Finite Group Databasebeta

← Group #331663

Character table — Group #331663

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222444444444488888888888888888888888888881616161616161616323232
order12222222444444444488888888222244444444888888888888888844448888444
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-11111-1-1-1-111111111-1-1-1-111111-1-1-111-1-1-1-1-1
χ311111111111111111111111111-1-111-1-1-1-111111111-1-1-1-111111111-11-1-1-1-111-1-1-1
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
χ51111111111111111111111-1-1-1-11111111111-1-111-1-1-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-111-1
χ61111111111111111111111-1-1-1-111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11
χ71111111111111111111111-1-1-1-1-1-111-1-1-1-111-1-111-1-111111111-1-1-1-1-1-11111-1-1-1-11
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-11-1-1111111-1
χ9111111111111111111-1-1-1-11111111111-1-11111-1-1111111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11-11
χ10111111111111111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-111-11-1
χ11111111111111111111-1-1-1-11111-1-111-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-11-1
χ12111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-11-1-1-111111-11
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
χ14111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-11-1-111-1-1-111
χ15111111111111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111111-1-1-1-1-111-111
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
χ17222222222-22-22-22-2-2-20000222200220000-2-22200-2-20000000000000-2000000000
χ18222222222-22-22-22-2-2-20000222200-2-2000022-2-200-2-200000000000002000000000
χ19222222222-22-22-22-2-2-20000-2-2-2-200220000-2-2-2-2002200000000000002000000000
χ20222222222-22-22-22-2-2-20000-2-2-2-200-2-20000222200220000000000000-2000000000
χ2122222222-22-22-22-22-2-2222200002200-2-2220000-2-200000000000000-20000000000
χ2222222222-22-22-22-22-2-222220000-2-20022-2-20000-2-20000000000000020000000000
χ2322222222-22-22-22-22-2-2-2-2-2-200002200-2-2-2-20000220000000000000020000000000
χ2422222222-22-22-22-22-2-2-2-2-2-20000-2-200222200002200000000000000-20000000000
χ252-222-22-2-2020-20-2020022-2-2i2i2−i2−i22-200002-2000000i2−i2i2i2−i2−i20000i2i2−i2−i20000i2−i200000
χ262-222-22-2-2020-20-2020022-2-2i2i2−i2−i2-220000-22000000i2−i2−i2−i2i2i20000i2i2−i2−i20000−i2i200000
χ272-222-22-2-2020-20-2020022-2-2−i2−i2i2i22-200002-2000000−i2i2−i2−i2i2i20000−i2−i2i2i20000−i2i200000
χ282-222-22-2-2020-20-2020022-2-2−i2−i2i2i2-220000-22000000−i2i2i2i2−i2−i20000−i2−i2i2i20000i2−i200000
χ292-222-22-2-2020-20-20200-2-222i2i2−i2−i22-20000-22000000i2−i2i2i2−i2−i20000−i2−i2i2i20000−i2i200000
χ302-222-22-2-2020-20-20200-2-222i2i2−i2−i2-2200002-2000000i2−i2−i2−i2i2i20000−i2−i2i2i20000i2−i200000
χ312-222-22-2-2020-20-20200-2-222−i2−i2i2i22-20000-22000000−i2i2−i2−i2i2i20000i2i2−i2−i20000i2−i200000
χ322-222-22-2-2020-20-20200-2-222−i2−i2i2i2-2200002-2000000−i2i2i2i2−i2−i20000i2i2−i2−i20000−i2i200000
χ332-22-22-22-220-20-202000i2−i2i2−i22-22-2002-20000002-2i2−i2000000i2i2−i2−i2i2−i2i2−i2000000i2−i2000
χ342-22-22-22-220-20-202000i2−i2i2−i22-22-200-22000000-22i2−i2000000−i2−i2i2i2i2−i2i2−i2000000−i2i2000
χ352-22-22-22-220-20-202000i2−i2i2−i2-22-22002-2000000-22i2−i2000000i2i2−i2−i2−i2i2−i2i2000000−i2i2000
χ362-22-22-22-220-20-202000i2−i2i2−i2-22-2200-220000002-2i2−i2000000−i2−i2i2i2−i2i2−i2i2000000i2−i2000
χ372-22-22-22-220-20-202000−i2i2−i2i22-22-2002-20000002-2−i2i2000000−i2−i2i2i2−i2i2−i2i2000000−i2i2000
χ382-22-22-22-220-20-202000−i2i2−i2i22-22-200-22000000-22−i2i2000000i2i2−i2−i2−i2i2−i2i2000000i2−i2000
χ392-22-22-22-220-20-202000−i2i2−i2i2-22-22002-2000000-22−i2i2000000−i2−i2i2i2i2−i2i2−i2000000i2−i2000
χ402-22-22-22-220-20-202000−i2i2−i2i2-22-2200-220000002-2−i2i2000000i2i2−i2−i2i2−i2i2−i2000000−i2i2000
χ412-2-2-2-222222-2-222-2-22-20000000000000000000000002i−2i2i−2i2i−2i2i−2i0000002-20000000
χ422-2-2-2-222222-2-222-2-22-20000000000000000000000002i−2i2i−2i−2i2i−2i2i000000-220000000
χ432-2-2-2-222222-2-222-2-22-2000000000000000000000000−2i2i−2i2i2i−2i2i−2i000000-220000000
χ442-2-2-2-222222-2-222-2-22-2000000000000000000000000−2i2i−2i2i−2i2i−2i2i0000002-20000000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000
χ46444-4-4-4-4400000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000-222-200000000000
χ47444-4-4-4-4400000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000002-2-2200000000000
χ48444-4-4-4-440000000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000002-2-2200000000000
χ49444-4-4-4-440000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000-222-200000000000
χ5044-44-4-44-44040-40-4000000000000000000000000000000022−22−2222000000000000000
χ5144-44-4-44-44040-40-40000000000000000000000000000000−222222−22000000000000000
χ5244-44-4-44-4-40-4040400000000000000000004i−4i00000000000000000000000000000
χ5344-44-4-44-4-40-404040000000000000000000−4i4i00000000000000000000000000000
χ5444-4-444-4-404040-40-40000000000000000000000000022−22−22220000000000000000000
χ5544-4-444-4-404040-40-400000000000000000000000000−222222−220000000000000000000
χ5644-4-444-4-40-40-40404000000000000004i−4i000000000000000000000000000000000
χ5744-4-444-4-40-40-4040400000000000000−4i4i000000000000000000000000000000000
χ584-444-44-4-40-404040-40000002i22i2−2i2−2i200000000000000−2i22i200000000000000000000000
χ594-444-44-4-40-404040-4000000−2i2−2i22i22i2000000000000002i2−2i200000000000000000000000
χ604-44-44-44-4-404040-40002i2−2i22i2−2i20000000000000000−2i22i20000000000000000000000000
χ614-44-44-44-4-404040-4000−2i22i2−2i22i200000000000000002i2−2i20000000000000000000000000
χ624-4-4-4-44444-4-444-4-44-4400000000000000000000000000000000000000000000000
χ634-4-4-4-4444-444-4-444-4-4400000000000000000000000000000000000000000000000
χ644-4-4-4-4444-4-444-4-4444-400000000000000000000000000000000000000000000000
χ658-8-888-8-88000000000000000000000000000000000000000000000000000000000

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