Finite Group Databasebeta

← Group #93059

Character table — Group #93059

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11112222222222444444444488888888161616161616161616161616161616161616161616161616
order1222224444444422444488884488888844444444888888881616161616161616
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
χ511111111111111-1-111-1-1-1-1-1-1-1-11111-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i
χ611111111111111-1-111-1-1-1-1-1-1-1-11111-1-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii
χ711111111111111-1-111-1-1-1-1-1-1-1-11111-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii
χ811111111111111-1-111-1-1-1-1-1-1-1-11111-1-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i
χ9111111-1-111-1-1-1-1111-1-1-1-1-1-1-11-111-1-11111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ10111111-1-111-1-1-1-1111-1-1-1-1-1-1-11-111-1-11111-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ11111111-1-111-1-1-1-1111-1-1-1-1-1-1-11-111-1-111-1-111-1-111ii−i−iii−i−i−i−iii−i−iii
χ12111111-1-111-1-1-1-1111-1-1-1-1-1-1-11-111-1-111-1-111-1-111−i−iii−i−iiiii−i−iii−i−i
χ13111111-1-111-1-1-1-1-1-11-1111111-1111-1-1-1-1ii−i−i−i−iiiii−i−i−i−iii-1-11111-1-1
χ14111111-1-111-1-1-1-1-1-11-1111111-1111-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i11-1-1-1-111
χ15111111-1-111-1-1-1-1-1-11-1111111-1111-1-1-1-1−i−iiiii−i−iii−i−i−i−iii11-1-1-1-111
χ16111111-1-111-1-1-1-1-1-11-1111111-1111-1-1-1-1−i−iiiii−i−i−i−iiiii−i−i-1-11111-1-1
χ1722222222222222222222-2-2-2-222-2-2-2-2-2-2000000000000000000000000
χ1822222222222222-2-222-2-22222-2-2-2-2-2-222000000000000000000000000
χ1922222222-2-2-2-2-2-222-22220000-2-20000000000000000000000i2−i2i2−i2i2−i2i2−i2
χ2022222222-2-2-2-2-2-222-22220000-2-20000000000000000000000−i2i2−i2i2−i2i2−i2i2
χ2122222222-2-2-2-2-2-2-2-2-22-2-200002200000000000000000000002−22−2−22−22
χ2222222222-2-2-2-2-2-2-2-2-22-2-20000220000000000000000000000−22−222−22−2
χ23222222-2-222-2-2-2-2222-2-2-222222-2-2-222-2-2000000000000000000000000
χ24222222-2-222-2-2-2-2-2-22-222-2-2-2-2-22-2-22222000000000000000000000000
χ25222222-2-2-2-2222222-2-2-2-20000-2200000000000000000000002−2−222−2−22
χ26222222-2-2-2-2222222-2-2-2-20000-220000000000000000000000−222−2−222−2
χ27222222-2-2-2-22222-2-2-2-22200002-20000000000000000000000i2−i2−i2i2−i2i2i2−i2
χ28222222-2-2-2-22222-2-2-2-22200002-20000000000000000000000−i2i2i2−i2i2−i2−i2i2
χ292222-2-222-2-222-2-2002-2002i2i−2i−2i0000002i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ302222-2-222-2-222-2-2002-2002i2i−2i−2i0000002i−2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ312222-2-222-2-222-2-2002-200−2i−2i2i2i000000−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ322222-2-222-2-222-2-2002-200−2i−2i2i2i000000−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ332222-2-2-2-2-2-2-2-2220022002i2i−2i−2i000000−2i2i1−i−1+i−1+i1−i1+i−1−i−1−i1+i0000000000000000
χ342222-2-2-2-2-2-2-2-2220022002i2i−2i−2i000000−2i2i−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000000000000000
χ352222-2-2-2-2-2-2-2-222002200−2i−2i2i2i0000002i−2i1+i−1−i−1−i1+i1−i−1+i−1+i1−i0000000000000000
χ362222-2-2-2-2-2-2-2-222002200−2i−2i2i2i0000002i−2i−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000000000000000
χ374444-4-44444-4-44400-4-400000000000000000000000000000000000000
χ384444-4-4-4-44444-4-400-4400000000000000000000000000000000000000
χ3944-4-4004i−4i4-4004i−4i0000000000000000000000000000002ζ−2ζ2ζ3−2ζ300000000
χ4044-4-4004i−4i4-4004i−4i000000000000000000000000000000−2ζ2ζ−2ζ32ζ300000000
χ4144-4-4004i−4i-4400−4i4i000000000000000000000000002ζ3−2ζ32ζ−2ζ000000000000
χ4244-4-4004i−4i-4400−4i4i00000000000000000000000000−2ζ32ζ3−2ζ2ζ000000000000
χ4344-4-400−4i4i4-400−4i4i0000000000000000000000000000002ζ3−2ζ32ζ−2ζ00000000
χ4444-4-400−4i4i4-400−4i4i000000000000000000000000000000−2ζ32ζ3−2ζ2ζ00000000
χ4544-4-400−4i4i-44004i−4i000000000000000000000000002ζ−2ζ2ζ3−2ζ3000000000000
χ4644-4-400−4i4i-44004i−4i00000000000000000000000000−2ζ2ζ−2ζ32ζ3000000000000
χ474-44-44-40000000000004i−4i22−2222−22002i2−2i20000000000000000000000000000
χ484-44-44-40000000000004i−4i−2222−222200−2i22i20000000000000000000000000000
χ494-44-44-4000000000000−4i4i22−2222−2200−2i22i20000000000000000000000000000
χ504-44-44-4000000000000−4i4i−2222−2222002i2−2i20000000000000000000000000000
χ514-44-4-44000000004-400002i2−2i2−2i22i200002i2−2i200000000000000000000000000
χ524-44-4-44000000004-40000−2i22i22i2−2i20000−2i22i200000000000000000000000000
χ534-44-4-4400000000-4400002i2−2i2−2i22i20000−2i22i200000000000000000000000000
χ544-44-4-4400000000-440000−2i22i22i2−2i200002i2−2i200000000000000000000000000
χ558-8-880000008i−8i00000000000000000000000000000000000000000000
χ568-8-88000000−8i8i00000000000000000000000000000000000000000000

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