Finite Group Databasebeta

← Group #255471

Character table — Group #255471

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444444448888888888888888888888888881616161616161616161616161616
order12222222222244444444444444444444444444444888888888888888844444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1111-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-1111111-1-11-1-1-1-111111111111111111-1-1-1-1-1-11-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-1111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-11111
χ7111111111111111111111111-1-1-1-111-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1111111
χ8111111111111111111111111-1-1-1-111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1111111-111-1-1-1-1
χ911111111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111111-1-1-1-1-111-1-1
χ1011111111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111111-1-111-1-1-1-1-111
χ1111111111-1-1-1-111111111-1-1-1-1111111-1-111-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-111-1-1111-1-111
χ1211111111-1-1-1-111111111-1-1-1-1111111-1-111-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11111111-1-1
χ1311111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1111111-1-1-1-11111-1-1-1-11-1-1-1-111-111-1-111
χ1411111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-111-1-1-1-11111-1-1-1-111111-1-111-1-1-11111-1-1
χ1511111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1111111-1-1-1-1-1-1-1-11111-111-1-1111-1-111-1-1
χ1611111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-111-1-1-1-111111111-1-1-1-1-11111-1-11-1-1-1-111
χ1722222222222222-2-2-222-222-2-20000-2-2222200-200000000000000000000-2000000-2000000
χ1822222222222222-2-2-222-222-2-20000-2-2-2-2-2-200-20000000000000000000020000002000000
χ19222222222222-2-2222-2-22-2-2222222-2-2000022-2-2-2-2-2000000000000000000000000000000
χ20222222222222-2-2222-2-22-2-222-2-2-2-2-2-20000-2-2-22222000000000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-200002200000020000000000000000000002-2000002-20000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-20000220000002000000000000000000000-2200000-220000
χ2322222222-2-2-2-222-2-2-222-2-2-2220000-2-222-2-200200000000000000000000-20000002000000
χ2422222222-2-2-2-222-2-2-222-2-2-2220000-2-2-2-222002000000000000000000002000000-2000000
χ2522222222-2-2-2-2-2-2222-2-2222-2-22222-2-20000-2-22-2-222000000000000000000000000000000
χ2622222222-2-2-2-2-2-2222-2-2222-2-2-2-2-2-2-2-2000022222-2-2000000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22222000022000000-20000000000000000000002-200000-220000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22222000022000000-2000000000000000000000-22000002-20000
χ2922-2-22-22-222-2-2002-2-2002002-222-2-20000002-20000000000000i2i2−i2−i2i2i2−i2−i20000000000i2−i2i2−i2
χ3022-2-22-22-222-2-2002-2-2002002-222-2-20000002-20000000000000−i2−i2i2i2−i2−i2i2i20000000000−i2i2−i2i2
χ3122-2-22-22-222-2-2002-2-2002002-2-2-222000000-220000000000000i2i2−i2−i2i2i2−i2−i20000000000−i2i2−i2i2
χ3222-2-22-22-222-2-2002-2-2002002-2-2-222000000-220000000000000−i2−i2i2i2−i2−i2i2i20000000000i2−i2i2−i2
χ3322-2-22-22-2-2-222002-2-200200-2222-2-2000000-220000000000000i2i2−i2−i2−i2−i2i2i20000000000i2−i2−i2i2
χ3422-2-22-22-2-2-222002-2-200200-2222-2-2000000-220000000000000−i2−i2i2i2i2i2−i2−i20000000000−i2i2i2−i2
χ3522-2-22-22-2-2-222002-2-200200-22-2-2220000002-20000000000000i2i2−i2−i2−i2−i2i2i20000000000−i2i2i2−i2
χ3622-2-22-22-2-2-222002-2-200200-22-2-2220000002-20000000000000−i2−i2i2i2i2i2−i2−i20000000000i2−i2−i2i2
χ372-222-2-22-22-22-2-2-20002202-2000000002-22-20000000i2i2−i2−i2i2i2−i2−i2i2−i2i2−i2i2−i2i2−i200000000000000
χ382-222-2-22-22-22-2-2-20002202-2000000002-22-20000000−i2−i2i2i2−i2−i2i2i2−i2i2−i2i2−i2i2−i2i200000000000000
χ392-222-2-22-22-22-2-2-20002202-200000000-22-220000000i2i2−i2−i2i2i2−i2−i2−i2i2−i2i2−i2i2−i2i200000000000000
χ402-222-2-22-22-22-2-2-20002202-200000000-22-220000000−i2−i2i2i2−i2−i2i2i2i2−i2i2−i2i2−i2i2−i200000000000000
χ412-222-2-22-2-22-22-2-2000220-22000000002-2-220000000i2i2−i2−i2−i2−i2i2i2i2−i2i2−i2−i2i2−i2i200000000000000
χ422-222-2-22-2-22-22-2-2000220-22000000002-2-220000000−i2−i2i2i2i2i2−i2−i2−i2i2−i2i2i2−i2i2−i200000000000000
χ432-222-2-22-2-22-22-2-2000220-2200000000-222-20000000i2i2−i2−i2−i2−i2i2i2−i2i2−i2i2i2−i2i2−i200000000000000
χ442-222-2-22-2-22-22-2-2000220-2200000000-222-20000000−i2−i2i2i2i2i2−i2−i2i2−i2i2−i2−i2i2−i2i200000000000000
χ452-2-222-2-2200002-222-22-2-200002-22-22-200000002-20000002i−2i2i−2i00000000000002i−2i0000000
χ462-2-222-2-2200002-222-22-2-200002-22-22-200000002-2000000−2i2i−2i2i0000000000000−2i2i0000000
χ472-2-222-2-2200002-222-22-2-20000-22-222-20000000-220000002i−2i2i−2i0000000000000−2i2i0000000
χ482-2-222-2-2200002-222-22-2-20000-22-222-20000000-22000000−2i2i−2i2i00000000000002i−2i0000000
χ492-2-222-2-220000-2222-2-22-200002-22-2-220000000-22002i−2i2i−2i0000000000000002i−2i000000000
χ502-2-222-2-220000-2222-2-22-200002-22-2-220000000-2200−2i2i−2i2i000000000000000−2i2i000000000
χ512-2-222-2-220000-2222-2-22-20000-22-22-2200000002-2002i−2i2i−2i000000000000000−2i2i000000000
χ522-2-222-2-220000-2222-2-22-20000-22-22-2200000002-200−2i2i−2i2i0000000000000002i−2i000000000
χ5344-44-44-4-400004-4000-44000000000000000000000022−22−222200000000000000000000000000
χ5444-44-44-4-400004-4000-440000000000000000000000−222222−2200000000000000000000000000
χ5544-44-44-4-40000-440004-40000000000000000000000000022−22−22220000000000000000000000
χ5644-44-44-4-40000-440004-400000000000000000000000000−222222−220000000000000000000000
χ5744-4-44-44-444-4-400-44400-400-4400000000000000000000000000000000000000000000000
χ5844-4-44-44-4-4-44400-44400-4004-400000000000000000000000000000000000000000000000
χ594-444-4-44-44-44-444000-4-40-440000000000000000000000000000000000000000000000000
χ604-444-4-44-4-44-4444000-4-404-40000000000000000000000000000000000000000000000000
χ614-44-444-4-40000004-4400-400004-4-440000000000000000000000000000000000000000000
χ624-44-444-4-40000004-4400-40000-444-40000000000000000000000000000000000000000000
χ634-44-444-4-4000000-44-400400000000000000000004i−4i000000000000000000000000000000
χ644-44-444-4-4000000-44-40040000000000000000000−4i4i000000000000000000000000000000
χ654-4-444-4-4400004-4-4-444-4400000000-4400000000000000000000000000000000000000000
χ664-4-444-4-440000-44-4-44-444000000004-400000000000000000000000000000000000000000
χ674-4-4-4-44444-4-4400000000000000000000000000000000000002-2-222-2-2200000000000000
χ684-4-4-4-44444-4-440000000000000000000000000000000000000-222-2-222-200000000000000
χ694-4-4-4-4444-444-400000000000000000000000000000000000002-2-22-222-200000000000000
χ704-4-4-4-4444-444-40000000000000000000000000000000000000-222-22-2-2200000000000000
χ71888-8-8-8-88000000000000000000000000000000000000000000000000000000000000000

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