Finite Group Databasebeta

← Group #131237

Character table — Group #131237

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size11112222224444888888888888161616161616161616161616161616161616161616161616
order12222244444444444444444444224444448888888888888888
χ111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111-1-1-1-1111-1-1-1-11-1-11111-1-1-1-11111-1-1-1-1
χ411111111111111111111-1-1-1-1111-1-1-1-11-1-1-1-1-1-11111-1-1-1-11111
χ51111111111111111-1-1-1-1111111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ61111111111111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111-1-1-1-1-1-1-1-111-11-1-11-1111111-1-1-1-1-1-1-1-11111
χ81111111111111111-1-1-1-1-1-1-1-111-11-1-11-111-1-1-1-111111111-1-1-1-1
χ9111111-1-1-1-111-1-111111111-1-1-1-1-111-1-1-11-1ii−i−iii−i−iii−i−iii−i−i
χ10111111-1-1-1-111-1-111111111-1-1-1-1-111-1-1-11-1−i−iii−i−iii−i−iii−i−iii
χ11111111-1-1-1-111-1-1111111-1-111-1-1-1-1-111-1-11ii−i−i−i−iiiii−i−i−i−iii
χ12111111-1-1-1-111-1-1111111-1-111-1-1-1-1-111-1-11−i−iiiii−i−i−i−iiiii−i−i
χ13111111-1-1-1-111-1-111-1-1-1-111-1-1-1-11-11-111-11ii−i−iii−i−i−i−iii−i−iii
χ14111111-1-1-1-111-1-111-1-1-1-111-1-1-1-11-11-111-11−i−iii−i−iiiii−i−iii−i−i
χ15111111-1-1-1-111-1-111-1-1-1-1-1-111-1-111-11-111-1ii−i−i−i−iii−i−iiiii−i−i
χ16111111-1-1-1-111-1-111-1-1-1-1-1-111-1-111-11-111-1−i−iiiii−i−iii−i−i−i−iii
χ1722222222222222-2-200002222-2-200-2-200000000000000000000
χ1822222222222222-2-20000-2-2-2-2-2-2002200000000000000000000
χ192222222222-2-2-2-22-2000000002-2020020-2-20000000000000000
χ202222222222-2-2-2-22-2000000002-20-200-20220000000000000000
χ212222222222-2-2-2-2-2222-2-20000-2220000-2000000000000000000
χ222222222222-2-2-2-2-22-2-2220000-22-200002000000000000000000
χ23222222-2-2-2-222-2-2-2-2000022-2-22200-2200000000000000000000
χ24222222-2-2-2-222-2-2-2-20000-2-22222002-200000000000000000000
χ25222222-2-2-2-2-2-2222-200000000-220200-20-220000000000000000
χ26222222-2-2-2-2-2-2222-200000000-220-200202-20000000000000000
χ27222222-2-2-2-2-2-222-2222-2-200002-2-200002000000000000000000
χ28222222-2-2-2-2-2-222-22-2-22200002-220000-2000000000000000000
χ2922-2-22-22i−2i2i−2i2-22i−2i0000002i−2i2-20000000000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i
χ3022-2-22-22i−2i2i−2i2-22i−2i0000002i−2i2-2000000000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i
χ3122-2-22-22i−2i2i−2i2-22i−2i000000−2i2i-220000000000000000001−i−1+i1+i−1−i−1−i1+i−1+i1−i
χ3222-2-22-22i−2i2i−2i2-22i−2i000000−2i2i-22000000000000000000−1+i1−i−1−i1+i1+i−1−i1−i−1+i
χ3322-2-22-2−2i2i−2i2i2-2−2i2i0000002i−2i-220000000000000000001+i−1−i1−i−1+i−1+i1−i−1−i1+i
χ3422-2-22-2−2i2i−2i2i2-2−2i2i0000002i−2i-22000000000000000000−1−i1+i−1+i1−i1−i−1+i1+i−1−i
χ3522-2-22-2−2i2i−2i2i2-2−2i2i000000−2i2i2-20000000000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i
χ3622-2-22-2−2i2i−2i2i2-2−2i2i000000−2i2i2-2000000000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i
χ374444-4-444-4-40000000000000000000000002i−2i2i−2i000000000000
χ384444-4-444-4-4000000000000000000000000−2i2i−2i2i000000000000
χ394444-4-4-4-4440000000000000000000000002-2-22000000000000
χ404444-4-4-4-444000000000000000000000000-222-2000000000000
χ4144-4-44-44i−4i4i−4i-44−4i4i000000000000000000000000000000000000
χ4244-4-44-4−4i4i−4i4i-444i−4i000000000000000000000000000000000000
χ4344-4-4-444i−4i−4i4i00000000000000000000000000002ζ3−2ζ32ζ−2ζ00000000
χ4444-4-4-444i−4i−4i4i0000000000000000000000000000−2ζ32ζ3−2ζ2ζ00000000
χ4544-4-4-44−4i4i4i−4i00000000000000000000000000002ζ−2ζ2ζ3−2ζ300000000
χ4644-4-4-44−4i4i4i−4i0000000000000000000000000000−2ζ2ζ−2ζ32ζ300000000
χ478-88-8000000000000004i−4i000000000000000000000000000000
χ488-88-800000000000000−4i4i000000000000000000000000000000
χ498-8-880000000000004i−4i00000000000000000000000000000000
χ508-8-88000000000000−4i4i00000000000000000000000000000000

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