Finite Group Databasebeta

← Group #450852

Character table — Group #450852

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222222222888888888888888888888888888888888888161616161616161616161616
order12222222222244444444444444444444444444444444444488888888444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1
χ31111111111111111111111111111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ5111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1
χ6111111111111111111111111-1-1-1-111-1-1111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ7111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-111-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1111111-1-1
χ911111111111111111111-1-1-1-11111111111-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111
χ1011111111111111111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1
χ1111111111111111111111-1-1-1-11111-1-111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ1211111111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-111
χ1311111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ1411111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-11111
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1111111
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111111111111111-1-1-1-1-1-1-1-1
χ1722222222-2-2-2-22-2222-2-2-2000022-2-22200-2-20000000000000022-2-20000000000000000
χ1822222222-2-2-2-22-2222-2-2-2000022-2-2-2-2002200000000000000-2-2220000000000000000
χ1922222222-2-2-2-22-2222-2-2-20000-2-2222200-2-200000000000000-2-2220000000000000000
χ2022222222-2-2-2-22-2222-2-2-20000-2-222-2-200220000000000000022-2-20000000000000000
χ2122222222-2-2-2-2-22-2-2-222222-2-200000022000000-2-200000000000022-2-2000000000000
χ2222222222-2-2-2-2-22-2-2-222222-2-2000000-2-200000022000000000000-2-222000000000000
χ2322222222-2-2-2-2-22-2-2-2222-2-22200000022000000-2-2000000000000-2-222000000000000
χ2422222222-2-2-2-2-22-2-2-2222-2-222000000-2-20000002200000000000022-2-2000000000000
χ252222-2-2-2-22-2-22-2-222-222-2000000000000002i2i−2i−2i002i2i−2i−2i22-2-200000000000000000000
χ262222-2-2-2-22-2-22-2-222-222-2000000000000002i2i−2i−2i00−2i−2i2i2i-2-22200000000000000000000
χ272222-2-2-2-22-2-22-2-222-222-200000000000000−2i−2i2i2i002i2i−2i−2i-2-22200000000000000000000
χ282222-2-2-2-22-2-22-2-222-222-200000000000000−2i−2i2i2i00−2i−2i2i2i22-2-200000000000000000000
χ2922-2-22-22-222-2-2-2-22-222-22000000002i−2i2i−2i2i−2i00002i−2i00000000000000002-20000000000
χ3022-2-22-22-222-2-2-2-22-222-22000000002i−2i−2i2i2i−2i0000−2i2i0000000000000000-220000000000
χ3122-2-22-22-222-2-2-2-22-222-2200000000−2i2i2i−2i−2i2i00002i−2i0000000000000000-220000000000
χ3222-2-22-22-222-2-2-2-22-222-2200000000−2i2i−2i2i−2i2i0000−2i2i00000000000000002-20000000000
χ3322-2-22-22-2-2-2222-2-22-22-2200000000002i−2i002-22-2−2i2i0000000000000000000000002i−2i00
χ3422-2-22-22-2-2-2222-2-22-22-2200000000002i−2i00-22-22−2i2i000000000000000000000000−2i2i00
χ3522-2-22-22-2-2-2222-2-22-22-220000000000−2i2i002-22-22i−2i000000000000000000000000−2i2i00
χ3622-2-22-22-2-2-2222-2-22-22-220000000000−2i2i00-22-222i−2i0000000000000000000000002i−2i00
χ3722-2-22-22-2-2-222-222-22-22-2000000002i−2i00−2i2i0000002-22-200000000000000000000002i−2i
χ3822-2-22-22-2-2-222-222-22-22-2000000002i−2i00−2i2i000000-22-220000000000000000000000−2i2i
χ3922-2-22-22-2-2-222-222-22-22-200000000−2i2i002i−2i0000002-22-20000000000000000000000−2i2i
χ4022-2-22-22-2-2-222-222-22-22-200000000−2i2i002i−2i000000-22-2200000000000000000000002i−2i
χ4122-2-2-22-222-22-2-2-2-222-2222i−2i2i−2i2i−2i2i−2i0000000000000000000000000000002-200000000
χ4222-2-2-22-222-22-2-2-2-222-2222i−2i2i−2i−2i2i−2i2i000000000000000000000000000000-2200000000
χ4322-2-2-22-222-22-2-2-2-222-222−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000-2200000000
χ4422-2-2-22-222-22-2-2-2-222-222−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000002-200000000
χ4522-2-2-22-22-22-222-22-2-2-2222i−2i−2i2i00000000000000002i−2i−2i2i0000000000000000002-20000
χ4622-2-2-22-22-22-222-22-2-2-2222i−2i−2i2i0000000000000000−2i2i2i−2i000000000000000000-220000
χ4722-2-2-22-22-22-222-22-2-2-222−2i2i2i−2i00000000000000002i−2i−2i2i000000000000000000-220000
χ4822-2-2-22-22-22-222-22-2-2-222−2i2i2i−2i0000000000000000−2i2i2i−2i0000000000000000002-20000
χ4922-2-2-22-22-22-22-22-2222-2-200002i−2i−2i2i0000002i−2i−2i2i00000000000000000000002-2000000
χ5022-2-2-22-22-22-22-22-2222-2-200002i−2i−2i2i000000−2i2i2i−2i0000000000000000000000-22000000
χ5122-2-2-22-22-22-22-22-2222-2-20000−2i2i2i−2i0000002i−2i−2i2i0000000000000000000000-22000000
χ5222-2-2-22-22-22-22-22-2222-2-20000−2i2i2i−2i000000−2i2i2i−2i00000000000000000000002-2000000
χ53444444444444-4-4-4-4-4-4-4-4000000000000000000000000000000000000000000000000
χ544444-4-4-4-44-4-4444-4-44-4-44000000000000000000000000000000000000000000000000
χ554444-4-4-4-4-444-44-4-4-4444-4000000000000000000000000000000000000000000000000
χ564444-4-4-4-4-444-4-4444-4-4-44000000000000000000000000000000000000000000000000
χ5744-4-44-44-444-4-444-44-4-44-4000000000000000000000000000000000000000000000000
χ5844-4-4-44-444-44-4444-4-44-4-4000000000000000000000000000000000000000000000000
χ594-44-44-4-440000000000000000000000000000000000002-22-22i2−2i2002i2−2i200000000000000
χ604-44-44-4-440000000000000000000000000000000000002-22-2−2i22i200−2i22i200000000000000
χ614-44-44-4-44000000000000000000000000000000000000-22-222i2−2i200−2i22i200000000000000
χ624-44-44-4-44000000000000000000000000000000000000-22-22−2i22i2002i2−2i200000000000000
χ634-44-4-444-40000000000000000000000000000000000002-2-22002i2−2i2002i2−2i2000000000000
χ644-44-4-444-40000000000000000000000000000000000002-2-2200−2i22i200−2i22i2000000000000
χ654-44-4-444-4000000000000000000000000000000000000-222-2002i2−2i200−2i22i2000000000000
χ664-44-4-444-4000000000000000000000000000000000000-222-200−2i22i2002i2−2i2000000000000
χ678-8-8888-8-8000000000000000000000000000000000000000000000000000000000000
χ688-8-88-8-888000000000000000000000000000000000000000000000000000000000000

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