Finite Group Databasebeta

← Group #72341449

Character table — Group #72341449

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11112266668888121212121212121232323232323232323232323232323232484848484848484848484848484848484848
order12442422444444222244443666121212121212121212121212244444888888888888
χ111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1
χ41111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ511-1-1-111-11-1ii−i−i11-1-11-11-111-1-111-1-1iiii−i−i−i−i1-1i−i1-1i−ii−i11-1-1ii−i−i
χ611-1-1-111-11-1ii−i−i11-1-11-11-111-1-111-1-1iiii−i−i−i−i-11i−i-11−ii−ii-1-111−i−iii
χ711-1-1-111-11-1−i−iii11-1-11-11-111-1-111-1-1−i−i−i−iiiii1-1−ii1-1−ii−ii11-1-1−i−iii
χ811-1-1-111-11-1−i−iii11-1-11-11-111-1-111-1-1−i−i−i−iiiii-11−ii-11i−ii−i-1-111ii−i−i
χ92222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1002200000000000000
χ102222222222-2-2-2-222222222-1-1-1-1-1-1-1-11111111100-2-200000000000000
χ112222-2-22-2-2200002-22-2-2-22222-2-2-2-22200000000000000000000000000
χ122222-2-22-2-2200002-22-2-2-222-1-11111-1-133−3−333−3−3000000000000000000
χ132222-2-22-2-2200002-22-2-2-222-1-11111-1-1−3−333−3−333000000000000000000
χ1422-2-22-222-2-200002-2-22-222-22222-2-2-2-200000000000000000000000000
χ1522-2-22-222-2-200002-2-22-222-2-1-1-1-11111−i3−i3i3i3i3i3−i3−i3000000000000000000
χ1622-2-22-222-2-200002-2-22-222-2-1-1-1-11111i3i3−i3−i3−i3−i3i3i3000000000000000000
χ1722-2-2-222-22-22i2i−2i−2i22-2-22-22-2-1-111-1-111−i−i−i−iiiii002i−2i00000000000000
χ1822-2-2-222-22-2−2i−2i2i2i22-2-22-22-2-1-111-1-111iiii−i−i−i−i00−2i2i00000000000000
χ1933333333333333-1-1-1-1-1-1-1-1000000000000000011-1-1111111-1-1-1-1-1-1-1-1
χ2033333333333333-1-1-1-1-1-1-1-10000000000000000-1-1-1-1-1-1-1-1-1-111111111
χ213333333333-3-3-3-3-1-1-1-1-1-1-1-10000000000000000111111-1-1-1-1-1-1-1-11111
χ223333333333-3-3-3-3-1-1-1-1-1-1-1-10000000000000000-1-111-1-111111111-1-1-1-1
χ2333-3-3-333-33-33i3i−3i−3i-1-111-11-1100000000000000001-1−ii1-1i−ii−i-1-111−i−iii
χ2433-3-3-333-33-33i3i−3i−3i-1-111-11-110000000000000000-11−ii-11−ii−ii11-1-1ii−i−i
χ2533-3-3-333-33-3−3i−3i3i3i-1-111-11-1100000000000000001-1i−i1-1−ii−ii-1-111ii−i−i
χ2633-3-3-333-33-3−3i−3i3i3i-1-111-11-110000000000000000-11i−i-11i−ii−i11-1-1−i−iii
χ27666666-2-2-2-200002-2-222-2-22000000000000000000000022-2-200000000
χ28666666-2-2-2-200002-2-222-2-220000000000000000000000-2-22200000000
χ29666666-2-2-2-20000-222-2-222-200000000000000002200-2-2000000000000
χ30666666-2-2-2-20000-222-2-222-20000000000000000-2-20022000000000000
χ316666-6-66-6-660000-22-2222-2-20000000000000000000000000000000000
χ326666-6-6-222-2000022-2-2-22-220000000000000000000000000000002-22-2
χ336666-6-6-222-2000022-2-2-22-22000000000000000000000000000000-22-22
χ346666-6-6-222-20000-2-2222-22-2000000000000000000000000002-22-20000
χ356666-6-6-222-20000-2-2222-22-200000000000000000000000000-22-220000
χ3666-6-66-666-6-60000-222-22-2-220000000000000000000000000000000000
χ3766-6-66-6-2-22200002222-2-2-2-20000000000000000000000000000002i−2i−2i2i
χ3866-6-66-6-2-22200002222-2-2-2-2000000000000000000000000000000−2i2i2i−2i
χ3966-6-66-6-2-2220000-2-2-2-22222000000000000000000000000002-2-220000
χ4066-6-66-6-2-2220000-2-2-2-2222200000000000000000000000000-222-20000
χ4166-6-6-66-22-2200002-22-222-2-200000000000000000000002i−2i−2i2i00000000
χ4266-6-6-66-22-2200002-22-222-2-20000000000000000000000−2i2i2i−2i00000000
χ4366-6-6-66-22-220000-22-22-2-22200000000000000002-200-22000000000000
χ4466-6-6-66-22-220000-22-22-2-2220000000000000000-22002-2000000000000
χ458-88i−8i0000002+2i−2−2i2−2i−2+2i000000002-200002i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000000000
χ468-88i−8i0000002+2i−2−2i2−2i−2+2i00000000-11−i3i33−3−ii−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7000000000000000000
χ478-88i−8i0000002+2i−2−2i2−2i−2+2i00000000-11i3−i3−33−ii−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11000000000000000000
χ488-88i−8i000000−2−2i2+2i−2+2i2−2i000000002-200002i−2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000000000
χ498-88i−8i000000−2−2i2+2i−2+2i2−2i00000000-11−i3i33−3−iiζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7000000000000000000
χ508-88i−8i000000−2−2i2+2i−2+2i2−2i00000000-11i3−i3−33−iiζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11000000000000000000
χ518-8−8i8i0000002−2i−2+2i2+2i−2−2i000000002-20000−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000000000
χ528-8−8i8i0000002−2i−2+2i2+2i−2−2i00000000-11−i3i3−33i−i−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7000000000000000000
χ538-8−8i8i0000002−2i−2+2i2+2i−2−2i00000000-11i3−i33−3i−i−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11000000000000000000
χ548-8−8i8i000000−2+2i2−2i−2−2i2+2i000000002-20000−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000000000
χ558-8−8i8i000000−2+2i2−2i−2−2i2+2i00000000-11−i3i3−33i−iζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7000000000000000000
χ568-8−8i8i000000−2+2i2−2i−2−2i2+2i00000000-11i3−i33−3i−iζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.