Finite Group Databasebeta

← Group #13166226

Character table — Group #13166226

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size11222224448888888888888888888888889918181818181818181836363636363636363636363636108108108108108108108108
order12236662663336666666666666666666662224444666624466121212121212121288888888
χ1111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-111111-1-111-1-1-1-1-1-1-1-1iiii−i−i−i−i
χ41111111111111111111111111111111111111-1-1-1-111111-1-111-1-1-1-1-1-1-1-1−i−i−i−iiiii
χ51111111111111111111111111111111111-1-1-1ii−i−i-1-1-1-1-1i−i-1-1iiii−i−i−i−iζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13
χ61111111111111111111111111111111111-1-1-1ii−i−i-1-1-1-1-1i−i-1-1iiii−i−i−i−i−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13
χ71111111111111111111111111111111111-1-1-1−i−iii-1-1-1-1-1−ii-1-1−i−i−i−iiiii−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23
χ81111111111111111111111111111111111-1-1-1−i−iii-1-1-1-1-1−ii-1-1−i−i−i−iiiiiζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23
χ91111111-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-111-1-111-1-11-11-11-11-1
χ101111111-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-111-1-111-1-1-11-11-11-11
χ111111111-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-11111-111-1-1-1-111-1-111i−ii−i−ii−ii
χ121111111-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-11111-111-1-1-1-111-1-111−ii−iii−ii−i
χ131111111-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i-1-1-1-11−ii11ii−i−i−i−iiiζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13
χ141111111-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i-1-1-1-11−ii11ii−i−i−i−iii−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13
χ151111111-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii-1-1-1-11i−i11−i−iiiii−i−i−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23
χ161111111-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii-1-1-1-11i−i11−i−iiiii−i−iζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23
χ17222-1-1-1-12-1-12-1-1222-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222222-1-1-1-1222-1-1-1-1-1-1-1-1-1-100000000
χ18222-1-1-1-12-1-12-1-1222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222-2-2-2-2-1-1-1-12-2-2-1-11111111100000000
χ19222-1-1-1-12-1-12-1-1222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-22i2i−2i−2i1111-22i−2i11−i−i−i−iiiii00000000
χ20222-1-1-1-12-1-12-1-1222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2−2i−2i2i2i1111-2−2i2i11iiii−i−i−i−i00000000
χ21222-1-1-1-1-2112-1-1222-1-1-1-1-1-1-2-2-2-2111111112222222-1-1-1-1-2-2-211-1-111-1-11100000000
χ22222-1-1-1-1-2112-1-1222-1-1-1-1-1-1-2-2-2-211111111222-2-2-2-2-1-1-1-1-2221111-1-111-1-100000000
χ23222-1-1-1-1-2112-1-1222-1-1-1-1-1-1-2-2-2-211111111-2-2-22i2i−2i−2i11112−2i2i-1-1−i−iiiii−i−i00000000
χ24222-1-1-1-1-2112-1-1222-1-1-1-1-1-1-2-2-2-211111111-2-2-2−2i−2i2i2i111122i−2i-1-1ii−i−i−i−iii00000000
χ2522-222-2-20002222-2-222-2-2-2-200000000000022-22-22-2-2-222000002-2002-20000000000
χ2622-222-2-20002222-2-222-2-2-2-200000000000022-2-22-22-2-22200000-2200-220000000000
χ2722-222-2-20002222-2-222-2-2-2-2000000000000-2-222i−2i−2i2i22-2-2000002i−2i00−2i2i0000000000
χ2822-222-2-20002222-2-222-2-2-2-2000000000000-2-22−2i2i2i−2i22-2-200000−2i2i002i−2i0000000000
χ2922-2-1-1110−i3i32-1-12-2-2-1-111110000−i3−i3−i3−i3i3i3i3i322-22-22-211-1-1000−i3i3-11−i3i3-11−i3i300000000
χ3022-2-1-1110−i3i32-1-12-2-2-1-111110000−i3−i3−i3−i3i3i3i3i322-2-22-2211-1-1000−i3i31-1i3−i31-1i3−i300000000
χ3122-2-1-1110−i3i32-1-12-2-2-1-111110000−i3−i3−i3−i3i3i3i3i3-2-222i−2i−2i2i-1-111000i3−i3−ii3−3i−i−3300000000
χ3222-2-1-1110−i3i32-1-12-2-2-1-111110000−i3−i3−i3−i3i3i3i3i3-2-22−2i2i2i−2i-1-111000i3−i3i−i−33−ii3−300000000
χ3322-2-1-1110i3−i32-1-12-2-2-1-111110000i3i3i3i3−i3−i3−i3−i322-22-22-211-1-1000i3−i3-11i3−i3-11i3−i300000000
χ3422-2-1-1110i3−i32-1-12-2-2-1-111110000i3i3i3i3−i3−i3−i3−i322-2-22-2211-1-1000i3−i31-1−i3i31-1−i3i300000000
χ3522-2-1-1110i3−i32-1-12-2-2-1-111110000i3i3i3i3−i3−i3−i3−i3-2-222i−2i−2i2i-1-111000−i3i3−ii−33i−i3−300000000
χ3622-2-1-1110i3−i32-1-12-2-2-1-111110000i3i3i3i3−i3−i3−i3−i3-2-22−2i2i2i−2i-1-111000−i3i3i−i3−3−ii−3300000000
χ374-404-400000444-400-4-400000000000000004-400000004-4000000000000000000000
χ384-404-400000444-400-4-40000000000000000-440000000-44000000000000000000000
χ394-40-22−2i32i30004-2-2-40022−2i3−2i32i32i30000000000004-400000−2i32i3-22000000000000000000000
χ404-40-22−2i32i30004-2-2-40022−2i3−2i32i32i3000000000000-44000002i3−2i32-2000000000000000000000
χ414-40-222i3−2i30004-2-2-400222i32i3−2i3−2i30000000000004-4000002i3−2i3-22000000000000000000000
χ424-40-222i3−2i30004-2-2-400222i32i3−2i3−2i3000000000000-4400000−2i32i32-2000000000000000000000
χ438888888888-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000000000
χ448888888-8-8-8-1-1-1-1-1-1-1-1-1-1-1-111111111111100000000000000000000000000000000
χ45888-4-4-4-48-4-4-11−3i321+3i32-1-1-11−3i321+3i321−3i321+3i321−3i321+3i32-1-1-1-11−3i321−3i321+3i321+3i321−3i321−3i321+3i321+3i3200000000000000000000000000000000
χ46888-4-4-4-48-4-4-11+3i321−3i32-1-1-11+3i321−3i321+3i321−3i321+3i321−3i32-1-1-1-11+3i321+3i321−3i321−3i321+3i321+3i321−3i321−3i3200000000000000000000000000000000
χ47888-4-4-4-4-844-11−3i321+3i32-1-1-11−3i321+3i321−3i321+3i321−3i321+3i321111−1+3i32−1+3i32−1−3i32−1−3i32−1+3i32−1+3i32−1−3i32−1−3i3200000000000000000000000000000000
χ48888-4-4-4-4-844-11+3i321−3i32-1-1-11+3i321−3i321+3i321−3i321+3i321−3i321111−1−3i32−1−3i32−1+3i32−1+3i32−1−3i32−1−3i32−1+3i32−1+3i3200000000000000000000000000000000
χ4988-888-8-8000-1-1-1-111-1-1111133-3-333-3-3-3-33300000000000000000000000000000000
χ5088-888-8-8000-1-1-1-111-1-11111-3-333-3-33333-3-300000000000000000000000000000000
χ5188-8-4-4440−4i34i3-11−3i321+3i32-1111−3i321+3i32−1+3i32−1−3i32−1+3i32−1−3i3233-3-3−3+i32−3+i323+i323+i323−i323−i32−3−i32−3−i3200000000000000000000000000000000
χ5288-8-4-4440−4i34i3-11+3i321−3i32-1111+3i321−3i32−1−3i32−1+3i32−1−3i32−1+3i32-3-3333+i323+i32−3+i32−3+i32−3−i32−3−i323−i323−i3200000000000000000000000000000000
χ5388-8-4-44404i3−4i3-11−3i321+3i32-1111−3i321+3i32−1+3i32−1−3i32−1+3i32−1−3i32-3-3333−i323−i32−3−i32−3−i32−3+i32−3+i323+i323+i3200000000000000000000000000000000
χ5488-8-4-44404i3−4i3-11+3i321−3i32-1111+3i321−3i32−1−3i32−1+3i32−1−3i32−1+3i3233-3-3−3−i32−3−i323−i323−i323+i323+i32−3+i32−3+i3200000000000000000000000000000000
χ558-808-800000-1-1-113-3113-3-333-33-33-33-33-33-300000000000000000000000000000000
χ568-808-800000-1-1-113-3113-3-33-33-33-33-33-33-3300000000000000000000000000000000
χ578-808-800000-1-1-11-3311-333-33-3-333-3-33-333-300000000000000000000000000000000
χ588-808-800000-1-1-11-3311-333-3-333-3-333-33-3-3300000000000000000000000000000000
χ598-80-44−4i34i3000-11−3i321+3i3213-3−1+3i32−1−3i32−3+i323+i323−i32−3−i323-33-3−3−3i323+3i32−3+3i323−3i32−3−3i323+3i32−3+3i323−3i3200000000000000000000000000000000
χ608-80-44−4i34i3000-11−3i321+3i3213-3−1+3i32−1−3i32−3+i323+i323−i32−3−i32-33-333+3i32−3−3i323−3i32−3+3i323+3i32−3−3i323−3i32−3+3i3200000000000000000000000000000000
χ618-80-44−4i34i3000-11+3i321−3i321-33−1−3i32−1+3i323+i32−3+i32−3−i323−i323-3-33−3+3i323−3i323+3i32−3−3i323−3i32−3+3i32−3−3i323+3i3200000000000000000000000000000000
χ628-80-44−4i34i3000-11+3i321−3i321-33−1−3i32−1+3i323+i32−3+i32−3−i323−i32-333-33−3i32−3+3i32−3−3i323+3i32−3+3i323−3i323+3i32−3−3i3200000000000000000000000000000000
χ638-80-444i3−4i3000-11−3i321+3i321-33−1+3i32−1−3i323−i32−3−i32−3+i323+i323-3-33−3−3i323+3i323−3i32−3+3i323+3i32−3−3i32−3+3i323−3i3200000000000000000000000000000000
χ648-80-444i3−4i3000-11−3i321+3i321-33−1+3i32−1−3i323−i32−3−i32−3+i323+i32-333-33+3i32−3−3i32−3+3i323−3i32−3−3i323+3i323−3i32−3+3i3200000000000000000000000000000000
χ658-80-444i3−4i3000-11+3i321−3i3213-3−1−3i32−1+3i32−3−i323−i323+i32−3+i323-33-3−3+3i323−3i32−3−3i323+3i32−3+3i323−3i32−3−3i323+3i3200000000000000000000000000000000
χ668-80-444i3−4i3000-11+3i321−3i3213-3−1−3i32−1+3i32−3−i323−i323+i32−3+i32-33-333−3i32−3+3i323+3i32−3−3i323−3i32−3+3i323+3i32−3−3i3200000000000000000000000000000000

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