Finite Group Databasebeta

← Group #172020

Character table — Group #172020

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222244444444444488888888888888888888161616161616161616161616161616161616
order12222222222244444444444444444444444488888888224444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-111-1-1-1-1-1-1111111111-1-1-11-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11-11111-1-1-1-11111
χ5111111111111111111111111-1-111-1-111-1-1-1-111111111-11-1-1-11-1-1-1-1-1-1-1-11111
χ6111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1111111111-1-1-1-1
χ7111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-111-1-11111-1-1-1-1-1-1-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111
χ911111111-1-1-1-111-1-1-1-11-1-11111111-1-1-1-1-1-1111111-1-1-1-1111-1-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-111-1-1-1-11-1-11111111-1-1-1-1-1-111-1-1-1-11111111-1-1-1-1-111-1-111-1-111
χ1111111111-1-1-1-111-1-1-1-11-1-111111-1-1-1-11111-1-11111-1-1-1-11-1-11-11-1-11111-1-1-1-111
χ1211111111-1-1-1-111-1-1-1-11-1-111111-1-1-1-11111-1-1-1-1-1-111111-1-11-1111-1-1-1-11111-1-1
χ1311111111-1-1-1-111-1-1-1-11-1-1111-1-11111-1-111-1-11111-1-1-1-1-11-111-1-1-111-1-11111-1-1
χ1411111111-1-1-1-111-1-1-1-11-1-1111-1-11111-1-111-1-1-1-1-1-11111-11-111-111-1-111-1-1-1-111
χ1511111111-1-1-1-111-1-1-1-11-1-1111-1-1-1-11111-1-1111111-1-1-1-1-1-11-11111-1-1-1-111-1-111
χ1611111111-1-1-1-111-1-1-1-11-1-1111-1-1-1-11111-1-111-1-1-1-11111-1-11-111-1-11111-1-111-1-1
χ172222222222222-222-2-2-2-2-22-2-2002200220000000000000-2000-2000000000000
χ182222222222222-222-2-2-2-2-22-2-200-2-200-2-2000000000000020002000000000000
χ19222222222222-22-2-222-2-2-2-22-222002200000000000000-2000-20000000000000
χ20222222222222-22-2-222-2-2-2-22-2-2-200-2-200000000000000200020000000000000
χ21222222222222-2-2-2-2-2-2222-2-220000000022-2-200000000002-200000000000000
χ22222222222222-2-2-2-2-2-2222-2-2200000000-2-2220000000000-2200000000000000
χ2322222222-2-2-2-22-2-2-222-2222-2-2002200-2-20000000000000-20002000000000000
χ2422222222-2-2-2-22-2-2-222-2222-2-200-2-2002200000000000002000-2000000000000
χ2522222222-2-2-2-2-2222-2-2-222-22-22200-2-200000000000000-200020000000000000
χ2622222222-2-2-2-2-2222-2-2-222-22-2-2-20022000000000000002000-20000000000000
χ2722222222-2-2-2-2-2-222222-2-2-2-220000000022220000000000-2-200000000000000
χ2822222222-2-2-2-2-2-222222-2-2-2-2200000000-2-2-2-200000000002200000000000000
χ2922-22-2-2-2222-2-202002-20000-202i−2i002i−2i000000i2i2−i2−i2i2i2−i2−i200000000002−22−20000
χ3022-22-2-2-2222-2-202002-20000-202i−2i002i−2i000000−i2−i2i2i2−i2−i2i2i20000000000−22−220000
χ3122-22-2-2-2222-2-202002-20000-20−2i2i00−2i2i000000i2i2−i2−i2i2i2−i2−i20000000000−22−220000
χ3222-22-2-2-2222-2-202002-20000-20−2i2i00−2i2i000000−i2−i2i2i2−i2−i2i2i200000000002−22−20000
χ3322-22-2-2-22-2-2220200-220000-202i−2i00−2i2i000000i2i2−i2−i2−i2−i2i2i200000000002−2−220000
χ3422-22-2-2-22-2-2220200-220000-202i−2i00−2i2i000000−i2−i2i2i2i2i2−i2−i20000000000−222−20000
χ3522-22-2-2-22-2-2220200-220000-20−2i2i002i−2i000000i2i2−i2−i2−i2−i2i2i20000000000−222−20000
χ3622-22-2-2-22-2-2220200-220000-20−2i2i002i−2i000000−i2−i2i2i2i2i2−i2−i200000000002−2−220000
χ372-22-22-2-222-22-2202-200000-200002i−2i002i−2i0000i2−i2i2−i2i2−i2i2−i2000000000000002−22−2
χ382-22-22-2-222-22-2202-200000-200002i−2i002i−2i0000−i2i2−i2i2−i2i2−i2i200000000000000−22−22
χ392-22-22-2-222-22-2202-200000-20000−2i2i00−2i2i0000i2−i2i2−i2i2−i2i2−i200000000000000−22−22
χ402-22-22-2-222-22-2202-200000-20000−2i2i00−2i2i0000−i2i2−i2i2−i2i2−i2i2000000000000002−22−2
χ412-22-22-2-22-22-2220-2200000-200002i−2i00−2i2i0000i2−i2i2−i2−i2i2−i2i2000000000000002−2−22
χ422-22-22-2-22-22-2220-2200000-200002i−2i00−2i2i0000−i2i2−i2i2i2−i2i2−i200000000000000−222−2
χ432-22-22-2-22-22-2220-2200000-20000−2i2i002i−2i0000i2−i2i2−i2−i2i2−i2i200000000000000−222−2
χ442-22-22-2-22-22-2220-2200000-20000−2i2i002i−2i0000−i2i2−i2i2i2−i2i2−i2000000000000002−2−22
χ45444-4-4-44-4000000000040000-400000000004-400000000000000000000000000
χ46444-4-4-44-4000000000040000-40000000000-4400000000000000000000000000
χ47444-4-4-44-40000000000-400004000000004i−4i0000000000000000000000000000
χ48444-4-4-44-40000000000-40000400000000−4i4i0000000000000000000000000000
χ4944-44-4-4-4444-4-40-400-4400004000000000000000000000000000000000000000
χ5044-44-4-4-44-4-4440-4004-400004000000000000000000000000000000000000000
χ514-44-44-4-444-44-4-40-440000040000000000000000000000000000000000000000
χ524-44-44-4-44-44-44-404-40000040000000000000000000000000000000000000000
χ534-4-444-44-4000000000004-4000000000000000000000000000002i−2i2i−2i00000000
χ544-4-444-44-4000000000004-400000000000000000000000000000−2i2i−2i2i00000000
χ554-4-444-44-400000000000-44000000000000000000000000000002i−2i−2i2i00000000
χ564-4-444-44-400000000000-4400000000000000000000000000000−2i2i2i−2i00000000
χ574-4-4-4-44444-4-440000000000000000000000002-2-222-2-22000000000000000000
χ584-4-4-4-44444-4-44000000000000000000000000-222-2-222-2000000000000000000
χ594-4-4-4-4444-444-40000000000000000000000002-2-22-222-2000000000000000000
χ604-4-4-4-4444-444-4000000000000000000000000-222-22-2-22000000000000000000
χ6188-8-888-8-8000000000000000000000000000000000000000000000000000000
χ628-888-88-8-8000000000000000000000000000000000000000000000000000000

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