Finite Group Databasebeta

← Group #165713

Character table — Group #165713

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size111111114444448888888888888888881616161616111111114444448888888888888888881616161616
order12222222444444224444888888888888244442222222244444422444488888888888824444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1
χ31111111111111111-1-1-1-111111111-1-1-1-1-11-1-1-11111111111111111-1-1-1-111111111-1-1-1-1-11-1-1-1
χ41111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-111
χ511111111111111-1-111-1-11111-1-1-1-111111-1-1-1-111111111111111-1-111-1-11111-1-1-1-111111-1-1-1-1
χ611111111111111-1-111-1-1-1-1-1-11111-1-1-1-11-1-11111111111111111-1-111-1-1-1-1-1-11111-1-1-1-11-1-111
χ711111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111
χ811111111111111-1-1-1-111-1-1-1-111111111-1-11-1-111111111111111-1-1-1-111-1-1-1-111111111-1-11-1-1
χ9222222222-2-22-2-200002200000000000000-200222222222-2-22-2-200002200000000000000-200
χ10222222222-2-22-2-20000-2-200000000000000200222222222-2-22-2-20000-2-200000000000000200
χ1122222222-22-2-22-2002200000000000000-2000022222222-22-2-22-2002200000000000000-20000
χ1222222222-22-2-22-200-2-2000000000000002000022222222-22-2-22-200-2-20000000000000020000
χ1322222222-2-22-2-222200000000000000000-200022222222-2-22-2-222200000000000000000-2000
χ1422222222-2-22-2-22-2-200000000000000000200022222222-2-22-2-22-2-2000000000000000002000
χ152-22-22-22-20200-20002i−2i00i2i2−i2−i2000022−2−2000002-22-22-22-20200-20002i−2i00i2i2−i2−i2000022−2−200000
χ162-22-22-22-20200-20002i−2i00−i2−i2i2i20000−2−222000002-22-22-22-20200-20002i−2i00−i2−i2i2i20000−2−22200000
χ172-22-22-22-20200-2000−2i2i00i2i2−i2−i20000−2−222000002-22-22-22-20200-2000−2i2i00i2i2−i2−i20000−2−22200000
χ182-22-22-22-20200-2000−2i2i00−i2−i2i2i2000022−2−2000002-22-22-22-20200-2000−2i2i00−i2−i2i2i2000022−2−200000
χ192-2-222-2-22200-20000002-20000i2i2−i2−i2i2−i2i2−i2000002-2-222-2-22200-20000002-20000i2i2−i2−i2i2−i2i2−i200000
χ202-2-222-2-22200-20000002-20000−i2−i2i2i2−i2i2−i2i2000002-2-222-2-22200-20000002-20000−i2−i2i2i2−i2i2−i2i200000
χ212-2-222-2-22200-2000000-220000i2i2−i2−i2−i2i2−i2i2000002-2-222-2-22200-2000000-220000i2i2−i2−i2−i2i2−i2i200000
χ222-2-222-2-22200-2000000-220000−i2−i2i2i2i2−i2i2−i2000002-2-222-2-22200-2000000-220000−i2−i2i2i2i2−i2i2−i200000
χ232-2-2-2-222200-20022-200002−22−22−22−20000000002-2-2-2-222200-20022-200002−22−22−22−2000000000
χ242-2-2-2-222200-20022-20000−22−22−22−220000000002-2-2-2-222200-20022-20000−22−22−22−22000000000
χ252-2-2-2-222200-2002-2200002−22−2−22−220000000002-2-2-2-222200-2002-2200002−22−2−22−22000000000
χ262-2-2-2-222200-2002-220000−22−222−22−20000000002-2-2-2-222200-2002-220000−22−222−22−2000000000
χ27444-4-4-4-4400000000000000002i−2i−2i2i000000000444-4-4-4-4400000000000000002i−2i−2i2i000000000
χ28444-4-4-4-440000000000000000−2i2i2i−2i000000000444-4-4-4-440000000000000000−2i2i2i−2i000000000
χ2944-44-4-44-40000000000002i−2i−2i2i000000000000044-44-4-44-40000000000002i−2i−2i2i0000000000000
χ3044-44-4-44-4000000000000−2i2i2i−2i000000000000044-44-4-44-4000000000000−2i2i2i−2i0000000000000
χ3144-4-444-4-4000000000000000000002i−2i−2i2i0000044-4-444-4-4000000000000000000002i−2i−2i2i00000
χ3244-4-444-4-400000000000000000000−2i2i2i−2i0000044-4-444-4-400000000000000000000−2i2i2i−2i00000
χ334-444-44-4-40000000000000000000000000002i−2i4-444-44-4-40000000000000000000000000002i−2i
χ344-444-44-4-4000000000000000000000000000−2i2i4-444-44-4-4000000000000000000000000000−2i2i
χ354-44-44-44-40-40040000000000000000000000004-44-44-44-40-4004000000000000000000000000
χ364-4-444-4-44-400400000000000000000000000004-4-444-4-44-40040000000000000000000000000
χ374-4-4-4-444400400-4000000000000000000000004-4-4-4-444400400-400000000000000000000000
χ381111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3911111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-111
χ401111111111111111-1-1-1-111111111-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111-1111
χ411111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11-11-1-1
χ4211111111111111-1-111-1-11111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-11111
χ4311111111111111-1-111-1-1-1-1-1-11111-1-1-1-11-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111-111-1-1
χ4411111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1
χ4511111111111111-1-1-1-111-1-1-1-111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111-111
χ46222222222-2-22-2-200002200000000000000-200-2-2-2-2-2-2-2-2-222-2220000-2-200000000000000200
χ47222222222-2-22-2-20000-2-200000000000000200-2-2-2-2-2-2-2-2-222-22200002200000000000000-200
χ4822222222-22-2-22-2002200000000000000-20000-2-2-2-2-2-2-2-22-222-2200-2-20000000000000020000
χ4922222222-22-2-22-200-2-20000000000000020000-2-2-2-2-2-2-2-22-222-22002200000000000000-20000
χ5022222222-2-22-2-222200000000000000000-2000-2-2-2-2-2-2-2-222-222-2-2-2000000000000000002000
χ5122222222-2-22-2-22-2-2000000000000000002000-2-2-2-2-2-2-2-222-222-22200000000000000000-2000
χ522-22-22-22-20200-20002i−2i00i2i2−i2−i2000022−2−200000-22-22-22-220-2002000−2i2i00−i2−i2i2i20000−2−22200000
χ532-22-22-22-20200-20002i−2i00−i2−i2i2i20000−2−22200000-22-22-22-220-2002000−2i2i00i2i2−i2−i2000022−2−200000
χ542-22-22-22-20200-2000−2i2i00i2i2−i2−i20000−2−22200000-22-22-22-220-20020002i−2i00−i2−i2i2i2000022−2−200000
χ552-22-22-22-20200-2000−2i2i00−i2−i2i2i2000022−2−200000-22-22-22-220-20020002i−2i00i2i2−i2−i20000−2−22200000
χ562-2-222-2-22200-20000002-20000i2i2−i2−i2i2−i2i2−i200000-222-2-222-2-2002000000-220000−i2−i2i2i2−i2i2−i2i200000
χ572-2-222-2-22200-20000002-20000−i2−i2i2i2−i2i2−i2i200000-222-2-222-2-2002000000-220000i2i2−i2−i2i2−i2i2−i200000
χ582-2-222-2-22200-2000000-220000i2i2−i2−i2−i2i2−i2i200000-222-2-222-2-20020000002-20000−i2−i2i2i2i2−i2i2−i200000
χ592-2-222-2-22200-2000000-220000−i2−i2i2i2i2−i2i2−i200000-222-2-222-2-20020000002-20000i2i2−i2−i2−i2i2−i2i200000
χ602-2-2-2-222200-20022-200002−22−22−22−2000000000-22222-2-2-200200-2-220000−22−22−22−22000000000
χ612-2-2-2-222200-20022-20000−22−22−22−22000000000-22222-2-2-200200-2-2200002−22−22−22−2000000000
χ622-2-2-2-222200-2002-2200002−22−2−22−22000000000-22222-2-2-200200-22-20000−22−222−22−2000000000
χ632-2-2-2-222200-2002-220000−22−222−22−2000000000-22222-2-2-200200-22-200002−22−2−22−22000000000
χ64444-4-4-4-4400000000000000002i−2i−2i2i000000000-4-4-44444-40000000000000000−2i2i2i−2i000000000
χ65444-4-4-4-440000000000000000−2i2i2i−2i000000000-4-4-44444-400000000000000002i−2i−2i2i000000000
χ6644-44-4-44-40000000000002i−2i−2i2i0000000000000-4-44-444-44000000000000−2i2i2i−2i0000000000000
χ6744-44-4-44-4000000000000−2i2i2i−2i0000000000000-4-44-444-440000000000002i−2i−2i2i0000000000000
χ6844-4-444-4-4000000000000000000002i−2i−2i2i00000-4-444-4-44400000000000000000000−2i2i2i−2i00000
χ6944-4-444-4-400000000000000000000−2i2i2i−2i00000-4-444-4-444000000000000000000002i−2i−2i2i00000
χ704-444-44-4-40000000000000000000000000002i−2i-44-4-44-444000000000000000000000000000−2i2i
χ714-444-44-4-4000000000000000000000000000−2i2i-44-4-44-4440000000000000000000000000002i−2i
χ724-44-44-44-40-4004000000000000000000000000-44-44-44-440400-4000000000000000000000000
χ734-4-444-4-44-40040000000000000000000000000-444-4-444-4400-40000000000000000000000000
χ744-4-4-4-444400400-400000000000000000000000-44444-4-4-400-400400000000000000000000000

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