Finite Group Databasebeta

← Group #312531

Character table — Group #312531

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888444444444488888888888888444444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-11-1-1-11111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-111-1-1-1-11111111111111111-11-1-1-1-1-1-1-1-111-1-1-1
χ411111111111111111111111111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1111
χ51111111111111111111111-1-1-1-1111111-1-11111-1-1-1-1-1-111-1-1-1-1-111111-1-111-1-1-1-1-1
χ61111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111
χ71111111111111111111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-1111
χ81111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111-111-1-1111111-1-1-1
χ911111111111111111-1-1-1-11111111-1-1111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-11
χ1011111111111111111-1-1-1-11111111-1-11111-1-111-1-1-1-1111111111-1-1-1-1-1-1-111-1-111-1
χ1111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-11-1-11111111111-1
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1111111-1-1-1-1-1-11
χ1311111111111111111-1-1-1-11-1-1-1-111-1-111-1-111-1-11111-1-1-1-11111-1111-1-111-1-1-1-111-1
χ1411111111111111111-1-1-1-11-1-1-1-111-1-111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-11
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111111-1-111-1-111-1-1-1-11
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1111111-1-111-1-1-1-11-11111-1-1-1-11111-1
χ17222222222-22-22-22-2-22222-2000000-2-2000022-2-20000002200000-20000000000000
χ18222222222-22-22-22-2-22222-2000000-2-20000-2-222000000-2-20000020000000000000
χ19222222222-22-22-22-2-2-2-2-2-2-20000002200002222000000-2-200000-20000000000000
χ20222222222-22-22-22-2-2-2-2-2-2-2000000220000-2-2-2-2000000220000020000000000000
χ2122222222-22-22-22-22-20000-222222200-2-2-2-200000000-2-2000000200000000000000
χ2222222222-22-22-22-22-20000-22222-2-200222200000000-2-2000000-200000000000000
χ2322222222-22-22-22-22-20000-2-2-2-2-22200-2-2220000000022000000-200000000000000
χ2422222222-22-22-22-22-20000-2-2-2-2-2-2-20022-2-20000000022000000200000000000000
χ252-22-2-222-22-2-222-2-22-20000200002i−2i002i−2i0000002i2i−2i−2i000000000000002-20000000
χ262-22-2-222-22-2-222-2-22-20000200002i−2i002i−2i000000−2i−2i2i2i00000000000000-220000000
χ272-22-2-222-22-2-222-2-22-2000020000−2i2i00−2i2i0000002i2i−2i−2i00000000000000-220000000
χ282-22-2-222-22-2-222-2-22-2000020000−2i2i00−2i2i000000−2i−2i2i2i000000000000002-20000000
χ292-22-2-222-2-222-2-222-2-22i2i−2i−2i20000002i−2i00000000000000000000002-200002i−2i00000
χ302-22-2-222-2-222-2-222-2-22i2i−2i−2i20000002i−2i0000000000000000000000-220000−2i2i00000
χ312-22-2-222-2-222-2-222-2-2−2i−2i2i2i2000000−2i2i00000000000000000000002-20000−2i2i00000
χ322-22-2-222-2-222-2-222-2-2−2i−2i2i2i2000000−2i2i0000000000000000000000-2200002i−2i00000
χ332-22-2-222-2-2-222-2-22222i2i−2i−2i-200002i−2i−2i2i−2i2i00000000000000000000002-2000000000
χ342-22-2-222-2-2-222-2-22222i2i−2i−2i-20000−2i2i−2i2i2i−2i0000000000000000000000-22000000000
χ352-22-2-222-2-2-222-2-2222−2i−2i2i2i-200002i−2i2i−2i−2i2i0000000000000000000000-22000000000
χ362-22-2-222-2-2-222-2-2222−2i−2i2i2i-20000−2i2i2i−2i2i−2i00000000000000000000002-2000000000
χ372-2-22-22-222020-20-2002i−2i2i−2i022−2−2000000002-200i2−i2i2−i22−22i−2ii2i2−i2−i200000000002−2000
χ382-2-22-22-222020-20-2002i−2i2i−2i022−2−200000000-2200i2−i2i2−i22−2−2i2i−i2−i2i2i20000000000−22000
χ392-2-22-22-222020-20-2002i−2i2i−2i0−2−222000000002-200−i2i2−i2i2−222i−2i−i2−i2i2i20000000000−22000
χ402-2-22-22-222020-20-2002i−2i2i−2i0−2−22200000000-2200−i2i2−i2i2−22−2i2ii2i2−i2−i200000000002−2000
χ412-2-22-22-222020-20-200−2i2i−2i2i022−2−2000000002-200−i2i2−i2i22−2−2i2i−i2−i2i2i200000000002−2000
χ422-2-22-22-222020-20-200−2i2i−2i2i022−2−200000000-2200−i2i2−i2i22−22i−2ii2i2−i2−i20000000000−22000
χ432-2-22-22-222020-20-200−2i2i−2i2i0−2−222000000002-200i2−i2i2−i2−22−2i2ii2i2−i2−i20000000000−22000
χ442-2-22-22-222020-20-200−2i2i−2i2i0−2−22200000000-2200i2−i2i2−i2−222i−2i−i2−i2i2i200000000002−2000
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000
χ4644-44-4-44-404040-40-40000004-44-4000000000000000000000000000000000000000
χ4744-44-4-44-404040-40-4000000-44-44000000000000000000000000000000000000000
χ4844-44-4-44-40-40-404040000000000000000000000000000002i2−2i22i2−2i2000000000000000
χ4944-44-4-44-40-40-40404000000000000000000000000000000−2i22i2−2i22i2000000000000000
χ5044-4-444-4-440-40-4040000000000000000000000022−22−222200000000000000000000000
χ5144-4-444-4-440-40-40400000000000000000000000−222222−2200000000000000000000000
χ5244-4-444-4-4-404040-4004-4-4400000000000000000000000000000000000000000000
χ5344-4-444-4-4-404040-400-444-400000000000000000000000000000000000000000000
χ544-4444-4-4-40000000000000022−22−2222000000000022−22000000002-2-22000000000000000
χ554-4444-4-4-40000000000000022−22−22220000000000−222200000000-222-2000000000000000
χ564-4444-4-4-400000000000000−222222−22000000000022−2200000000-222-2000000000000000
χ574-4444-4-4-400000000000000−222222−220000000000−2222000000002-2-22000000000000000
χ584-44-4-444-444-4-444-4-440000-40000000000000000000000000000000000000000000
χ594-4-44-44-44-40-4040400000002222−22−220000000000000000−2222000000000000000000000
χ604-4-44-44-44-40-404040000000−22−222222000000000000000022−22000000000000000000000
χ614-4-4-44-444040-40-404000000000000000000000000000000000000000000000022−220
χ624-4-4-44-444040-40-4040000000000000000000000000000000000000000000000−22220
χ634-4-4-44-4440-404040-400000000000000004-40000000000000000000000000000000
χ644-4-4-44-4440-404040-40000000000000000-440000000000000000000000000000000
χ65888-8-8-8-88000000000000000000000000000000000000000000000000000000000

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