Finite Group Databasebeta

← Group #11788929

Character table — Group #11788929

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size11222444444448888888881212121212121212121212121616181818182424242424242424242436364848484872727272
order12244336688121266121212242424242244888824242424242422444466881212242488121224244488
χ1111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-111-1-1111111-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1111111-1-1-1-1
χ41111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ5111111111-1-11111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-111-1-1
χ6111111111-1-11111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-111-1-111
χ7111111111-1-11111111-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-1-1-111-1-111-1-1-1-111
χ8111111111-1-11111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-111-1-111-1-1-1-11111-1-1
χ9111-1-11111i−i-1-111-1-1-1ii−i−i1-11-1ii−i−iii−i−ii−i11-1-11-11-1i−i1-1i−ii−i1-1i−i1-1i−i
χ10111-1-11111i−i-1-111-1-1-1ii−i−i1-11-1ii−i−iii−i−ii−i11-1-1-111-1−ii1-1i−ii−i-11−ii-11−ii
χ11111-1-11111i−i-1-111-1-1-1ii−i−i-11-11−i−iii−i−iiii−i11-1-11-1-11i−i-11−iii−i1-1i−i-11−ii
χ12111-1-11111i−i-1-111-1-1-1ii−i−i-11-11−i−iii−i−iiii−i11-1-1-11-11−ii-11−iii−i-11−ii1-1i−i
χ13111-1-11111−ii-1-111-1-1-1−i−iii1-11-1−i−iii−i−iii−ii11-1-11-11-1−ii1-1−ii−ii1-1−ii1-1−ii
χ14111-1-11111−ii-1-111-1-1-1−i−iii1-11-1−i−iii−i−iii−ii11-1-1-111-1i−i1-1−ii−ii-11i−i-11i−i
χ15111-1-11111−ii-1-111-1-1-1−i−iii-11-11ii−i−iii−i−i−ii11-1-11-1-11−ii-11i−i−ii1-1−ii-11i−i
χ16111-1-11111−ii-1-111-1-1-1−i−iii-11-11ii−i−iii−i−i−ii11-1-1-11-11i−i-11i−i−ii-11i−i1-1−ii
χ17222222222222222222222200000000000022-2-2-2-20000000000-2-200000000
χ18222222222-2-22222222-2-2-2-2000000000000-2-2-2-2-2-200000000002200000000
χ19222-2-222222i−2i-2-222-2-2-22i2i−2i−2i0000000000002i−2i-2-2220000000000−2i2i00000000
χ20222-2-22222−2i2i-2-222-2-2-2−2i−2i2i2i000000000000−2i2i-2-22200000000002i−2i00000000
χ2122-22-2222200-2-2-2-22-22000000002i−2i2i−2i2i2i−2i−2i002-22-200000000−2i2i0000000000
χ2222-22-2222200-2-2-2-22-2200000000−2i2i−2i2i−2i−2i2i2i002-22-2000000002i−2i0000000000
χ2322-22-2222200-2-2-2-22-22000022-2-20000000000-22-22002200-2-2000000000000
χ2422-22-2222200-2-2-2-22-220000-2-2220000000000-22-2200-2-20022000000000000
χ2522-2-2222220022-2-2-22-2000000002-2-222222002-2-2200000000-2-20000000000
χ2622-2-2222220022-2-2-22-200000000-222-2-2-2-2-2002-2-2200000000220000000000
χ2722-2-2222220022-2-2-22-200002-2-220000000000-222-2002-200-22000000000000
χ2822-2-2222220022-2-2-22-20000-222-20000000000-222-200-22002-2000000000000
χ29444441-2-2144-2-21-2-211-2-2-2-2000000000000110000220022000000-1-1-1-10000
χ30444441-2-2144-2-21-2-211-2-2-2-2000000000000110000-2-200-2-200000011110000
χ31444441-2-21-4-4-2-21-2-2112222000000000000-1-100002200-2-2000000-1-1110000
χ32444441-2-21-4-4-2-21-2-2112222000000000000-1-10000-2-2002200000011-1-10000
χ3344444-211-24411-211-2-2111122222222-1-1-1-1-2-2000000-1-100-1-1-1-10000000000
χ3444444-211-24411-211-2-21111-2-2-2-2-2-2-2-21111-2-2000000110011110000000000
χ3544444-211-2-4-411-211-2-2-1-1-1-12222-2-2-2-2111122000000-1-100-1-1110000000000
χ3644444-211-2-4-411-211-2-2-1-1-1-1-2-2-2-22222-1-1-1-122000000110011-1-10000000000
χ37444-4-41-2-214i−4i221-22-1-1−2i−2i2i2i000000000000i−i00002-2002i−2i000000-11−ii0000
χ38444-4-41-2-214i−4i221-22-1-1−2i−2i2i2i000000000000i−i0000-2200−2i2i0000001-1i−i0000
χ39444-4-41-2-21−4i4i221-22-1-12i2i−2i−2i000000000000−ii00002-200−2i2i000000-11i−i0000
χ40444-4-41-2-21−4i4i221-22-1-12i2i−2i−2i000000000000−ii0000-22002i−2i0000001-1−ii0000
χ41444-4-4-211-24i−4i-1-1-21-122ii−i−i2-22-22i2i−2i−2i−i−iii−2i2i000000-1100-11−ii0000000000
χ42444-4-4-211-24i−4i-1-1-21-122ii−i−i-22-22−2i−2i2i2iii−i−i−2i2i0000001-1001-1i−i0000000000
χ43444-4-4-211-2−4i4i-1-1-21-122−i−iii2-22-2−2i−2i2i2iii−i−i2i−2i000000-1100-11i−i0000000000
χ44444-4-4-211-2−4i4i-1-1-21-122−i−iii-22-222i2i−2i−2i−i−iii2i−2i0000001-1001-1−ii0000000000
χ4544-44-4-211-200-1-12-112-23i−3i3i−3i22-2-22i−2i2i−2i−i−iii00000000-1-10011i−i0000000000
χ4644-44-4-211-200-1-12-112-23i−3i3i−3i-2-222−2i2i−2i2iii−i−i000000001100-1-1−ii0000000000
χ4744-44-4-211-200-1-12-112-2−3i3i−3i3i22-2-2−2i2i−2i2iii−i−i00000000-1-10011−ii0000000000
χ4844-44-4-211-200-1-12-112-2−3i3i−3i3i-2-2222i−2i2i−2i−i−iii000000001100-1-1i−i0000000000
χ4944-4-44-211-200112-1-1-223-3-332-2-222-2-22-1-1-1-100000000-11001-1110000000000
χ5044-4-44-211-200112-1-1-223-3-33-222-2-222-21111000000001-100-11-1-10000000000
χ5144-4-44-211-200112-1-1-22-333-32-2-22-222-2111100000000-11001-1-1-10000000000
χ5244-4-44-211-200112-1-1-22-333-3-222-22-2-22-1-1-1-1000000001-100-11110000000000
χ5388-88-82-4-420044-24-4-22000000000000000000000000000000000000000000
χ5488-8-882-4-4200-4-4-2442-2000000000000000000000000000000000000000000
χ558-800088-8-8000000000000000000000000000000000000000000000000000
χ568-8000-42-24006i−6i00000000000000000−2ζ7+2ζ232ζ7−2ζ232ζ5−2ζ13−2ζ5+2ζ1300000000000000000000000000
χ578-8000-42-24006i−6i000000000000000002ζ7−2ζ23−2ζ7+2ζ23−2ζ5+2ζ132ζ5−2ζ1300000000000000000000000000
χ588-8000-42-2400−6i6i000000000000000002ζ5−2ζ13−2ζ5+2ζ13−2ζ7+2ζ232ζ7−2ζ2300000000000000000000000000
χ598-8000-42-2400−6i6i00000000000000000−2ζ5+2ζ132ζ5−2ζ132ζ7−2ζ23−2ζ7+2ζ2300000000000000000000000000
χ6016-160004-88-4000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.