Finite Group Databasebeta

← Group #149484

Character table — Group #149484

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222244444444444488888888888888888888161616161616161616161616161616161616
order12224444224422222244444444444444444488888888444444444444444444
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ91111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1iiii−i−i−i−i1-11-11-1ii−i−iii−i−iii−i−i
χ101111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1−i−i−i−iiiii1-11-11-1−i−iii−i−iii−i−iii
χ111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111iiii−i−i−i−i1-1-11-11ii−i−i−i−iii−i−iii
χ121111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111−i−i−i−iiiii1-1-11-11−i−iiiii−i−iii−i−i
χ131111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-111iiii−i−i−i−i-111-1-11−i−iiiii−i−i−i−iii
χ141111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-111−i−i−i−iiiii-111-1-11ii−i−i−i−iiiii−i−i
χ151111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1iiii−i−i−i−i-11-111-1−i−iii−i−iiiii−i−i
χ161111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1−i−i−i−iiiii-11-111-1ii−i−iii−i−i−i−iii
χ172222222222222-2-22-2-222-2-2-2-2000000002222000000000000-2-2000000000000
χ182222222222222-2-22-2-222-2-2-2-200000000-2-2-2-200000000000022000000000000
χ19222222222222-22-2-22-2-2-222-2-20000222200000000000000-2-200000000000000
χ20222222222222-22-2-22-2-2-222-2-20000-2-2-2-2000000000000002200000000000000
χ21222222222222-2-22-2-22-2-2-2-22222220000000000000000-2-20000000000000000
χ22222222222222-2-22-2-22-2-2-2-222-2-2-2-20000000000000000220000000000000000
χ232222-2-2-2-222-2-222-222-2-2-2-2-22222-2-20000000000000000-220000000000000000
χ242222-2-2-2-222-2-222-222-2-2-2-2-222-2-22200000000000000002-20000000000000000
χ252222-2-2-2-222-2-22-222-22-2-222-2-2000022-2-200000000000000-2200000000000000
χ262222-2-2-2-222-2-22-222-22-2-222-2-20000-2-222000000000000002-200000000000000
χ272222-2-2-2-222-2-2-222-22222-2-2-2-20000000022-2-2000000000000-22000000000000
χ282222-2-2-2-222-2-2-222-22222-2-2-2-200000000-2-2220000000000002-2000000000000
χ2922-2-222-2-22-22-222-2-2-222-22-22-2000000000000000000000000002-22-200000000
χ3022-2-222-2-22-22-222-2-2-222-22-22-200000000000000000000000000-22-2200000000
χ3122-2-222-2-22-22-22-22-22-22-2-22-220000000000000000000000000000002-22-20000
χ3222-2-222-2-22-22-22-22-22-22-2-22-22000000000000000000000000000000-22-220000
χ3322-2-222-2-22-22-2-2222-2-2-222-2-2200000000000000000000000000000000002-22-2
χ3422-2-222-2-22-22-2-2222-2-2-222-2-220000000000000000000000000000000000-22-22
χ3522-2-222-2-22-22-2-2-2-2222-22-222-20000000000002i2i−2i−2i2i2i−2i−2i000000000000000000
χ3622-2-222-2-22-22-2-2-2-2222-22-222-2000000000000−2i−2i2i2i−2i−2i2i2i000000000000000000
χ3722-2-2-2-2222-2-22222-2-2-2-22-222-200000000000022-2-2-2-222000000000000000000
χ3822-2-2-2-2222-2-22222-2-2-2-22-222-2000000000000-2-22222-2-2000000000000000000
χ3922-2-2-2-2222-2-222-2-2-222-222-2-2200000000000000000000000000000000002i−2i−2i2i
χ4022-2-2-2-2222-2-222-2-2-222-222-2-220000000000000000000000000000000000−2i2i2i−2i
χ4122-2-2-2-2222-2-22-22-22-222-2-22-220000000000000000000000000000002i−2i−2i2i0000
χ4222-2-2-2-2222-2-22-22-22-222-2-22-22000000000000000000000000000000−2i2i2i−2i0000
χ4322-2-2-2-2222-2-22-2-2222-22-22-22-2000000000000000000000000002i−2i−2i2i00000000
χ4422-2-2-2-2222-2-22-2-2222-22-22-22-200000000000000000000000000−2i2i2i−2i00000000
χ4544444444-4-4-4-40000000000000000000000002-22-22-22-2000000000000000000
χ4644444444-4-4-4-4000000000000000000000000-22-22-22-22000000000000000000
χ474444-4-4-4-4-4-4440000000000000000000000002i−2i2i−2i−2i2i−2i2i000000000000000000
χ484444-4-4-4-4-4-444000000000000000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000
χ4944-4-444-4-4-44-440000000000000000000000002i−2i−2i2i2i−2i−2i2i000000000000000000
χ5044-4-444-4-4-44-44000000000000000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000
χ5144-4-4-4-444-444-40000000000000000000000002-2-22-222-2000000000000000000
χ5244-4-4-4-444-444-4000000000000000000000000-222-22-2-22000000000000000000
χ534-44-44i−4i4i−4i00000000000000002-22i−2i2-22i−2i2-22i−2i00000000000000000000000000
χ544-44-44i−4i4i−4i00000000000000002-22i−2i-22−2i2i-22−2i2i00000000000000000000000000
χ554-44-44i−4i4i−4i0000000000000000-22−2i2i2-22i−2i-22−2i2i00000000000000000000000000
χ564-44-44i−4i4i−4i0000000000000000-22−2i2i-22−2i2i2-22i−2i00000000000000000000000000
χ574-44-4−4i4i−4i4i00000000000000002-2−2i2i2-2−2i2i2-2−2i2i00000000000000000000000000
χ584-44-4−4i4i−4i4i00000000000000002-2−2i2i-222i−2i-222i−2i00000000000000000000000000
χ594-44-4−4i4i−4i4i0000000000000000-222i−2i2-2−2i2i-222i−2i00000000000000000000000000
χ604-44-4−4i4i−4i4i0000000000000000-222i−2i-222i−2i2-2−2i2i00000000000000000000000000
χ618-8-888i−8i−8i8i000000000000000000000000000000000000000000000000000000
χ628-8-88−8i8i8i−8i000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).