Finite Group Databasebeta

← Group #93913

Character table — Group #93913

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size11112222224444888888888888161616161616161616161616161616161616161616161616
order1222224444224444448888888844448888888888881616161616161616
χ111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ611111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ711111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ811111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ911-1-1-111-11-11-11-1i−ii−i11-1-1i−ii−i11-1-1ii−i−iζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3
χ1011-1-1-111-11-11-11-1i−ii−i11-1-1i−ii−i11-1-1ii−i−i−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3
χ1111-1-1-111-11-11-11-1i−ii−i11-1-1i−ii−i-1-111−i−iiiζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3
χ1211-1-1-111-11-11-11-1i−ii−i11-1-1i−ii−i-1-111−i−iii−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3
χ1311-1-1-111-11-11-11-1−ii−ii11-1-1−ii−ii11-1-1−i−iiiζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ
χ1411-1-1-111-11-11-11-1−ii−ii11-1-1−ii−ii11-1-1−i−iii−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ
χ1511-1-1-111-11-11-11-1−ii−ii11-1-1−ii−ii-1-111ii−i−iζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ
χ1611-1-1-111-11-11-11-1−ii−ii11-1-1−ii−ii-1-111ii−i−i−ζ3−ζ3ζ3ζ3−ζ−ζζζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ
χ17222222222222222222-2-2-2-2-2-2-2-2000000000000000000000000
χ1822222222222222-2-2-2-2-2-2-2-22222000000000000000000000000
χ19222222-2-2-2-222-2-2000000002i−2i−2i2i000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000
χ20222222-2-2-2-222-2-2000000002i−2i−2i2i00000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000
χ21222222-2-2-2-222-2-200000000−2i2i2i−2i000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000
χ22222222-2-2-2-222-2-200000000−2i2i2i−2i00000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000
χ23222222-2-2-2-2-2-22222-2-2000000000000000000000000i2−i2i2−i2i2−i2i2−i2
χ24222222-2-2-2-2-2-22222-2-2000000000000000000000000−i2i2−i2i2−i2i2−i2i2
χ25222222-2-2-2-2-2-222-2-2220000000000000000000000002−22−2−22−22
χ26222222-2-2-2-2-2-222-2-222000000000000000000000000−22−222−22−2
χ2722-2-2-222-22-22-22-22i−2i2i−2i-2-222−2i2i−2i2i000000000000000000000000
χ2822-2-2-222-22-22-22-2−2i2i−2i2i-2-2222i−2i2i−2i000000000000000000000000
χ2922-2-2-22-22-222-2-220000000022-2-200000000i2−i2−i2i2i2−i2−i2i200000000
χ3022-2-2-22-22-222-2-220000000022-2-200000000−i2i2i2−i2−i2i2i2−i200000000
χ3122-2-2-22-22-222-2-2200000000-2-222000000002−2−22−222−200000000
χ3222-2-2-22-22-222-2-2200000000-2-22200000000−222−22−2−2200000000
χ3322-2-2-22-22-22-222-22i−2i−2i2i0000000000000000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i
χ3422-2-2-22-22-22-222-22i−2i−2i2i000000000000000000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i
χ3522-2-2-22-22-22-222-2−2i2i2i−2i0000000000000000000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i
χ3622-2-2-22-22-22-222-2−2i2i2i−2i000000000000000000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i
χ374444444444-4-4-4-4000000000000000000000000000000000000
χ384444-4-44-4-44000000000000000000002i−2i2i−2i0000000000000000
χ394444-4-44-4-4400000000000000000000−2i2i−2i2i0000000000000000
χ404444-4-4-444-400000000000000002i−2i2i−2i00000000000000000000
χ414444-4-4-444-40000000000000000−2i2i−2i2i00000000000000000000
χ4244-4-44-444-4-4000000000000000000002-2-220000000000000000
χ4344-4-44-444-4-400000000000000000000-222-20000000000000000
χ4444-4-44-4-4-44400000000000000002i−2i−2i2i00000000000000000000
χ4544-4-44-4-4-4440000000000000000−2i2i2i−2i00000000000000000000
χ4644-4-4-444-44-4-44-44000000000000000000000000000000000000
χ478-88-8000000000000002i2−2i22i2−2i20000000000000000000000000000
χ488-88-800000000000000−2i22i2−2i22i20000000000000000000000000000
χ498-8-88000000000000002i2−2i2−2i22i20000000000000000000000000000
χ508-8-8800000000000000−2i22i22i2−2i20000000000000000000000000000

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