Finite Group Databasebeta

← Group #449521

Character table — Group #449521

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222444444444444444444444444888888888888161616161616161616161616161616161616
order12222222222222222222222222222222222222222222224444444444444444444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111111111-1-1-1-1
χ911111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-111-1-111-1-1
χ1011111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-111
χ1111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-111
χ1211111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111-1-11111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-111
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-11111-1-111-1-1-1-111
χ172222222222-2-2-2-222-2-2-2-22222-2-2-2-200000000000000000000000022-2-2002-200000000000000
χ182222222222-2-2-2-222-2-2-2-22222-2-2-2-2000000000000000000000000-2-22200-2200000000000000
χ192222222222-2-2-2-222-2-2-2-2-2-2-2-2222200000000000000000000000022-2-200-2200000000000000
χ202222222222-2-2-2-222-2-2-2-2-2-2-2-22222000000000000000000000000-2-222002-200000000000000
χ2122222222-2-222-2-2-2-222-2-222-2-222-2-20000000000000000000022-2-200002-20000000000000000
χ2222222222-2-222-2-2-2-222-2-222-2-222-2-200000000000000000000-2-2220000-220000000000000000
χ2322222222-2-222-2-2-2-222-2-2-2-222-2-2220000000000000000000022-2-20000-220000000000000000
χ2422222222-2-222-2-2-2-222-2-2-2-222-2-22200000000000000000000-2-22200002-20000000000000000
χ2522222222-2-2-2-222-2-2-2-22222-2-2-2-222000000000000000022-2-20000000000002-2000000000000
χ2622222222-2-2-2-222-2-2-2-22222-2-2-2-2220000000000000000-2-222000000000000-22000000000000
χ2722222222-2-2-2-222-2-2-2-222-2-22222-2-2000000000000000022-2-2000000000000-22000000000000
χ2822222222-2-2-2-222-2-2-2-222-2-22222-2-20000000000000000-2-2220000000000002-2000000000000
χ292222-2-2-2-2222-22-2-2-22-22-200000000000000002222-2-2-2-2000000002i−2i2i−2i00000000000000002i−2i
χ302222-2-2-2-2222-22-2-2-22-22-200000000000000002222-2-2-2-200000000−2i2i−2i2i0000000000000000−2i2i
χ312222-2-2-2-2222-22-2-2-22-22-20000000000000000-2-2-2-22222000000002i−2i2i−2i0000000000000000−2i2i
χ322222-2-2-2-2222-22-2-2-22-22-20000000000000000-2-2-2-2222200000000−2i2i−2i2i00000000000000002i−2i
χ332222-2-2-2-222-22-22-2-2-22-22000000002222-2-2-2-200000000000000002i−2i−2i2i000000000000002i−2i00
χ342222-2-2-2-222-22-22-2-2-22-22000000002222-2-2-2-20000000000000000−2i2i2i−2i00000000000000−2i2i00
χ352222-2-2-2-222-22-22-2-2-22-2200000000-2-2-2-2222200000000000000002i−2i−2i2i00000000000000−2i2i00
χ362222-2-2-2-222-22-22-2-2-22-2200000000-2-2-2-222220000000000000000−2i2i2i−2i000000000000002i−2i00
χ3722-2-222-2-22-2222-22-2-2-2-220000000022-2-222-2-20000000000002i−2i2i−2i000000000000002i−2i000000
χ3822-2-222-2-22-2222-22-2-2-2-220000000022-2-222-2-2000000000000−2i2i−2i2i00000000000000−2i2i000000
χ3922-2-222-2-22-2222-22-2-2-2-2200000000-2-222-2-2220000000000002i−2i2i−2i00000000000000−2i2i000000
χ4022-2-222-2-22-2222-22-2-2-2-2200000000-2-222-2-222000000000000−2i2i−2i2i000000000000002i−2i000000
χ4122-2-222-2-2-2222-22-22-2-22-2000000000000000022-2-222-2-200002i−2i−2i2i00000000000000002i−2i0000
χ4222-2-222-2-2-2222-22-22-2-22-2000000000000000022-2-222-2-20000−2i2i2i−2i0000000000000000−2i2i0000
χ4322-2-222-2-2-2222-22-22-2-22-20000000000000000-2-222-2-22200002i−2i−2i2i0000000000000000−2i2i0000
χ4422-2-222-2-2-2222-22-22-2-22-20000000000000000-2-222-2-2220000−2i2i2i−2i00000000000000002i−2i0000
χ4522-2-2-2-2222-2-22-2-2-222-2220000000022-2-2-2-222000000002-22-2000000000000002-20000000000
χ4622-2-2-2-2222-2-22-2-2-222-2220000000022-2-2-2-22200000000-22-2200000000000000-220000000000
χ4722-2-2-2-2222-2-22-2-2-222-22200000000-2-22222-2-2000000002-22-200000000000000-220000000000
χ4822-2-2-2-2222-2-22-2-2-222-22200000000-2-22222-2-200000000-22-22000000000000002-20000000000
χ4922-2-2-2-222-222-2-2-22-2-2222000000000000000022-2-2-2-2222-2-2200000000000000002-200000000
χ5022-2-2-2-222-222-2-2-22-2-2222000000000000000022-2-2-2-222-222-20000000000000000-2200000000
χ5122-2-2-2-222-222-2-2-22-2-22220000000000000000-2-22222-2-22-2-220000000000000000-2200000000
χ5222-2-2-2-222-222-2-2-22-2-22220000000000000000-2-22222-2-2-222-200000000000000002-200000000
χ534444-4-4-4-4-4-44-4-44444-4-44000000000000000000000000000000000000000000000000000000
χ544444-4-4-4-4-4-4-444-444-444-4000000000000000000000000000000000000000000000000000000
χ5544-4-444-4-44-4-4-4-444-4444-4000000000000000000000000000000000000000000000000000000
χ5644-4-444-4-4-44-4-44-4-4444-44000000000000000000000000000000000000000000000000000000
χ5744-4-4-4-4444-44-444-44-44-4-4000000000000000000000000000000000000000000000000000000
χ5844-4-4-4-444-44-44444-44-4-4-4000000000000000000000000000000000000000000000000000000
χ594-44-44-44-40000000000000000004-42-22-22-22-22-22-22-22-2000000000000000000000000000000
χ604-44-44-44-40000000000000000004-4-22-22-22-22-22-22-22-22000000000000000000000000000000
χ614-44-44-44-4000000000000000000-442-22-22-22-2-22-22-22-22000000000000000000000000000000
χ624-44-44-44-4000000000000000000-44-22-22-22-222-22-22-22-2000000000000000000000000000000
χ634-44-4-44-4400000000000000004-4002-22-2-22-222-22-2-22-22000000000000000000000000000000
χ644-44-4-44-4400000000000000004-400-22-222-22-2-22-222-22-2000000000000000000000000000000
χ654-44-4-44-440000000000000000-44002-22-2-22-22-22-222-22-2000000000000000000000000000000
χ664-44-4-44-440000000000000000-4400-22-222-22-22-22-2-22-22000000000000000000000000000000
χ674-4-444-4-44000000000000004-400002-2-222-2-222-2-222-2-22000000000000000000000000000000
χ684-4-444-4-44000000000000004-40000-222-2-222-2-222-2-222-2000000000000000000000000000000
χ694-4-444-4-4400000000000000-4400002-2-222-2-22-222-2-222-2000000000000000000000000000000
χ704-4-444-4-4400000000000000-440000-222-2-222-22-2-222-2-22000000000000000000000000000000
χ714-4-44-444-40000000000004-40000002-2-22-222-22-2-22-222-2000000000000000000000000000000
χ724-4-44-444-40000000000004-4000000-222-22-2-22-222-22-2-22000000000000000000000000000000
χ734-4-44-444-4000000000000-440000002-2-22-222-2-222-22-2-22000000000000000000000000000000
χ744-4-44-444-4000000000000-44000000-222-22-2-222-2-22-222-2000000000000000000000000000000

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