Finite Group Databasebeta

← Group #337658

Character table — Group #337658

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222444444444488888888888888888888888888881616161616161616323232
order12222222444444444488888888224444444444888888888888888844448888244
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-111-1-11111-1-1-1-11111111111-11-1-111-1-1-1-1-1
χ311111111111111111111111111-1-11111-1-111-1-111111111-1-1-1-111111-1-1-1-1-111-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-111-1-1-1-1111
χ51111111111111111111111-1-1-1-11111-1-1111111-1-1111111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-111-1
χ61111111111111111111111-1-1-1-111-1-11111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-11
χ71111111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-11
χ81111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11-1-1-1111111-1
χ9111111111111111111-1-1-1-111111111111111-1-111-1-1-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-11-11
χ10111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1111111-1-11111-1-1-1-1-1-111-1-111-11-1
χ11111111111111111111-1-1-1-11111-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-11-1
χ12111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-11-1-111111-11
χ13111111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111111-1-1
χ14111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111111-1-1-111-1-1-111
χ15111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-11-1-1-1-111-111
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1111111111111-1-1-1-11-1-1
χ17222222222-22-22-22-2-2-2000022220022-2-200-2-200-2-20000000000000020000000000
χ18222222222-22-22-22-2-2-20000222200-2-222002200-2-200000000000000-20000000000
χ19222222222-22-22-22-2-2-20000-2-2-2-200222200-2-2002200000000000000-20000000000
χ20222222222-22-22-22-2-2-20000-2-2-2-200-2-2-2-2002200220000000000000020000000000
χ2122222222-22-22-22-22-2-222220000220000-2-20022000000-2-2000000000-2000000000
χ2222222222-22-22-22-22-2-222220000-2-200002200-2-2000000-2-20000000002000000000
χ2322222222-22-22-22-22-2-2-2-2-2-20000220000-2-200-2-2000000220000000002000000000
χ2422222222-22-22-22-22-2-2-2-2-2-20000-2-2000022002200000022000000000-2000000000
χ2522-2-22-22-2020-20-202002i2i−2i−2ii2i2−i2−i22-2000000002i−2ii2−i2000000i2i2−i2−i222−2−200002−200000
χ2622-2-22-22-2020-20-202002i2i−2i−2ii2i2−i2−i2-2200000000−2i2ii2−i2000000−i2−i2i2i222−2−20000−2200000
χ2722-2-22-22-2020-20-202002i2i−2i−2i−i2−i2i2i22-2000000002i−2i−i2i2000000−i2−i2i2i2−2−2220000−2200000
χ2822-2-22-22-2020-20-202002i2i−2i−2i−i2−i2i2i2-2200000000−2i2i−i2i2000000i2i2−i2−i2−2−22200002−200000
χ2922-2-22-22-2020-20-20200−2i−2i2i2ii2i2−i2−i22-200000000−2i2ii2−i2000000i2i2−i2−i2−2−2220000−2200000
χ3022-2-22-22-2020-20-20200−2i−2i2i2ii2i2−i2−i2-22000000002i−2ii2−i2000000−i2−i2i2i2−2−22200002−200000
χ3122-2-22-22-2020-20-20200−2i−2i2i2i−i2−i2i2i22-200000000−2i2i−i2i2000000−i2−i2i2i222−2−200002−200000
χ3222-2-22-22-2020-20-20200−2i−2i2i2i−i2−i2i2i2-22000000002i−2i−i2i2000000i2i2−i2−i222−2−20000−2200000
χ332-22-2-222-2-202020-2000i2−i2i2−i22i−2i2i−2i00002i−2i002-20000i2i2−i2−i2i2−i200002−22−20000002−2000
χ342-22-2-222-2-202020-2000i2−i2i2−i22i−2i2i−2i0000−2i2i00-220000−i2−i2i2i2i2−i200002−22−2000000−22000
χ352-22-2-222-2-202020-2000i2−i2i2−i2−2i2i−2i2i00002i−2i00-220000−i2−i2i2i2i2−i20000−22−220000002−2000
χ362-22-2-222-2-202020-2000i2−i2i2−i2−2i2i−2i2i0000−2i2i002-20000i2i2−i2−i2i2−i20000−22−22000000−22000
χ372-22-2-222-2-202020-2000−i2i2−i2i22i−2i2i−2i00002i−2i002-20000−i2−i2i2i2−i2i20000−22−22000000−22000
χ382-22-2-222-2-202020-2000−i2i2−i2i22i−2i2i−2i0000−2i2i00-220000i2i2−i2−i2−i2i20000−22−220000002−2000
χ392-22-2-222-2-202020-2000−i2i2−i2i2−2i2i−2i2i00002i−2i00-220000i2i2−i2−i2−i2i200002−22−2000000−22000
χ402-22-2-222-2-202020-2000−i2i2−i2i2−2i2i−2i2i0000−2i2i002-20000−i2−i2i2i2−i2i200002−22−20000002−2000
χ412-2-2-222-2222-2-222-2-22-200000000000000000000002-22-2002i−2i2i−2i0000002i−2i0000000
χ422-2-2-222-2222-2-222-2-22-200000000000000000000002-22-200−2i2i−2i2i000000−2i2i0000000
χ432-2-2-222-2222-2-222-2-22-20000000000000000000000-22-22002i−2i2i−2i000000−2i2i0000000
χ442-2-2-222-2222-2-222-2-22-20000000000000000000000-22-2200−2i2i−2i2i0000002i−2i0000000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000
χ4644-44-44-4-44040-40-400000000000004-400000000000000000000000000000000000
χ4744-44-44-4-44040-40-40000000000000-4400000000000000000000000000000000000
χ4844-44-44-4-4-40-4040400000000000000000000000002i2−2i2−2i22i2000000000000000000000
χ4944-44-44-4-4-40-404040000000000000000000000000−2i22i22i2−2i2000000000000000000000
χ5044-4-44-44-40-404040-40000002i22i2−2i2−2i2000000000000−2i22i20000000000000000000000000
χ5144-4-44-44-40-404040-4000000−2i2−2i22i22i20000000000002i2−2i20000000000000000000000000
χ524-4444-4-4-404040-40-400000000000000000000000000000022−22−2222000000000000000
χ534-4444-4-4-404040-40-4000000000000000000000000000000−222222−22000000000000000
χ544-4444-4-4-40-40-4040400000000000000004i−4i0000000000000000000000000000000
χ554-4444-4-4-40-40-404040000000000000000−4i4i0000000000000000000000000000000
χ564-44-4-444-440-40-4040002i2−2i22i2−2i20000000000000000000000−2i22i20000000000000000000
χ574-44-4-444-440-40-404000−2i22i2−2i22i200000000000000000000002i2−2i20000000000000000000
χ584-4-44-4-444000000000022−22−222222−22−22220000000000000000000000002-2-2200000000000
χ594-4-44-4-444000000000022−22−2222−222222−22000000000000000000000000-222-200000000000
χ604-4-44-4-4440000000000−222222−2222−22−2222000000000000000000000000-222-200000000000
χ614-4-44-4-4440000000000−222222−22−222222−220000000000000000000000002-2-2200000000000
χ624-4-4-444-444-4-444-4-44-4400000000000000000000000000000000000000000000000
χ634-4-4-444-44-444-4-444-4-4400000000000000000000000000000000000000000000000
χ644-4-4-444-44-4-444-4-4444-400000000000000000000000000000000000000000000000
χ65888-8-8-8-88000000000000000000000000000000000000000000000000000000000

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