Finite Group Databasebeta

← Group #350573

Character table — Group #350573

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222222244444444444444444444444444444422224444444444444888888888888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ611111111111111111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11-1-1-1-11111111111111111-1-1-1-1-1-1-1-111
χ811111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1
χ911111111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11-1
χ1011111111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-11
χ1111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-11
χ1211111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-111-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-11-1
χ1311111111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-11111-1-1-11
χ1411111111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1111-1
χ1511111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-1111-1
χ1611111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1-1111111-1-1-1-1-1-1-1-1111111-1-111-1-1-11
χ1722222222222222-2-222-2-20000000022-2-222222222-2-2-2-2-2-2-2000000000000000000000000000000
χ1822222222222222-2-222-2-20000000022-2-2-2-2-2-2-2-2-2-2-2-22222-2000000000000000000000000000000
χ19222222222222-2-222-2-22222222222-2-22200000000-2-20000-2-2-2-2-200000000000000000000000000
χ20222222222222-2-222-2-222-2-2-2-2-2-2-2-2-2-22200000000-2-20000-2222200000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-200000000-2-2-2-2000000002200002000022-2-222-2-2000000000000000000
χ22222222222222-2-2-2-2-2-2-2-200000000-2-2-2-20000000022000020000-2-222-2-222000000000000000000
χ2322222222-2-2-2-222-2-222-2-200000000-2-2222222-2-2-2-2-2-2-2-2222000000000000000000000000000000
χ2422222222-2-2-2-222-2-222-2-200000000-2-222-2-2-2-22222-2-222-2-22000000000000000000000000000000
χ2522222222-2-2-2-2-2-222-2-2222222-2-2-2-222-2-200000000-2-200002-2-22200000000000000000000000000
χ2622222222-2-2-2-2-2-222-2-222-2-2-2-2222222-2-200000000-2-20000222-2-200000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-200000000222200000000220000-2000022-2-2-2-222000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-200000000222200000000220000-20000-2-22222-2-2000000000000000000
χ292-22-222-2-200002-22-22-22-200002i2i−2i−2i0000000022-2-22-2002-20002i−2i2i−2i2i−2i0000000000000000000000
χ302-22-222-2-200002-22-22-22-200002i2i−2i−2i00000000-2-2222-200-220002i−2i−2i2i−2i2i0000000000000000000000
χ312-22-222-2-200002-22-22-22-20000−2i−2i2i2i0000000022-2-22-2002-2000−2i2i−2i2i−2i2i0000000000000000000000
χ322-22-222-2-200002-22-22-22-20000−2i−2i2i2i00000000-2-2222-200-22000−2i2i2i−2i2i−2i0000000000000000000000
χ332-22-222-2-200002-2-222-2-222i2i−2i−2i00000000000022-2-2-2200-2202i−2i0000002i−2i2i−2i000000000000000000
χ342-22-222-2-200002-2-222-2-222i2i−2i−2i000000000000-2-222-22002-202i−2i000000−2i2i−2i2i000000000000000000
χ352-22-222-2-200002-2-222-2-22−2i−2i2i2i00000000000022-2-2-2200-220−2i2i000000−2i2i−2i2i000000000000000000
χ362-22-222-2-200002-2-222-2-22−2i−2i2i2i000000000000-2-222-22002-20−2i2i0000002i−2i2i−2i000000000000000000
χ372-22-222-2-20000-222-2-222-200002i2i−2i−2i000022-2-20000-222-200000−2i2i00002i−2i−2i2i000000000000000000
χ382-22-222-2-20000-222-2-222-200002i2i−2i−2i0000-2-2220000-22-2200000−2i2i0000−2i2i2i−2i000000000000000000
χ392-22-222-2-20000-222-2-222-20000−2i−2i2i2i000022-2-20000-222-2000002i−2i0000−2i2i2i−2i000000000000000000
χ402-22-222-2-20000-222-2-222-20000−2i−2i2i2i0000-2-2220000-22-22000002i−2i00002i−2i−2i2i000000000000000000
χ412-22-222-2-20000-22-22-22-222i2i−2i−2i0000000022-2-200002-2-22000−2i2i002i−2i−2i2i0000000000000000000000
χ422-22-222-2-20000-22-22-22-222i2i−2i−2i00000000-2-22200002-22-2000−2i2i00−2i2i2i−2i0000000000000000000000
χ432-22-222-2-20000-22-22-22-22−2i−2i2i2i0000000022-2-200002-2-220002i−2i00−2i2i2i−2i0000000000000000000000
χ442-22-222-2-20000-22-22-22-22−2i−2i2i2i00000000-2-22200002-22-20002i−2i002i−2i−2i2i0000000000000000000000
χ452-2-222-22-222-2-2002200-2-22-22-22-22-2002-2000000000000000000000000000i2i2−i2−i2i2i2−i2−i2i2−i2i2−i2000000
χ462-2-222-22-222-2-2002200-2-22-22-22-22-2002-2000000000000000000000000000−i2−i2i2i2−i2−i2i2i2−i2i2−i2i2000000
χ472-2-222-22-222-2-2002200-2-2-22-22-22-22002-2000000000000000000000000000i2i2−i2−i2i2i2−i2−i2−i2i2−i2i2000000
χ482-2-222-22-222-2-2002200-2-2-22-22-22-22002-2000000000000000000000000000−i2−i2i2i2−i2−i2i2i2i2−i2i2−i2000000
χ492-2-222-22-2-2-222002200-2-22-22-2-22-2200-22000000000000000000000000000i2i2−i2−i2−i2−i2i2i2i2−i2−i2i2000000
χ502-2-222-22-2-2-222002200-2-22-22-2-22-2200-22000000000000000000000000000−i2−i2i2i2i2i2−i2−i2−i2i2i2−i2000000
χ512-2-222-22-2-2-222002200-2-2-22-222-22-200-22000000000000000000000000000i2i2−i2−i2−i2−i2i2i2−i2i2i2−i2000000
χ522-2-222-22-2-2-222002200-2-2-22-222-22-200-22000000000000000000000000000−i2−i2i2i2i2i2−i2−i2i2−i2−i2i2000000
χ532-2-22-22-222-22-22200-2-200000000002-2002i−2i2i−2i2i−2i2i−2i0000000000000000000i2−i2i2−i2i2−i2i2−i200002−22−200
χ542-2-22-22-222-22-22200-2-200000000002-2002i−2i2i−2i2i−2i2i−2i0000000000000000000−i2i2−i2i2−i2i2−i2i20000−22−2200
χ552-2-22-22-222-22-22200-2-200000000002-200−2i2i−2i2i−2i2i−2i2i0000000000000000000i2−i2i2−i2i2−i2i2−i20000−22−2200
χ562-2-22-22-222-22-22200-2-200000000002-200−2i2i−2i2i−2i2i−2i2i0000000000000000000−i2i2−i2i2−i2i2−i2i200002−22−200
χ572-2-22-22-22-22-222200-2-20000000000-22002i−2i2i−2i−2i2i−2i2i0000000000000000000i2−i2i2−i2−i2i2−i2i200002−2−2200
χ582-2-22-22-22-22-222200-2-20000000000-22002i−2i2i−2i−2i2i−2i2i0000000000000000000−i2i2−i2i2i2−i2i2−i20000−222−200
χ592-2-22-22-22-22-222200-2-20000000000-2200−2i2i−2i2i2i−2i2i−2i0000000000000000000i2−i2i2−i2−i2i2−i2i20000−222−200
χ602-2-22-22-22-22-222200-2-20000000000-2200−2i2i−2i2i2i−2i2i−2i0000000000000000000−i2i2−i2i2i2−i2i2−i200002−2−2200
χ614444-4-4-4-44-4-44000000000000000000000000000000000000000000000002-2-222-2-220000000000
χ624444-4-4-4-44-4-4400000000000000000000000000000000000000000000000-222-2-222-20000000000
χ634444-4-4-4-4-444-4000000000000000000000000000000000000000000000002-2-22-222-20000000000
χ644444-4-4-4-4-444-400000000000000000000000000000000000000000000000-222-22-2-220000000000
χ6544-4-44-4-440000004-400-4400004i−4i−4i4i0000000000000000000000000000000000000000000000000
χ6644-4-44-4-440000004-400-440000−4i4i4i−4i0000000000000000000000000000000000000000000000000
χ6744-4-44-4-44000000-44004-44i−4i−4i4i00000000000000000000000000000000000000000000000000000
χ6844-4-44-4-44000000-44004-4−4i4i4i−4i00000000000000000000000000000000000000000000000000000
χ6944-4-4-444-400004-400-440000000000000000004i−4i−4i4i0000000000000000000000000000000000000
χ7044-4-4-444-400004-400-44000000000000000000−4i4i4i−4i0000000000000000000000000000000000000
χ7144-4-4-444-40000-44004-4000000000000004i−4i−4i4i00000000000000000000000000000000000000000
χ7244-4-4-444-40000-44004-400000000000000−4i4i4i−4i00000000000000000000000000000000000000000
χ734-4-444-44-444-4-400-4-400440000000000-44000000000000000000000000000000000000000000000
χ744-4-444-44-4-4-44400-4-4004400000000004-4000000000000000000000000000000000000000000000
χ754-4-44-44-444-44-4-4-400440000000000-4400000000000000000000000000000000000000000000000
χ764-4-44-44-44-44-44-4-4004400000000004-400000000000000000000000000000000000000000000000
χ778-88-8-8-888000000000000000000000000000000000000000000000000000000000000000000000

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