Finite Group Databasebeta

← Group #10593153

Character table — Group #10593153

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36
size111188889999121212121818181818181818181818182424242436363636
order1244361212224422444444888888886612128888
χ1111111111111111111111111111111111111
χ211111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ3111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ4111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ511-1-111-1-111-1-111-1-111-1-1iiii−i−i−i−i11-1-1ii−i−i
χ611-1-111-1-111-1-111-1-111-1-1−i−i−i−iiiii11-1-1−i−iii
χ711-1-111-1-111-1-1-1-11111-1-1iiii−i−i−i−i-1-111−i−iii
χ811-1-111-1-111-1-1-1-11111-1-1−i−i−i−iiiii-1-111ii−i−i
χ91-1i−i1-1i−i1-1i−i1-1i−i1-1i−iζζ−ζ−ζζ3ζ3−ζ3−ζ31-1i−iζ−ζζ3−ζ3
χ101-1i−i1-1i−i1-1i−i1-1i−i1-1i−i−ζ−ζζζ−ζ3−ζ3ζ3ζ31-1i−i−ζζ−ζ3ζ3
χ111-1i−i1-1i−i1-1i−i-11−ii1-1i−iζζ−ζ−ζζ3ζ3−ζ3−ζ3-11−ii−ζζ−ζ3ζ3
χ121-1i−i1-1i−i1-1i−i-11−ii1-1i−i−ζ−ζζζ−ζ3−ζ3ζ3ζ3-11−iiζ−ζζ3−ζ3
χ131-1−ii1-1−ii1-1−ii1-1−ii1-1−iiζ3ζ3−ζ3−ζ3ζζ−ζ−ζ1-1−iiζ3−ζ3ζ−ζ
χ141-1−ii1-1−ii1-1−ii1-1−ii1-1−ii−ζ3−ζ3ζ3ζ3−ζ−ζζζ1-1−ii−ζ3ζ3−ζζ
χ151-1−ii1-1−ii1-1−ii-11i−i1-1−iiζ3ζ3−ζ3−ζ3ζζ−ζ−ζ-11i−i−ζ3ζ3−ζζ
χ161-1−ii1-1−ii1-1−ii-11i−i1-1−ii−ζ3−ζ3ζ3ζ3−ζ−ζζζ-11i−iζ3−ζ3ζ−ζ
χ172222222222220000-2-2-2-20000000000000000
χ1822222222-2-2-2-200000000i2−i2i2−i2i2−i2i2−i200000000
χ1922222222-2-2-2-200000000−i2i2−i2i2−i2i2−i2i200000000
χ2022-2-222-2-222-2-20000-2-2220000000000000000
χ2122-2-222-2-2-2-222000000002−22−2−22−2200000000
χ2222-2-222-2-2-2-22200000000−22−222−22−200000000
χ232-22i−2i2-22i−2i2-22i−2i0000-22−2i2i0000000000000000
χ242-22i−2i2-22i−2i-22−2i2i000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i00000000
χ252-22i−2i2-22i−2i-22−2i2i00000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i00000000
χ262-2−2i2i2-2−2i2i2-2−2i2i0000-222i−2i0000000000000000
χ272-2−2i2i2-2−2i2i-222i−2i000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i00000000
χ282-2−2i2i2-2−2i2i-222i−2i00000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i00000000
χ298888-1-1-1-100002222000000000000-1-1-1-10000
χ308888-1-1-1-10000-2-2-2-200000000000011110000
χ3188-8-8-1-111000022-2-2000000000000-1-1110000
χ3288-8-8-1-1110000-2-22200000000000011-1-10000
χ338-88i−8i-11−ii00002-22i−2i000000000000-11−ii0000
χ348-88i−8i-11−ii0000-22−2i2i0000000000001-1i−i0000
χ358-8−8i8i-11i−i00002-2−2i2i000000000000-11i−i0000
χ368-8−8i8i-11i−i0000-222i−2i0000000000001-1−ii0000

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