Finite Group Databasebeta

← Group #13146451

Character table — Group #13146451

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size112222244499181818181818181818242424242424242436363636363636363636363636108108108108108108108108
order122366626644488881212121236666666488121224242424242424241616161616161616
χ111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111-1-1-1-11111111111111-1-111-1-1-1-1-1-1-1-1iiii−i−i−i−i
χ41111111111111-1-1-1-11111111111111-1-111-1-1-1-1-1-1-1-1−i−i−i−iiiii
χ51111111111-1-1-1ii−i−i-1-1-1-111111111-1i−i-1-1iiii−i−i−i−iζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13
χ61111111111-1-1-1ii−i−i-1-1-1-111111111-1i−i-1-1iiii−i−i−i−i−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13
χ71111111111-1-1-1−i−iii-1-1-1-111111111-1−ii-1-1−i−i−i−iiiii−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23
χ81111111111-1-1-1−i−iii-1-1-1-111111111-1−ii-1-1−i−i−i−iiiiiζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23
χ91111111-1-1-1111111111111111-1-1-1-1-1-1-1-1-111-1-111-1-11-11-11-11-1
χ101111111-1-1-1111111111111111-1-1-1-1-1-1-1-1-111-1-111-1-1-11-11-11-11
χ111111111-1-1-1111-1-1-1-111111111-1-1-1-1-111-1-1-1-111-1-111i−ii−i−ii−ii
χ121111111-1-1-1111-1-1-1-111111111-1-1-1-1-111-1-1-1-111-1-111−ii−iii−ii−i
χ131111111-1-1-1-1-1-1ii−i−i-1-1-1-11111-1-1-1-11−ii11ii−i−i−i−iiiζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13
χ141111111-1-1-1-1-1-1ii−i−i-1-1-1-11111-1-1-1-11−ii11ii−i−i−i−iii−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13
χ151111111-1-1-1-1-1-1−i−iii-1-1-1-11111-1-1-1-11i−i11−i−iiiii−i−i−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23
χ161111111-1-1-1-1-1-1−i−iii-1-1-1-11111-1-1-1-11i−i11−i−iiiii−i−iζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23
χ1722-22-2-2200022-22-22-2-2-22222-2-20000000002-2002-20000000000
χ1822-22-2-2200022-2-22-22-2-22222-2-2000000000-2200-220000000000
χ1922-22-2-22000-2-222i−2i−2i2i22-2-222-2-20000000002i−2i00−2i2i0000000000
χ2022-22-2-22000-2-22−2i2i2i−2i22-2-222-2-2000000000−2i2i002i−2i0000000000
χ214-40400-40004i−4i00000004i−4i4-4000000000000000000000000000
χ224-40400-4000−4i4i0000000−4i4i4-4000000000000000000000000000
χ23666-3-3-3-36-3-32222i2i−2i−2i-1-1-1-10000000022i−2i-1-1−i−i−i−iiiii00000000
χ24666-3-3-3-36-3-3222−2i−2i2i2i-1-1-1-1000000002−2i2i-1-1iiii−i−i−i−i00000000
χ25666-3-3-3-36-3-3-2-2-22222111100000000-22211-1-1-1-1-1-1-1-100000000
χ26666-3-3-3-36-3-3-2-2-2-2-2-2-2111100000000-2-2-2111111111100000000
χ27666-3-3-3-3-6332222i2i−2i−2i-1-1-1-100000000-2−2i2i11−i−iiiii−i−i00000000
χ28666-3-3-3-3-633222−2i−2i2i2i-1-1-1-100000000-22i−2i11ii−i−i−i−iii00000000
χ29666-3-3-3-3-633-2-2-222221111000000002-2-2-1-1-1-111-1-11100000000
χ30666-3-3-3-3-633-2-2-2-2-2-2-2111100000000222-1-111-1-111-1-100000000
χ3166-6-333-30−3i33i322-22i−2i−2i2i11-1-100000000000−i3i3−ii3−3i−i3−300000000
χ3266-6-333-30−3i33i322-2−2i2i2i−2i11-1-100000000000−i3i3i−i−33−ii−3300000000
χ3366-6-333-30−3i33i3-2-222-22-2-1-11100000000000i3−i3-11−i3i3-11i3−i300000000
χ3466-6-333-30−3i33i3-2-22-22-22-1-11100000000000i3−i31-1i3−i31-1−i3i300000000
χ3566-6-333-303i3−3i322-22i−2i−2i2i11-1-100000000000i3−i3−ii−33i−i−3300000000
χ3666-6-333-303i3−3i322-2−2i2i2i−2i11-1-100000000000i3−i3i−i3−3−ii3−300000000
χ3766-6-333-303i3−3i3-2-222-22-2-1-11100000000000−i3i3-11i3−i3-11−i3i300000000
χ3866-6-333-303i3−3i3-2-22-22-22-1-11100000000000−i3i31-1−i3i31-1i3−i300000000
χ39888888888800000000000-1-1-1-1-1-1-1-1000000000000000000000
χ408888888-8-8-800000000000-1-1-1-11111000000000000000000000
χ4188-88-8-8800000000000000-1-11133-3-3000000000000000000000
χ4288-88-8-8800000000000000-1-111-3-333000000000000000000000
χ438-80800-800000000000000-113-33-33-3000000000000000000000
χ448-80800-800000000000000-113-3-33-33000000000000000000000
χ458-80800-800000000000000-11-333-3-33000000000000000000000
χ468-80800-800000000000000-11-33-333-3000000000000000000000
χ4712-120-6−6i36i360004i−4i0000023−23−2i2i00000000000000000000000000000
χ4812-120-6−6i36i36000−4i4i00000−23232i−2i00000000000000000000000000000
χ4912-120-66i3−6i360004i−4i00000−2323−2i2i00000000000000000000000000000
χ5012-120-66i3−6i36000−4i4i0000023−232i−2i00000000000000000000000000000

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