Finite Group Databasebeta

← Group #171920

Character table — Group #171920

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222244444444444488888888888888888888161616161616161616161616161616161616
order12222222444444444444444444444444444488888888444444444488888888
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
χ5111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1
χ911111111-1-1-1-1-1-11-1-11-1-1111111-1-111-1-111-1-11111-1-1-1-11-11-11-111-1-111-1-111-1-1
χ1011111111-1-1-1-1-1-11-1-11-1-1111111-1-111-1-111-1-1-1-1-1-111111-11-11-1-1-111-1-111-1-111
χ1111111111-1-1-1-1-1-11-1-11-1-1111111-1-1-1-111-1-1111111-1-1-1-11-1-11-1111-1-1-1-111-1-111
χ1211111111-1-1-1-1-1-11-1-11-1-1111111-1-1-1-111-1-111-1-1-1-111111-1-11-11-1-11111-1-111-1-1
χ1311111111-1-1-1-1-1-11-1-11-1-11111-1-11111-1-1-1-1111111-1-1-1-1-11-111-1-1-11111-1-1-1-111
χ1411111111-1-1-1-1-1-11-1-11-1-11111-1-11111-1-1-1-111-1-1-1-11111-11-111-111-1-1-1-11111-1-1
χ1511111111-1-1-1-1-1-11-1-11-1-11111-1-111-1-11111-1-11111-1-1-1-1-111-1-11-1-111-1-11111-1-1
χ1611111111-1-1-1-1-1-11-1-11-1-11111-1-111-1-11111-1-1-1-1-1-11111-111-1-1111-1-111-1-1-1-111
χ1722222222222222-2-2-2-2-2-222-2-222-2-20000000000000000-220000000000000000
χ1822222222222222-2-2-2-2-2-222-2-2-2-22200000000000000002-20000000000000000
χ19222222222222-2-2222-2-2-2-2-22-20000000022220000000000-2-200000000000000
χ20222222222222-2-2222-2-2-2-2-22-200000000-2-2-2-200000000002200000000000000
χ21222222222222-2-2-2-2-2222-2-2-22000022220000000000000000-2-2000000000000
χ22222222222222-2-2-2-2-2222-2-2-220000-2-2-2-2000000000000000022000000000000
χ2322222222-2-2-2-2222-2-2-222-2-22-20000000022-2-20000000000-2200000000000000
χ2422222222-2-2-2-2222-2-2-222-2-22-200000000-2-22200000000002-200000000000000
χ2522222222-2-2-2-222-2222-2-2-2-2-22000022-2-20000000000000000-22000000000000
χ2622222222-2-2-2-222-2222-2-2-2-2-220000-2-22200000000000000002-2000000000000
χ2722222222-2-2-2-2-2-2-222-22222-2-222220000000000000000-2-20000000000000000
χ2822222222-2-2-2-2-2-2-222-22222-2-2-2-2-2-20000000000000000220000000000000000
χ292-2222-2-2-222-2-200-22-20000020000000002i−2i2i−2ii2i2−i2−i2i2i2−i2−i2000000000000002−22−2
χ302-2222-2-2-222-2-200-22-20000020000000002i−2i2i−2i−i2−i2i2i2−i2−i2i2i200000000000000−22−22
χ312-2222-2-2-222-2-200-22-2000002000000000−2i2i−2i2ii2i2−i2−i2i2i2−i2−i200000000000000−22−22
χ322-2222-2-2-222-2-200-22-2000002000000000−2i2i−2i2i−i2−i2i2i2−i2−i2i2i2000000000000002−22−2
χ332-2222-2-2-2-2-22200-2-220000020000000002i−2i−2i2ii2i2−i2−i2−i2−i2i2i2000000000000002−2−22
χ342-2222-2-2-2-2-22200-2-220000020000000002i−2i−2i2i−i2−i2i2i2i2i2−i2−i200000000000000−222−2
χ352-2222-2-2-2-2-22200-2-22000002000000000−2i2i2i−2ii2i2−i2−i2−i2−i2i2i200000000000000−222−2
χ362-2222-2-2-2-2-22200-2-22000002000000000−2i2i2i−2i−i2−i2i2i2i2i2−i2−i2000000000000002−2−22
χ372-22-2-2-2222-22-20000022-2000-200002i−2i2i−2i0000i2−i2i2−i2i2−i2i2−i200000000002−22−20000
χ382-22-2-2-2222-22-20000022-2000-200002i−2i2i−2i0000−i2i2−i2i2−i2i2−i2i20000000000−22−220000
χ392-22-2-2-2222-22-20000022-2000-20000−2i2i−2i2i0000i2−i2i2−i2i2−i2i2−i20000000000−22−220000
χ402-22-2-2-2222-22-20000022-2000-20000−2i2i−2i2i0000−i2i2−i2i2−i2i2−i2i200000000002−22−20000
χ412-22-2-2-222-22-22000002-22000-200002i−2i−2i2i0000i2−i2i2−i2−i2i2−i2i200000000002−2−220000
χ422-22-2-2-222-22-22000002-22000-200002i−2i−2i2i0000−i2i2−i2i2i2−i2i2−i20000000000−222−20000
χ432-22-2-2-222-22-22000002-22000-20000−2i2i2i−2i0000i2−i2i2−i2−i2i2−i2i20000000000−222−20000
χ442-22-2-2-222-22-22000002-22000-20000−2i2i2i−2i0000−i2i2−i2i2i2−i2i2−i200000000002−2−220000
χ45444-4-44-4-44-4-440000000000000000000000002-2-222-2-22000000000000000000
χ46444-4-44-4-44-4-44000000000000000000000000-222-2-222-2000000000000000000
χ47444-4-44-4-4-444-40000000000000000000000002-2-22-222-2000000000000000000
χ48444-4-44-4-4-444-4000000000000000000000000-222-22-2-22000000000000000000
χ494-4444-4-4-444-4-4004-4400000-4000000000000000000000000000000000000000
χ504-4444-4-4-4-4-4440044-400000-4000000000000000000000000000000000000000
χ514-44-4-4-4444-44-400000-4-44000400000000000000000000000000000000000000
χ524-44-4-4-444-44-4400000-44-4000400000000000000000000000000000000000000
χ534-4-44-444-40000000000004-400004i−4i0000000000000000000000000000000000
χ544-4-44-444-40000000000004-40000−4i4i0000000000000000000000000000000000
χ554-4-44-444-4000000000000-44004i−4i000000000000000000000000000000000000
χ564-4-44-444-4000000000000-4400−4i4i000000000000000000000000000000000000
χ574-4-4-444-4400004i−4i0000000000000000000000000000000000002i−2i2-200000000
χ584-4-4-444-4400004i−4i000000000000000000000000000000000000−2i2i-2200000000
χ594-4-4-444-440000−4i4i0000000000000000000000000000000000002i−2i-2200000000
χ604-4-4-444-440000−4i4i000000000000000000000000000000000000−2i2i2-200000000
χ6188-88-8-8-88000000000000000000000000000000000000000000000000000000
χ6288-8-88-88-8000000000000000000000000000000000000000000000000000000

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