Finite Group Databasebeta

← Group #314656

Character table — Group #314656

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12222222222244444444888888884444444488888888888822444444888888884444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-1111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1111111-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-1111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-111-1-111-1-111-1-111
χ1111111111-1-1-1-1111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111-1-111-1-1-1-111-1-111
χ1211111111-1-1-1-1111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-111-1-11111-1-111-1-1
χ1311111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-11111-1-1-1-111-1-1-1-11111-1-1-1-111
χ1411111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1
χ1511111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-1111111-1-1-1-111-1-11111-1-1
χ1611111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-11111-1-11111-1-111-1-1-1-111
χ1722222222222222-2-2-222-200000000-2-222-2-2-2-200000000000022-2-2-2-222000000000000000000000000
χ1822222222222222-2-2-222-200000000-2-222-2-2-2-2000000000000-2-22222-2-2000000000000000000000000
χ19222222222222-2-2222-2-2222222222-2-2-2-2-2-222-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ20222222222222-2-2222-2-22-2-2-2-2-2-2-2-2-2-2-2-2-2-22222222222-2-2-2-200000000000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-20000000022-2-222-2-2000000000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ22222222222222-2-2-2-2-2-2-2-20000000022-2-222-2-200000000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ2322222222-2-2-2-222-2-2-222-200000000-2-2-2-222220000000000002222-2-2-2-2000000000000000000000000
χ2422222222-2-2-2-222-2-2-222-200000000-2-2-2-22222000000000000-2-2-2-22222000000000000000000000000
χ2522222222-2-2-2-2-2-2222-2-2222222222-2-22222-2-2-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ2622222222-2-2-2-2-2-2222-2-22-2-2-2-2-2-2-2-2-2-22222-2-22222-2-2-2-2222200000000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2000000002222-2-222000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2000000002222-2-22200000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ2922-22-2-2-2222-2-222000-2-202222−2−2−2−2002-2000022−2−222−2−222−2−2002i−2i2i−2i00i2−i2i2−i2i2−i2i2−i20000000000000000
χ3022-22-2-2-2222-2-222000-2-202222−2−2−2−2002-2000022−2−222−2−222−2−200−2i2i−2i2i00−i2i2−i2i2−i2i2−i2i20000000000000000
χ3122-22-2-2-2222-2-222000-2-20−2−2−2−22222002-20000−2−222−2−222−2−222002i−2i2i−2i00−i2i2−i2i2−i2i2−i2i20000000000000000
χ3222-22-2-2-2222-2-222000-2-20−2−2−2−22222002-20000−2−222−2−222−2−22200−2i2i−2i2i00i2−i2i2−i2i2−i2i2−i20000000000000000
χ3322-22-2-2-2222-2-2-2-20002202222−2−2−2−200-220000−2−222−2−22222−2−22-200002-22−2−222−2−220000000000000000
χ3422-22-2-2-2222-2-2-2-20002202222−2−2−2−200-220000−2−222−2−22222−2−2-220000-22−222−2−222−20000000000000000
χ3522-22-2-2-2222-2-2-2-2000220−2−2−2−2222200-22000022−2−222−2−2−2−2222-200002-2−222−2−222−20000000000000000
χ3622-22-2-2-2222-2-2-2-2000220−2−2−2−2222200-22000022−2−222−2−2−2−222-220000-222−2−222−2−220000000000000000
χ3722-22-2-2-22-2-22222000-2-202222−2−2−2−200-22000022−2−2−2−222−2−222002i−2i−2i2i00i2−i2i2−i2−i2i2−i2i20000000000000000
χ3822-22-2-2-22-2-22222000-2-202222−2−2−2−200-22000022−2−2−2−222−2−22200−2i2i2i−2i00−i2i2−i2i2i2−i2i2−i20000000000000000
χ3922-22-2-2-22-2-22222000-2-20−2−2−2−2222200-220000−2−22222−2−222−2−2002i−2i−2i2i00−i2i2−i2i2i2−i2i2−i20000000000000000
χ4022-22-2-2-22-2-22222000-2-20−2−2−2−2222200-220000−2−22222−2−222−2−200−2i2i2i−2i00i2−i2i2−i2−i2i2−i2i20000000000000000
χ4122-22-2-2-22-2-222-2-20002202222−2−2−2−2002-20000−2−22222−2−2−2−2222-20000-22−222−22−2−220000000000000000
χ4222-22-2-2-22-2-222-2-20002202222−2−2−2−2002-20000−2−22222−2−2−2−222-2200002-22−2−22−222−20000000000000000
χ4322-22-2-2-22-2-222-2-2000220−2−2−2−22222002-2000022−2−2−2−22222−2−22-20000-222−2−22−222−20000000000000000
χ4422-22-2-2-22-2-222-2-2000220−2−2−2−22222002-2000022−2−2−2−22222−2−2-2200002-2−222−22−2−220000000000000000
χ452-2-222-22-200002-2-22-22-2222-2-222-2-22-20000002-22-2000000000000000000000000002i−2i002i−2i00000000
χ462-2-222-22-200002-2-22-22-2222-2-222-2-22-20000002-22-200000000000000000000000000−2i2i00−2i2i00000000
χ472-2-222-22-200002-2-22-22-22-2-222-2-2222-2000000-22-22000000000000000000000000002i−2i00−2i2i00000000
χ482-2-222-22-200002-2-22-22-22-2-222-2-2222-2000000-22-2200000000000000000000000000−2i2i002i−2i00000000
χ492-2-222-22-20000-22-22-2-22222-2-222-2-2-22000000-22-220000000000000000000000002i−2i002i−2i0000000000
χ502-2-222-22-20000-22-22-2-22222-2-222-2-2-22000000-22-22000000000000000000000000−2i2i00−2i2i0000000000
χ512-2-222-22-20000-22-22-2-222-2-222-2-222-220000002-22-20000000000000000000000002i−2i00−2i2i0000000000
χ522-2-222-22-20000-22-22-2-222-2-222-2-222-220000002-22-2000000000000000000000000−2i2i002i−2i0000000000
χ532-2-2-2-22222-22-200-2-220022-22-22-22-20000002-2000000002-22-20000000000000000000000002−22−22−22−2
χ542-2-2-2-22222-22-200-2-220022-22-22-22-20000002-2000000002-22-2000000000000000000000000−22−22−22−22
χ552-2-2-2-22222-22-200-2-22002-22-22-22-220000002-200000000-22-220000000000000000000000002−22−2−22−22
χ562-2-2-2-22222-22-200-2-22002-22-22-22-220000002-200000000-22-22000000000000000000000000−22−222−22−2
χ572-2-2-2-2222-22-2200-2-220022-22-22-22-2000000-2200000000-22-220000000000000000000000002−2−222−2−22
χ582-2-2-2-2222-22-2200-2-220022-22-22-22-2000000-2200000000-22-22000000000000000000000000−222−2−222−2
χ592-2-2-2-2222-22-2200-2-22002-22-22-22-22000000-22000000002-22-20000000000000000000000002−2−22−222−2
χ602-2-2-2-2222-22-2200-2-22002-22-22-22-22000000-22000000002-22-2000000000000000000000000−222−22−2−22
χ61444-4-4-44-40000004-4-40044-4-444-4-440000000000000000000000000000000000000000000000000000
χ62444-4-4-44-40000004-4-4004-444-4-444-40000000000000000000000000000000000000000000000000000
χ63444-4-4-44-4000000-44400-4000000000000000000004-44-4000000000000000000000000000000000000
χ64444-4-4-44-4000000-44400-400000000000000000000-44-44000000000000000000000000000000000000
χ6544-4-444-4-400000000000022−22−2222−222222−2200004-400000022−22−2222000000000000000000000000000000000000
χ6644-4-444-4-400000000000022−22−2222−222222−220000-44000000−222222−22000000000000000000000000000000000000
χ6744-4-444-4-4000000000000−222222−2222−22−222200004-4000000−222222−22000000000000000000000000000000000000
χ6844-4-444-4-4000000000000−222222−2222−22−22220000-4400000022−22−2222000000000000000000000000000000000000
χ694-444-44-4-400004-4000-4402222−22−22−22−2222220000000022−22−22220000000000000000000000000000000000000000
χ704-444-44-4-400004-4000-440−22−2222222222−22−2200000000−222222−220000000000000000000000000000000000000000
χ714-444-44-4-40000-440004-402222−22−22−22−22222200000000−222222−220000000000000000000000000000000000000000
χ724-444-44-4-40000-440004-40−22−2222222222−22−220000000022−22−22220000000000000000000000000000000000000000
χ734-44-44-4-444-4-440000000022−2222−22−2222−2222000000000000000022−22−222200000000000000000000000000000000
χ744-44-44-4-444-4-4400000000−2222−222222−2222−220000000000000000−222222−2200000000000000000000000000000000
χ754-44-44-4-44-444-40000000022−2222−22−2222−22220000000000000000−222222−2200000000000000000000000000000000
χ764-44-44-4-44-444-400000000−2222−222222−2222−22000000000000000022−22−222200000000000000000000000000000000
χ774-4-444-44-400004-44-444-4-400000000-4400000000000000000000000000000000000000000000000000
χ784-4-444-44-40000-444-44-44-4000000004-400000000000000000000000000000000000000000000000000
χ794-4-4-4-44444-44-40044-400-400000000000000-4400000000000000000000000000000000000000000000
χ804-4-4-4-4444-44-440044-400-4000000000000004-400000000000000000000000000000000000000000000

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