Finite Group Databasebeta

← Group #337809

Character table — Group #337809

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222444444444488888888888888888888888888881616161616161616323232
order12222222444444444488888888224444444444888888888888888824448888444
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-1-1-111111111-1-1-1-1111111111-1-1-111-1-1-1-1-1
χ311111111111111111111111111-1-1111111-1-1-1-111111111-1-1-1-11111-11-1-1-1-111-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1111
χ51111111111111111111111-1-1-1-11111111111-1-111-1-1-1-1-1-11111-1-1-1-1-11-1-1-1-1-1-111-1
χ61111111111111111111111-1-1-1-111-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1-1-111-1-111-1-11
χ71111111111111111111111-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11-1-1-1111111-1
χ9111111111111111111-1-1-1-11111111111-1-11111-1-1111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-11-11
χ10111111111111111111-1-1-1-1111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-11-1
χ11111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-11-1
χ12111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-11-1-111111-11
χ13111111111111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111111-1-1
χ14111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-11-1-111-1-1-111
χ15111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-1-1-1-111-111
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111111111111111-1-1-1-11-1-1
χ17222222222-22-22-22-2-2-20000222222000000-2-2-2-200-2-200000000000020000000000
χ18222222222-22-22-22-2-2-200002222-2-2000000222200-2-2000000000000-20000000000
χ19222222222-22-22-22-2-2-20000-2-2-2-222000000-2-2220022000000000000-20000000000
χ20222222222-22-22-22-2-2-20000-2-2-2-2-2-200000022-2-2002200000000000020000000000
χ2122222222-22-22-22-22-2-2222200000022-2-2220000-2-2000000000000000-2000000000
χ2222222222-22-22-22-22-2-22222000000-2-222-2-20000-2-20000000000000002000000000
χ2322222222-22-22-22-22-2-2-2-2-2-200000022-2-2-2-20000220000000000000002000000000
χ2422222222-22-22-22-22-2-2-2-2-2-2000000-2-22222000022000000000000000-2000000000
χ252-2222-2-2-2-20-2020200022−2−222-2-2000000002i−2i2i−2i2−2000000i2i2−i2−i222−2−20000i2−i200000
χ262-2222-2-2-2-20-2020200022−2−222-2-200000000−2i2i−2i2i2−2000000−i2−i2i2i222−2−20000−i2i200000
χ272-2222-2-2-2-20-2020200022−2−2-2-222000000002i−2i−2i2i2−2000000i2i2−i2−i2−2−2220000−i2i200000
χ282-2222-2-2-2-20-2020200022−2−2-2-22200000000−2i2i2i−2i2−2000000−i2−i2i2i2−2−2220000i2−i200000
χ292-2222-2-2-2-20-20202000−2−22222-2-2000000002i−2i2i−2i−22000000−i2−i2i2i2−2−2220000−i2i200000
χ302-2222-2-2-2-20-20202000−2−22222-2-200000000−2i2i−2i2i−22000000i2i2−i2−i2−2−2220000i2−i200000
χ312-2222-2-2-2-20-20202000−2−222-2-222000000002i−2i−2i2i−22000000−i2−i2i2i222−2−20000i2−i200000
χ322-2222-2-2-2-20-20202000−2−222-2-22200000000−2i2i2i−2i−22000000i2i2−i2−i222−2−20000−i2i200000
χ332-22-2-2-22222-2-222-2-22-200000000000000000000000022-2-22i−2i2i−2i0000002i−2i0000000
χ342-22-2-2-22222-2-222-2-22-200000000000000000000000022-2-2−2i2i−2i2i000000−2i2i0000000
χ352-22-2-2-22222-2-222-2-22-2000000000000000000000000-2-2222i−2i2i−2i000000−2i2i0000000
χ362-22-2-2-22222-2-222-2-22-2000000000000000000000000-2-222−2i2i−2i2i0000002i−2i0000000
χ372-2-22-222-202020-20-2002i−2i2i−2i2−22−2002i−2i002-20000002−2i2−i2i2−i20000i2−i2i2−i20000002−2000
χ382-2-22-222-202020-20-2002i−2i2i−2i2−22−200−2i2i00-220000002−2−i2i2−i2i20000i2−i2i2−i2000000−22000
χ392-2-22-222-202020-20-2002i−2i2i−2i−22−22002i−2i002-2000000−22−i2i2−i2i20000−i2i2−i2i2000000−22000
χ402-2-22-222-202020-20-2002i−2i2i−2i−22−2200−2i2i00-22000000−22i2−i2i2−i20000−i2i2−i2i20000002−2000
χ412-2-22-222-202020-20-200−2i2i−2i2i2−22−2002i−2i00-220000002−2i2−i2i2−i20000−i2i2−i2i2000000−22000
χ422-2-22-222-202020-20-200−2i2i−2i2i2−22−200−2i2i002-20000002−2−i2i2−i2i20000−i2i2−i2i20000002−2000
χ432-2-22-222-202020-20-200−2i2i−2i2i−22−22002i−2i00-22000000−22−i2i2−i2i20000i2−i2i2−i20000002−2000
χ442-2-22-222-202020-20-200−2i2i−2i2i−22−2200−2i2i002-2000000−22i2−i2i2−i20000i2−i2i2−i2000000−22000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000
χ46444-4-44-4-440-40-404000000000004-40000000000000000000000000000000000000
χ47444-4-44-4-440-40-40400000000000-440000000000000000000000000000000000000
χ48444-4-44-4-4-404040-4000000000000000000000000000000022−22−2222000000000000000
χ49444-4-44-4-4-404040-40000000000000000000000000000000−222222−22000000000000000
χ5044-44-4-4-4400000000002i2−2i2−2i22i222−22−22220000000000000000000000002i−2i−2i2i00000000000
χ5144-44-4-4-4400000000002i2−2i2−2i22i2−222222−22000000000000000000000000−2i2i2i−2i00000000000
χ5244-44-4-4-440000000000−2i22i22i2−2i222−22−2222000000000000000000000000−2i2i2i−2i00000000000
χ5344-44-4-4-440000000000−2i22i22i2−2i2−222222−220000000000000000000000002i−2i−2i2i00000000000
χ5444-4-44-44-4040-40-404000000000000000000000000002i2−2i2−2i22i20000000000000000000
χ5544-4-44-44-4040-40-40400000000000000000000000000−2i22i22i2−2i20000000000000000000
χ5644-4-44-44-40-404040-4000000000000004i−4i000000000000000000000000000000000
χ5744-4-44-44-40-404040-400000000000000−4i4i000000000000000000000000000000000
χ584-4444-4-4-44040-40-40002222−22−220000000000000000−22220000000000000000000000000
χ594-4444-4-4-44040-40-4000−22−222222000000000000000022−220000000000000000000000000
χ604-44-4-4-4444-4-444-4-44-4400000000000000000000000000000000000000000000000
χ614-44-4-4-444-444-4-444-4-4400000000000000000000000000000000000000000000000
χ624-44-4-4-444-4-444-4-4444-400000000000000000000000000000000000000000000000
χ634-4-44-444-40-40-4040400000022−2222−2200000000000000−222200000000000000000000000
χ644-4-44-444-40-40-40404000000−2222−22220000000000000022−2200000000000000000000000
χ658-8-8-888-88000000000000000000000000000000000000000000000000000000000

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