Finite Group Databasebeta

← Group #171914

Character table — Group #171914

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222244444444444488888888888888888888161616161616161616161616161616161616
order12222222444444444444444422444444444488888888444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-111111111-111-1-1-11111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-111-1-111-1-1111111111-1-1-1-11-1-1-1-1-1-1-1-11111
χ6111111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11-1-1-1-1111111111-1-1-1-1
χ7111111111111111111111111-1-1-1-1-1-111-1-11111111111-1-1-111-1-1-1-1-11111-1-1-1-1
χ8111111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-111-11111-1-1-1-11111
χ911111111-1-1-1-11-1-1-1-1-1-11111111-1-11111-1-1-1-11111-1-1-1-111-11-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-11-1-1-1-1-1-11111111-1-11111-1-1-1-1-1-1-1-1111111-11-1-1-1-111-1-111-1-111
χ1111111111-1-1-1-11-1-1-1-1-1-11111111-1-1-1-1-1-111111111-1-1-1-1-11-1-11111-1-1-1-111-1-111
χ1211111111-1-1-1-11-1-1-1-1-1-11111111-1-1-1-1-1-11111-1-1-1-11111-11-1-111-1-11111-1-111-1-1
χ1311111111-1-1-1-11-1-1-1-1-1-111111-1-11111-1-1-1-1111111-1-1-1-11-11-11-1-1-111-1-11111-1-1
χ1411111111-1-1-1-11-1-1-1-1-1-111111-1-11111-1-1-1-111-1-1-1-111111-11-11-111-1-111-1-1-1-111
χ1511111111-1-1-1-11-1-1-1-1-1-111111-1-111-1-11111-1-11111-1-1-1-1-1-111-11-1-11111-1-1-1-111
χ1611111111-1-1-1-11-1-1-1-1-1-111111-1-111-1-11111-1-1-1-1-1-11111-1-111-1111-1-1-1-11111-1-1
χ172222222222222-2-222-2-2-2-2-22-200000022002200000000000-2-20000000000000
χ182222222222222-2-222-2-2-2-2-22-2000000-2-200-2-200000000000220000000000000
χ19222222222222-222-2-2-2-2-222-2-200002200220000000000-20000-2000000000000
χ20222222222222-222-2-2-2-2-222-2-20000-2-200-2-20000000000200002000000000000
χ21222222222222-2-2-2-2-2222-2-2-2222-2-200000000000000000-22000000000000000
χ22222222222222-2-2-2-2-2222-2-2-22-2-222000000000000000002-2000000000000000
χ2322222222-2-2-2-2222-2-222-2-2-22-20000002200-2-200000000000-220000000000000
χ2422222222-2-2-2-2222-2-222-2-2-22-2000000-2-20022000000000002-20000000000000
χ2522222222-2-2-2-2-22222-2-22-2-2-22222200000000000000000-2-2000000000000000
χ2622222222-2-2-2-2-22222-2-22-2-2-22-2-2-2-20000000000000000022000000000000000
χ2722222222-2-2-2-2-2-2-22222-222-2-200002200-2-20000000000-200002000000000000
χ2822222222-2-2-2-2-2-2-22222-222-2-20000-2-20022000000000020000-2000000000000
χ2922-222-2-2-222-2-2-2002-200000200000002i−2i002i−2ii2i2−i2−i2i2i2−i2−i200000000002−22−20000
χ3022-222-2-2-222-2-2-2002-200000200000002i−2i002i−2i−i2−i2i2i2−i2−i2i2i20000000000−22−220000
χ3122-222-2-2-222-2-2-2002-20000020000000−2i2i00−2i2ii2i2−i2−i2i2i2−i2−i20000000000−22−220000
χ3222-222-2-2-222-2-2-2002-20000020000000−2i2i00−2i2i−i2−i2i2i2−i2−i2i2i200000000002−22−20000
χ3322-222-2-2-2-2-222-200-2200000200000002i−2i00−2i2ii2i2−i2−i2−i2−i2i2i200000000002−2−220000
χ3422-222-2-2-2-2-222-200-2200000200000002i−2i00−2i2i−i2−i2i2i2i2i2−i2−i20000000000−222−20000
χ3522-222-2-2-2-2-222-200-220000020000000−2i2i002i−2ii2i2−i2−i2−i2−i2i2i20000000000−222−20000
χ3622-222-2-2-2-2-222-200-220000020000000−2i2i002i−2i−i2−i2i2i2i2i2−i2−i200000000002−2−220000
χ372-2-22-222-22i−2i2i−2i02i−2i000002-20000002-2002i−2i002−22−2i2−i2i2−i2000000000000002−2i2−i2
χ382-2-22-222-22i−2i2i−2i02i−2i000002-20000002-2002i−2i00−22−22−i2i2−i2i200000000000000−22−i2i2
χ392-2-22-222-22i−2i2i−2i02i−2i000002-2000000-2200−2i2i002−22−2i2−i2i2−i200000000000000−22−i2i2
χ402-2-22-222-22i−2i2i−2i02i−2i000002-2000000-2200−2i2i00−22−22−i2i2−i2i2000000000000002−2i2−i2
χ412-2-22-222-2−2i2i−2i2i0−2i2i000002-20000002-200−2i2i002−22−2−i2i2−i2i2000000000000002−2−i2i2
χ422-2-22-222-2−2i2i−2i2i0−2i2i000002-20000002-200−2i2i00−22−22i2−i2i2−i200000000000000−22i2−i2
χ432-2-22-222-2−2i2i−2i2i0−2i2i000002-2000000-22002i−2i002−22−2−i2i2−i2i200000000000000−22i2−i2
χ442-2-22-222-2−2i2i−2i2i0−2i2i000002-2000000-22002i−2i00−22−22i2−i2i2−i2000000000000002−2−i2i2
χ4544-444-4-4-444-4-4400-4400000-4000000000000000000000000000000000000000
χ4644-444-4-4-4-4-4444004-400000-4000000000000000000000000000000000000000
χ4744-4-4-44-440000000004i−4i00000000000000000000000000000002i−2i2-200000000
χ4844-4-4-44-440000000004i−4i0000000000000000000000000000000−2i2i-2200000000
χ4944-4-4-44-44000000000−4i4i00000000000000000000000000000002i−2i-2200000000
χ5044-4-4-44-44000000000−4i4i0000000000000000000000000000000−2i2i2-200000000
χ514-444-4-4-444i−4i−4i4i0000000000000000000000002i−2i−2i2i-222-2000000000000000000
χ524-444-4-4-444i−4i−4i4i000000000000000000000000−2i2i2i−2i2-2-22000000000000000000
χ534-444-4-4-44−4i4i4i−4i0000000000000000000000002i−2i−2i2i2-2-22000000000000000000
χ544-444-4-4-44−4i4i4i−4i000000000000000000000000−2i2i2i−2i-222-2000000000000000000
χ554-4-44-444-44i−4i4i−4i0−4i4i00000-440000000000000000000000000000000000000000
χ564-4-44-444-4−4i4i−4i4i04i−4i00000-440000000000000000000000000000000000000000
χ574-4-4-44-444000000000004000-4004i−4i0000000000000000000000000000000000
χ584-4-4-44-444000000000004000-400−4i4i0000000000000000000000000000000000
χ594-4-4-44-44400000000000-400044-4000000000000000000000000000000000000
χ604-4-4-44-44400000000000-40004-44000000000000000000000000000000000000
χ61888-8-8-88-8000000000000000000000000000000000000000000000000000000
χ628-88-888-8-8000000000000000000000000000000000000000000000000000000

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