Finite Group Databasebeta

← Group #92829

Character table — Group #92829

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11112222222222444444444488888888161616161616161616161616161616161616161616161616
order122222222244444488888888444488882222444416161616161616161616161616161616
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ61111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ71111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ81111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ911111-1-1-11-1-1-1-1-111iiii−i−i−i−i11-1-1ii−i−i11-1-1ii−i−iζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3
χ1011111-1-1-11-1-1-1-1-111iiii−i−i−i−i11-1-1ii−i−i11-1-1ii−i−i−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3
χ1111111-1-1-11-1-1-1-1-111iiii−i−i−i−i11-1-1ii−i−i-1-111−i−iiiζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3
χ1211111-1-1-11-1-1-1-1-111iiii−i−i−i−i11-1-1ii−i−i-1-111−i−iii−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3
χ1311111-1-1-11-1-1-1-1-111−i−i−i−iiiii11-1-1−i−iii11-1-1−i−iiiζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ
χ1411111-1-1-11-1-1-1-1-111−i−i−i−iiiii11-1-1−i−iii11-1-1−i−iii−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ
χ1511111-1-1-11-1-1-1-1-111−i−i−i−iiiii11-1-1−i−iii-1-111ii−i−iζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ
χ1611111-1-1-11-1-1-1-1-111−i−i−i−iiiii11-1-1−i−iii-1-111ii−i−i−ζ3−ζ3ζ3ζ3−ζ−ζζζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ
χ17222222222222222222-2-222-2-2-2-2-2-22-22-2000000000000000000000000
χ182222222222222222-2-222-2-222-2-2-2-2-22-22000000000000000000000000
χ1922222-2-2-22-2-2-2-2-2222i2i−2i−2i−2i−2i2i2i-2-2222i−2i−2i2i000000000000000000000000
χ2022222-2-2-22-2-2-2-2-222−2i−2i2i2i2i2i−2i−2i-2-222−2i2i2i−2i000000000000000000000000
χ212222-222-2-2-22-22-22-2002i2i00−2i−2i00000−2i02i000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000
χ222222-222-2-2-22-22-22-2002i2i00−2i−2i00000−2i02i00000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000
χ232222-222-2-2-22-22-22-200−2i−2i002i2i000002i0−2i000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000
χ242222-222-2-2-22-22-22-200−2i−2i002i2i000002i0−2i00000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000
χ252222-222-2-2-2-22-22-222i2i00−2i−2i000000−2i02i000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i
χ262222-222-2-2-2-22-22-222i2i00−2i−2i000000−2i02i00000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i
χ272222-222-2-2-2-22-22-22−2i−2i002i2i0000002i0−2i000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i
χ282222-222-2-2-2-22-22-22−2i−2i002i2i0000002i0−2i00000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i
χ292222-2-2-22-222-22-2-22220022000000-20-2000000000000000002−2−22−222−2
χ302222-2-2-22-222-22-2-22220022000000-20-200000000000000000−222−22−2−22
χ312222-2-2-22-222-22-2-22-2-200-2-200000020200000000000000000i2−i2−i2i2i2−i2−i2i2
χ322222-2-2-22-222-22-2-22-2-200-2-200000020200000000000000000−i2i2i2−i2−i2i2i2−i2
χ332222-2-2-22-22-22-222-20022002200000-20-2000000002−2−22−222−200000000
χ342222-2-2-22-22-22-222-20022002200000-20-200000000−222−22−2−2200000000
χ352222-2-2-22-22-22-222-200-2-200-2-20000020200000000i2−i2−i2i2i2−i2−i2i200000000
χ362222-2-2-22-22-22-222-200-2-200-2-20000020200000000−i2i2i2−i2−i2i2i2−i200000000
χ374444444444-4-4-4-4-4-40000000000000000000000000000000000000000
χ3844444-4-4-44-44444-4-40000000000000000000000000000000000000000
χ3944-4-400040-40000002i2−2i22i2−2i22i2−2i22i2−2i22-22-20000000000000000000000000000
χ4044-4-400040-40000002i2−2i2−2i22i22i2−2i2−2i22i2-22-220000000000000000000000000000
χ4144-4-400040-4000000−2i22i22i2−2i2−2i22i22i2−2i2-22-220000000000000000000000000000
χ4244-4-400040-4000000−2i22i2−2i22i2−2i22i2−2i22i22-22-20000000000000000000000000000
χ4344-4-4000-40400000022−2222−22−2222−22222-2-220000000000000000000000000000
χ4444-4-4000-40400000022−22−2222−222222−22-222-20000000000000000000000000000
χ4544-4-4000-404000000−222222−2222−22−2222-222-20000000000000000000000000000
χ4644-4-4000-404000000−2222−222222−2222−222-2-220000000000000000000000000000
χ474-4-444000-4044-4-400000000000000000000002i−2i2i−2i0000000000000000
χ484-4-444000-4044-4-40000000000000000000000−2i2i−2i2i0000000000000000
χ494-4-444000-40-4-44400000000000000000000002-2-220000000000000000
χ504-4-444000-40-4-4440000000000000000000000-222-20000000000000000
χ514-4-44-4000404-4-440000000000000000002-22-200000000000000000000
χ524-4-44-4000404-4-44000000000000000000-22-2200000000000000000000
χ534-4-44-400040-444-40000000000000000002-2-2200000000000000000000
χ544-4-44-400040-444-4000000000000000000-222-200000000000000000000
χ558-88-808-80000000000000000000000000000000000000000000000000
χ568-88-80-880000000000000000000000000000000000000000000000000

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