Finite Group Databasebeta

← Group #333403

Character table — Group #333403

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444488888888888888888888888844444444224444448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-111-1-1-1-1-111-1-1-111-1-111-1-1-1-1
χ3111111111111111111111111111111111111111111-1-111-1-111-1-11-1-11-1-1-1-111-1-111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111
χ51111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111-111-1-1-1-1-1-111-11
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1111-1-1-1-111-1-1-1-11-1
χ71111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111-1-1-1-1-111-1-111111-1
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1111111111-1-1-11
χ9111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-1111-1-1-1-111-1-11-1
χ10111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-11-1-1-1-1-1-1111111-11
χ11111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111111-111-1-111-1-1-1-1-1-1-11
χ12111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11-1111111-1-1111-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1111111-1-1-1-1-1-1
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-11-11-1-111-1-1-1-11111
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11-11-1-1-1-1-11111-1-111
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-11111-1-1-1-11111-1-1
χ17222222222-22-22-22-2-2-2000022220000-2-2-2-200000000002200-2-200-2002000000000000
χ18222222222-22-22-22-2-2-2000022220000-2-2-2-20000000000-2-2002200200-2000000000000
χ19222222222-22-22-22-2-2-20000-2-2-2-200002222000000000022002200-200-2000000000000
χ20222222222-22-22-22-2-2-20000-2-2-2-2000022220000000000-2-200-2-2002002000000000000
χ2122222222-22-22-22-22-2-222220000-2-2-2-20000000000002200-2-200000-220000000000000
χ2222222222-22-22-22-22-2-222220000-2-2-2-2000000000000-2-20022000002-20000000000000
χ2322222222-22-22-22-22-2-2-2-2-2-20000222200000000000022002200000-2-20000000000000
χ2422222222-22-22-22-22-2-2-2-2-2-200002222000000000000-2-200-2-200000220000000000000
χ252-22-222-2-2020-20-202000000i2i2−i2−i222-2-2i2i2−i2−i2i2i2i2i2−i2−i2−i2−i22i−2i002i−2i00000000002−2002−20000
χ262-22-222-2-2020-20-202000000i2i2−i2−i222-2-2i2i2−i2−i2i2i2i2i2−i2−i2−i2−i2−2i2i00−2i2i0000000000−2200−220000
χ272-22-222-2-2020-20-202000000i2i2−i2−i2-2-222i2i2−i2−i2−i2−i2−i2−i2i2i2i2i22i−2i00−2i2i0000000000−22002−20000
χ282-22-222-2-2020-20-202000000i2i2−i2−i2-2-222i2i2−i2−i2−i2−i2−i2−i2i2i2i2i2−2i2i002i−2i00000000002−200−220000
χ292-22-222-2-2020-20-202000000−i2−i2i2i222-2-2−i2−i2i2i2−i2−i2−i2−i2i2i2i2i22i−2i002i−2i0000000000−2200−220000
χ302-22-222-2-2020-20-202000000−i2−i2i2i222-2-2−i2−i2i2i2−i2−i2−i2−i2i2i2i2i2−2i2i00−2i2i00000000002−2002−20000
χ312-22-222-2-2020-20-202000000−i2−i2i2i2-2-222−i2−i2i2i2i2i2i2i2−i2−i2−i2−i22i−2i00−2i2i00000000002−200−220000
χ322-22-222-2-2020-20-202000000−i2−i2i2i2-2-222−i2−i2i2i2i2i2i2i2−i2−i2−i2−i2−2i2i002i−2i0000000000−22002−20000
χ332-2-222-22-2-202020-2000i2i2−i2−i20000i2−i2i2−i22i−2i2i−2i22−2−222−2−2002-2002i−2i00000000002−200i2−i200
χ342-2-222-22-2-202020-2000i2i2−i2−i20000i2−i2i2−i22i−2i2i−2i22−2−222−2−200-2200−2i2i0000000000−2200−i2i200
χ352-2-222-22-2-202020-2000i2i2−i2−i20000i2−i2i2−i2−2i2i−2i2i−2−222−2−222002-200−2i2i0000000000−2200i2−i200
χ362-2-222-22-2-202020-2000i2i2−i2−i20000i2−i2i2−i2−2i2i−2i2i−2−222−2−22200-22002i−2i00000000002−200−i2i200
χ372-2-222-22-2-202020-2000−i2−i2i2i20000−i2i2−i2i22i−2i2i−2i−2−222−2−222002-2002i−2i0000000000−2200−i2i200
χ382-2-222-22-2-202020-2000−i2−i2i2i20000−i2i2−i2i22i−2i2i−2i−2−222−2−22200-2200−2i2i00000000002−200i2−i200
χ392-2-222-22-2-202020-2000−i2−i2i2i20000−i2i2−i2i2−2i2i−2i2i22−2−222−2−2002-200−2i2i00000000002−200−i2i200
χ402-2-222-22-2-202020-2000−i2−i2i2i20000−i2i2−i2i2−2i2i−2i2i22−2−222−2−200-22002i−2i0000000000−2200i2−i200
χ412-2-2-2-2222-2-222-2-222-2200000000000000002-22-22-22-2000000002-200002-20000000000
χ422-2-2-2-2222-2-222-2-222-2200000000000000002-22-22-22-200000000-220000-220000000000
χ432-2-2-2-2222-2-222-2-222-220000000000000000-22-22-22-22000000002-20000-220000000000
χ442-2-2-2-2222-2-222-2-222-220000000000000000-22-22-22-2200000000-2200002-20000000000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ46444-4-4-44-44040-40-4000000000000000000022−22−222222−22−222200000000000000000000000000
χ47444-4-4-44-44040-40-40000000000000000000−222222−22−222222−2200000000000000000000000000
χ48444-4-4-44-4-40-4040400000004i−4i4i−4i000000000000000000000000000000000000000000
χ49444-4-4-44-4-40-404040000000−4i4i−4i4i000000000000000000000000000000000000000000
χ5044-44-44-4-404040-40-4004-44-40000000000000000000000000000000000000000000000
χ5144-44-44-4-404040-40-400-44-440000000000000000000000000000000000000000000000
χ5244-44-44-4-40-40-404040000000000000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000
χ5344-44-44-4-40-40-40404000000000000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000
χ5444-4-44-4-440000000000000000002i2−2i2−2i22i222−22−2222−2i−2i2i2i2i2i−2i−2i00000000000000000000000000
χ5544-4-44-4-440000000000000000002i2−2i2−2i22i2−222222−222i2i−2i−2i−2i−2i2i2i00000000000000000000000000
χ5644-4-44-4-44000000000000000000−2i22i22i2−2i222−22−22222i2i−2i−2i−2i−2i2i2i00000000000000000000000000
χ5744-4-44-4-44000000000000000000−2i22i22i2−2i2−222222−22−2i−2i2i2i2i2i−2i−2i00000000000000000000000000
χ584-444-4-4-4400000000002i2−2i2−2i22i222−22−2222000000002i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ594-444-4-4-4400000000002i2−2i2−2i22i2−222222−2200000000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ604-444-4-4-440000000000−2i22i22i2−2i222−22−222200000000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ614-444-4-4-440000000000−2i22i22i2−2i2−222222−22000000002i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ624-44-444-4-40-404040-40000002i22i2−2i2−2i20000−2i2−2i22i22i20000000000000000000000000000000000
χ634-44-444-4-40-404040-4000000−2i2−2i22i22i200002i22i2−2i2−2i20000000000000000000000000000000000
χ644-4-444-44-440-40-4040002i22i2−2i2−2i20000−2i22i2−2i22i200000000000000000000000000000000000000
χ654-4-444-44-440-40-404000−2i2−2i22i22i200002i2−2i22i2−2i200000000000000000000000000000000000000
χ664-4-4-4-444444-4-444-4-4-4400000000000000000000000000000000000000000000000000
χ674-4-4-4-44444-4-444-4-444-400000000000000000000000000000000000000000000000000
χ684-4-4-4-4444-444-4-444-44-400000000000000000000000000000000000000000000000000

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