-22-220000-2-20000−2i2i2i2i−2i−2i0022-200000000−2i2i0000000000
χ2422-22-2222200-2-2−2i−2i2i2i-2-22-220000-2-200002i−2i−2i−2i2i2i0022-2000000002i−2i0000000000
χ2522-2-22222200220000-2-2-22-20000-2-22-2-22000000002-22002-200-22000000000000
χ2622-2-22222200220000-2-2-22-20000-2-2-222-2000000002-2200-22002-2000000000000
χ2722-2-22222200222222-2-2-22-20000220000-2-2222200-22-200000000-2-20000000000
χ2822-2-2222220022-2-2-2-2-2-2-22-2000022000022-2-2-2-200-22-200000000220000000000
χ29444441-2-2144-2-200001-2-211-2-2-2-200000000000011000220022000000-1-1-1-10000
χ30444441-2-2144-2-200001-2-211-2-2-2-200000000000011000-2-200-2-200000011110000
χ31444441-2-21-4-4-2-200001-2-2112222000000000000-1-10002200-2-2000000-1-1110000
χ32444441-2-21-4-4-2-200001-2-2112222000000000000-1-1000-2-2002200000011-1-10000
χ3344444-211-244112222-211-2-2111100222222-1-1-1-1-2-200000-1-100-1-1-1-10000000000
χ3444444-211-24411-2-2-2-2-211-2-2111100-2-2-2-2-2-21111-2-200000110011110000000000
χ3544444-211-2-4-4112222-211-2-2-1-1-1-100-2-2-2-222-1-1-1-12200000110011-1-10000000000
χ3644444-211-2-4-411-2-2-2-2-211-2-2-1-1-1-1002222-2-211112200000-1-100-1-1110000000000
χ37444-4-41-2-214i−4i2200001-22-1-1−2i−2i2i2i000000000000i−i0002-2002i−2i000000-11−ii0000
χ38444-4-41-2-214i−4i2200001-22-1-1−2i−2i2i2i000000000000i−i000-2200−2i2i0000001-1i−i0000
χ39444-4-41-2-21−4i4i2200001-22-1-12i2i−2i−2i000000000000−ii0002-200−2i2i000000-11i−i0000
χ40444-4-41-2-21−4i4i2200001-22-1-12i2i−2i−2i000000000000−ii000-22002i−2i0000001-1−ii0000
χ41444-4-4-211-24i−4i-1-12i2i−2i−2i-21-122ii−i−i002-22-22i−2i−i−iii−2i2i00000-1100-11−ii0000000000
χ42444-4-4-211-24i−4i-1-1−2i−2i2i2i-21-122ii−i−i00-22-22−2i2iii−i−i−2i2i000001-1001-1i−i0000000000
χ43444-4-4-211-2−4i4i-1-12i2i−2i−2i-21-122−i−iii00-22-222i−2i−i−iii2i−2i000001-1001-1−ii0000000000
χ44444-4-4-211-2−4i4i-1-1−2i−2i2i2i-21-122−i−iii002-22-2−2i2iii−i−i2i−2i00000-1100-11i−i0000000000
χ4544-44-4-211-200-1-12i2i−2i−2i2-112-23i−3i3i−3i0022-2-2−2i2i−i−iii0000000-1-10011i−i0000000000
χ4644-44-4-211-200-1-12i2i−2i−2i2-112-2−3i3i−3i3i00-2-222−2i2i−i−iii00000001100-1-1i−i0000000000
χ4744-44-4-211-200-1-1−2i−2i2i2i2-112-23i−3i3i−3i00-2-2222i−2iii−i−i00000001100-1-1−ii0000000000
χ4844-44-4-211-200-1-1−2i−2i2i2i2-112-2−3i3i−3i3i0022-2-22i−2iii−i−i0000000-1-10011−ii0000000000
χ4944-4-44-211-2001122222-1-1-223-3-33002-2-22-2-2-1-1-1-10000000-11001-1110000000000
χ5044-4-44-211-2001122222-1-1-22-333-300-222-2-2-2-1-1-1-100000001-100-11110000000000
χ5144-4-44-211-20011-2-2-2-22-1-1-223-3-3300-222-222111100000001-100-11-1-10000000000
χ5244-4-44-211-20011-2-2-2-22-1-1-22-333-3002-2-222211110000000-11001-1-1-10000000000
χ534-400044-4-400002i2−2i22i2−2i2000000000-440000002i2−2i22i2−2i20000000000000000000000000
χ544-400044-4-4000022−22−22220000000004-400000022−22−22220000000000000000000000000
χ554-400044-4-40000−222222−220000000004-4000000−222222−220000000000000000000000000
χ564-400044-4-40000−2i22i2−2i22i2000000000-44000000−2i22i2−2i22i20000000000000000000000000
χ5788-88-82-4-4200440000-24-4-2200000000000000000000000000000000000000000
χ5888-8-882-4-4200-4-40000-2442-200000000000000000000000000000000000000000
χ598-8000-42-24006i−6i4ζ−4ζ4ζ3−4ζ300000000000000000−2ζ2ζ−2ζ32ζ30000000000000000000000000
χ608-8000-42-24006i−6i−4ζ4ζ−4ζ34ζ3000000000000000002ζ−2ζ2ζ3−2ζ30000000000000000000000000
χ618-8000-42-2400−6i6i4ζ3−4ζ34ζ−4ζ00000000000000000−2ζ32ζ3−2ζ2ζ0000000000000000000000000
χ628-8000-42-2400−6i6i−4ζ34ζ3−4ζ4ζ000000000000000002ζ3−2ζ32ζ−2ζ0000000000000000000000000
χ6316-160004-88-4000000000000000000000000000000000000000000000000000000

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