Finite Group Databasebeta

← Group #422293

Character table — Group #422293

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222222224444444488888888888888888888888816161616161616161616161616161616
order12222222222244444444444488882222444444444488888888882224448888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-11111111111-1-1-1-111-111-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1111111-1-1-1-11111111111-1-11-1-11-1-1-1-111-1-1-1-1
χ41111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-11111
χ5111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111
χ7111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-111-1111111-1-1-1-1
χ911111111111111111111-1-1-1-111111111-1-11111-1-1-1-111-1-1-1-11111-1-1-111-111-1-1-1-111-1-1
χ1011111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111
χ1111111111111111111111-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111
χ1211111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111-1-1111-1-11111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-111-1-111
χ1411111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-11-1-111-1-111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-111-1-1-1111111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1111111-1-1-1-1-1-111
χ17222222222222-2-2-2-2-2-2-2-2222200000000-2-2000000000000002i2i−2i−2i00000000002i−2i0000
χ18222222222222-2-2-2-2-2-2-2-2222200000000-2-200000000000000−2i−2i2i2i0000000000−2i2i0000
χ19222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000022000000000000002i2i−2i−2i0000000000−2i2i0000
χ20222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000002200000000000000−2i−2i2i2i00000000002i−2i0000
χ2122222222-2-2-2-22-222-2-22-222-2-2000000002-222-2-20000000000000000200-20000000000
χ2222222222-2-2-2-22-222-2-22-222-2-2000000002-2-2-2220000000000000000-20020000000000
χ2322222222-2-2-2-22-222-2-22-2-2-22200000000-2222-2-20000000000000000-20020000000000
χ2422222222-2-2-2-22-222-2-22-2-2-22200000000-22-2-2220000000000000000200-20000000000
χ2522222222-2-2-2-2-22-2-222-2222-2-222220000-2200000000-2-222-2-200000000000000000000
χ2622222222-2-2-2-2-22-2-222-2222-2-2-2-2-2-20000-220000000022-2-22200000000000000000000
χ2722222222-2-2-2-2-22-2-222-22-2-222222200002-200000000-2-2-2-22200000000000000000000
χ2822222222-2-2-2-2-22-2-222-22-2-222-2-2-2-200002-2000000002222-2-200000000000000000000
χ2922-2-2-222-222-2-2222-2-2-2-22000000000000002i−2i2i−2i2i2i−2i−2i0000000000000000002-2000000
χ3022-2-2-222-222-2-2222-2-2-2-22000000000000002i−2i2i−2i−2i−2i2i2i000000000000000000-22000000
χ3122-2-2-222-222-2-2222-2-2-2-2200000000000000−2i2i−2i2i2i2i−2i−2i000000000000000000-22000000
χ3222-2-2-222-222-2-2222-2-2-2-2200000000000000−2i2i−2i2i−2i−2i2i2i0000000000000000002-2000000
χ3322-2-2-222-2-2-2222-22-222-2-20000000022-2-2002i−2i−2i2i000000000000000000002i−2i00000000
χ3422-2-2-222-2-2-2222-22-222-2-20000000022-2-200−2i2i2i−2i00000000000000000000−2i2i00000000
χ3522-2-2-222-2-2-2222-22-222-2-200000000-2-222002i−2i−2i2i00000000000000000000−2i2i00000000
χ3622-2-2-222-2-2-2222-22-222-2-200000000-2-22200−2i2i2i−2i000000000000000000002i−2i00000000
χ372-222-22-2-22-22-222-2-22-22-200002i2i−2i−2i00000000002i−2i2i−2i2i−2i000000002-200000000000000
χ382-222-22-2-22-22-222-2-22-22-200002i2i−2i−2i0000000000−2i2i−2i2i2i−2i00000000-2200000000000000
χ392-222-22-2-22-22-222-2-22-22-20000−2i−2i2i2i00000000002i−2i2i−2i−2i2i00000000-2200000000000000
χ402-222-22-2-22-22-222-2-22-22-20000−2i−2i2i2i0000000000−2i2i−2i2i−2i2i000000002-200000000000000
χ412-222-22-2-2-22-22-22222-2-2-200002i2i−2i−2i2-22-20000000000−2i2i000000000002i−2i00000000000
χ422-222-22-2-2-22-22-22222-2-2-200002i2i−2i−2i-22-220000000000−2i2i00000000000−2i2i00000000000
χ432-222-22-2-2-22-22-22222-2-2-20000−2i−2i2i2i2-22-200000000002i−2i00000000000−2i2i00000000000
χ442-222-22-2-2-22-22-22222-2-2-20000−2i−2i2i2i-22-2200000000002i−2i000000000002i−2i00000000000
χ452-2-2-222-222-2-2222-22-22-2-20000000000000000002-2-220000002i−2i2i−2i000000000000002i−2i
χ462-2-2-222-222-2-2222-22-22-2-20000000000000000002-2-22000000−2i2i−2i2i00000000000000−2i2i
χ472-2-2-222-222-2-2222-22-22-2-2000000000000000000-222-20000002i−2i2i−2i00000000000000−2i2i
χ482-2-2-222-222-2-2222-22-22-2-2000000000000000000-222-2000000−2i2i−2i2i000000000000002i−2i
χ492-2-2-222-222-2-22-2-22-22-222000000002-2-2200000000000000002-2-220000000000002-200
χ502-2-2-222-222-2-22-2-22-22-222000000002-2-220000000000000000-222-2000000000000-2200
χ512-2-2-222-222-2-22-2-22-22-22200000000-222-200000000000000002-2-22000000000000-2200
χ522-2-2-222-222-2-22-2-22-22-22200000000-222-20000000000000000-222-20000000000002-200
χ53444-44-4-4-4000000000000004i−4i2i2−2i22i2−2i200000000000000000022−2200000000000000000000
χ54444-44-4-4-4000000000000004i−4i−2i22i2−2i22i2000000000000000000−222200000000000000000000
χ55444-44-4-4-400000000000000−4i4i2i2−2i22i2−2i2000000000000000000−222200000000000000000000
χ56444-44-4-4-400000000000000−4i4i−2i22i2−2i22i200000000000000000022−2200000000000000000000
χ5744-4-4-444-444-4-4-4-4-44444-4000000000000000000000000000000000000000000000000
χ5844-4-4-444-4-4-444-44-44-4-444000000000000000000000000000000000000000000000000
χ594-444-44-4-44-44-4-4-444-44-44000000000000000000000000000000000000000000000000
χ604-444-44-4-4-44-444-4-4-4-4444000000000000000000000000000000000000000000000000
χ614-44-4-4-4440000000000004-40022−22−2222000000000000000022−220000000000000000000000
χ624-44-4-4-4440000000000004-400−222222−220000000000000000−22220000000000000000000000
χ634-44-4-4-444000000000000-440022−22−22220000000000000000−22220000000000000000000000
χ644-44-4-4-444000000000000-4400−222222−22000000000000000022−220000000000000000000000
χ654-4-4-444-44-444-44-4-444-4-44000000000000000000000000000000000000000000000000
χ664-4-4-444-44-444-4-444-4-444-4000000000000000000000000000000000000000000000000
χ6788-88-8-8-88000000000000000000000000000000000000000000000000000000000000
χ688-8-888-88-8000000000000000000000000000000000000000000000000000000000000

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