Finite Group Databasebeta

← Group #98685

Character table — Group #98685

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222244444444444488888888888888888888161616161616161616161616161616161616
order12222222444444444444444422444444444488888888224444888888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111
χ5111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-11111
χ6111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ7111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111
χ911111111-1-1-1-1-1111111-1-1-1-1-111-1-111-1-1-1-1-1-1iiii−i−i−i−i111-1-11ii−i−iii−i−iii−i−i
χ1011111111-1-1-1-1-1111111-1-1-1-1-111-1-111-1-1-1-1-1-1−i−i−i−iiiii111-1-11−i−iii−i−iii−i−iii
χ1111111111-1-1-1-1-1111111-1-1-1-1-111-1-1-1-1111111iiii−i−i−i−i-1-11-11-1−i−iiiii−i−i−i−iii
χ1211111111-1-1-1-1-1111111-1-1-1-1-111-1-1-1-1111111−i−i−i−iiiii-1-11-11-1ii−i−i−i−iiiii−i−i
χ1311111111-1-1-1-1-1111111-1-1-1-1-1-1-11111-1-11111iiii−i−i−i−i-1-1-11-11−i−iii−i−iiiii−i−i
χ1411111111-1-1-1-1-1111111-1-1-1-1-1-1-11111-1-11111−i−i−i−iiiii-1-1-11-11ii−i−iii−i−i−i−iii
χ1511111111-1-1-1-1-1111111-1-1-1-1-1-1-111-1-111-1-1-1-1iiii−i−i−i−i11-111-1ii−i−i−i−iii−i−iii
χ1611111111-1-1-1-1-1111111-1-1-1-1-1-1-111-1-111-1-1-1-1−i−i−i−iiiii11-111-1−i−iiiii−i−iii−i−i
χ17222222222222222-2-2-2-2-2-2-22-20000000022-2-2000000002-20000000000000000
χ18222222222222222-2-2-2-2-2-2-22-200000000-2-22200000000-220000000000000000
χ19222222222222-2-2-222-2-22-2-2-222222000000000000000000-2-200000000000000
χ20222222222222-2-2-222-2-22-2-2-22-2-2-2-20000000000000000002200000000000000
χ21222222222222-2-2-2-2-222-222-2-2000022220000000000000000-2-2000000000000
χ22222222222222-2-2-2-2-222-222-2-20000-2-2-2-2000000000000000022000000000000
χ2322222222-2-2-2-22-2-222-2-2-2222-222-2-2000000000000000000-2200000000000000
χ2422222222-2-2-2-22-2-222-2-2-2222-2-2-2220000000000000000002-200000000000000
χ2522222222-2-2-2-22-2-2-2-2222-2-222000022-2-200000000000000002-2000000000000
χ2622222222-2-2-2-22-2-2-2-2222-2-2220000-2-2220000000000000000-22000000000000
χ2722222222-2-2-2-2-222-2-2-2-2222-220000000022-2-200000000-220000000000000000
χ2822222222-2-2-2-2-222-2-2-2-2222-2200000000-2-222000000002-20000000000000000
χ2922-22-2-22-22i−2i2i−2i000002-202i−2i0000002-22i−2i00001+i1+i−1−i−1−i1−i1−i−1+i−1+i000000000000001+i−1−i1−i−1+i
χ3022-22-2-22-22i−2i2i−2i000002-202i−2i0000002-22i−2i0000−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000000000−1−i1+i−1+i1−i
χ3122-22-2-22-22i−2i2i−2i000002-202i−2i000000-22−2i2i00001+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000000000−1−i1+i−1+i1−i
χ3222-22-2-22-22i−2i2i−2i000002-202i−2i000000-22−2i2i0000−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000000000001+i−1−i1−i−1+i
χ3322-22-2-22-2−2i2i−2i2i000002-20−2i2i0000002-2−2i2i00001−i1−i−1+i−1+i1+i1+i−1−i−1−i000000000000001−i−1+i1+i−1−i
χ3422-22-2-22-2−2i2i−2i2i000002-20−2i2i0000002-2−2i2i0000−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000000000−1+i1−i−1−i1+i
χ3522-22-2-22-2−2i2i−2i2i000002-20−2i2i000000-222i−2i00001−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000000000−1+i1−i−1−i1+i
χ3622-22-2-22-2−2i2i−2i2i000002-20−2i2i000000-222i−2i0000−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000000000001−i−1+i1+i−1−i
χ372-2-2-22-22222-2-20002-2002000-22-22-200000000i2−i2i2−i2i2−i2i2−i20000000000i2−i2i2−i20000
χ382-2-2-22-22222-2-20002-2002000-22-22-200000000−i2i2−i2i2−i2i2−i2i20000000000−i2i2−i2i20000
χ392-2-2-22-22222-2-20002-2002000-2-22-2200000000i2−i2i2−i2i2−i2i2−i20000000000−i2i2−i2i20000
χ402-2-2-22-22222-2-20002-2002000-2-22-2200000000−i2i2−i2i2−i2i2−i2i20000000000i2−i2i2−i20000
χ412-2-2-22-222-2-2220002-200-200022-2-22000000002−22−2−22−2200000000002−2−220000
χ422-2-2-22-222-2-2220002-200-200022-2-2200000000−22−222−22−20000000000−222−20000
χ432-2-2-22-222-2-2220002-200-20002-222-2000000002−22−2−22−220000000000−222−20000
χ442-2-2-22-222-2-2220002-200-20002-222-200000000−22−222−22−200000000002−2−220000
χ4544-44-4-44-44i−4i4i−4i00000-440−4i4i0000000000000000000000000000000000000000
χ4644-44-4-44-4−4i4i−4i4i00000-4404i−4i0000000000000000000000000000000000000000
χ4744-4-4-44-4400004000000000-40000000000000000000000000002i−2i2i−2i00000000
χ4844-4-4-44-4400004000000000-4000000000000000000000000000−2i2i−2i2i00000000
χ4944-4-4-44-440000-400000000040000000000000000000000000002-2-2200000000
χ5044-4-4-44-440000-40000000004000000000000000000000000000-222-200000000
χ514-44-4-444-44i−4i−4i4i0000000000000000000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ000000000000000000
χ524-44-4-444-44i−4i−4i4i000000000000000000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ000000000000000000
χ534-44-4-444-4−4i4i4i−4i0000000000000000000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ3000000000000000000
χ544-44-4-444-4−4i4i4i−4i000000000000000000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ3000000000000000000
χ554-4-4444-4-4000004-400000000000000000004i−4i00000000000000000000000000
χ564-4-4444-4-4000004-40000000000000000000−4i4i00000000000000000000000000
χ574-4-4444-4-400000-44000000000000000004i−4i0000000000000000000000000000
χ584-4-4444-4-400000-4400000000000000000−4i4i0000000000000000000000000000
χ594-4-4-44-44444-4-4000-4400-4000400000000000000000000000000000000000000
χ604-4-4-44-444-4-444000-44004000-400000000000000000000000000000000000000
χ61888-88-8-8-8000000000000000000000000000000000000000000000000000000
χ628-888-8-8-88000000000000000000000000000000000000000000000000000000

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