Finite Group Databasebeta

← Group #335683

Character table — Group #335683

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222444444444488888888888888888888888888881616161616161616323232
order12222222444444444488888888222244444444888888888888888844448888444
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1111-1-1-1-1-1
χ311111111111111111111111111-1-111-1-1-1-111111111-1-1-1-1111111111-1-1-1-1-111-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-111-1-1-1-1-1111
χ51111111111111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11-1-1
χ61111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-111111-111
χ71111111111111111111111-1-1-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111111111-1-1-1-1-111-1-1-1111-1-1
χ9111111111111111111-1-1-1-111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-11-1-1-1-111-1
χ10111111111111111111-1-1-1-1111111-1-11111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11
χ11111111111111111111-1-1-1-11111-1-111-1-1-1-111-1-1-1-11111111111-1-1-1-1-111-111-1-1-1-11
χ12111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11-1-1-1111111-1
χ13111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-11-1-1111-11
χ14111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-11-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-11111-11-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1111111111-1-1-111-1-11-11
χ172222222222-2-2-222-2-2-2000022222200-2-222000000-2-2000000000000000-20000000
χ182222222222-2-2-222-2-2-200002222-2-20022-2-2000000-2-200000000000000020000000
χ192222222222-2-2-222-2-2-20000-2-2-2-2220022-2-200000022000000000000000-20000000
χ202222222222-2-2-222-2-2-20000-2-2-2-2-2-200-2-2220000002200000000000000020000000
χ2122222222-2-2222-2-22-2-22222000000220000-2-222-2-200000000000000-20000000000
χ2222222222-2-2222-2-22-2-22222000000-2-2000022-2-2-2-20000000000000020000000000
χ2322222222-2-2222-2-22-2-2-2-2-2-2000000220000-2-2-2-2220000000000000020000000000
χ2422222222-2-2222-2-22-2-2-2-2-2-2000000-2-2000022222200000000000000-20000000000
χ2522-22-2-2-22002-2-2002002i2i−2i−2ii2i2−i2−i2002-20000002i−2i00i2−i20000i2i2−i2−i222−2−20000002−2000
χ2622-22-2-2-22002-2-2002002i2i−2i−2ii2i2−i2−i200-22000000−2i2i00i2−i20000−i2−i2i2i222−2−2000000−22000
χ2722-22-2-2-22002-2-2002002i2i−2i−2i−i2−i2i2i2002-20000002i−2i00−i2i20000−i2−i2i2i2−2−222000000−22000
χ2822-22-2-2-22002-2-2002002i2i−2i−2i−i2−i2i2i200-22000000−2i2i00−i2i20000i2i2−i2−i2−2−2220000002−2000
χ2922-22-2-2-22002-2-200200−2i−2i2i2ii2i2−i2−i2002-2000000−2i2i00i2−i20000i2i2−i2−i2−2−222000000−22000
χ3022-22-2-2-22002-2-200200−2i−2i2i2ii2i2−i2−i200-220000002i−2i00i2−i20000−i2−i2i2i2−2−2220000002−2000
χ3122-22-2-2-22002-2-200200−2i−2i2i2i−i2−i2i2i2002-2000000−2i2i00−i2i20000−i2−i2i2i222−2−20000002−2000
χ3222-22-2-2-22002-2-200200−2i−2i2i2i−i2−i2i2i200-220000002i−2i00−i2i20000i2i2−i2−i222−2−2000000−22000
χ332-22-2-22-2222-22-2-2-22-2200000000000000000000000022-2-22i−2i2i−2i000002i−2i00000000
χ342-22-2-22-2222-22-2-2-22-2200000000000000000000000022-2-2−2i2i−2i2i00000−2i2i00000000
χ352-22-2-22-2222-22-2-2-22-22000000000000000000000000-2-2222i−2i2i−2i00000−2i2i00000000
χ362-22-2-22-2222-22-2-2-22-22000000000000000000000000-2-222−2i2i−2i2i000002i−2i00000000
χ372-2-2222-2-22-20002-2000i2−i2i2−i22-22-22-200002-20000i2−i200i2−i2i2−i20000i2−i2i2−i20000i2−i200000
χ382-2-2222-2-22-20002-2000i2−i2i2−i22-22-2-220000-220000i2−i200−i2i2−i2i20000i2−i2i2−i20000−i2i200000
χ392-2-2222-2-22-20002-2000i2−i2i2−i2-22-222-20000-220000i2−i200−i2i2−i2i20000−i2i2−i2i20000i2−i200000
χ402-2-2222-2-22-20002-2000i2−i2i2−i2-22-22-2200002-20000i2−i200i2−i2i2−i20000−i2i2−i2i20000−i2i200000
χ412-2-2222-2-22-20002-2000−i2i2−i2i22-22-22-200002-20000−i2i200−i2i2−i2i20000−i2i2−i2i20000−i2i200000
χ422-2-2222-2-22-20002-2000−i2i2−i2i22-22-2-220000-220000−i2i200i2−i2i2−i20000−i2i2−i2i20000i2−i200000
χ432-2-2222-2-22-20002-2000−i2i2−i2i2-22-222-20000-220000−i2i200i2−i2i2−i20000i2−i2i2−i20000−i2i200000
χ442-2-2222-2-22-20002-2000−i2i2−i2i2-22-22-2200002-20000−i2i200−i2i2−i2i20000i2−i2i2−i20000i2−i200000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000
χ4644-44-4-4-4400-44400-40000002i22i2−2i2−2i200000000000000−2i22i200000000000000000000000
χ4744-44-4-4-4400-44400-4000000−2i2−2i22i22i2000000000000002i2−2i200000000000000000000000
χ4844-4-4-444-44-4000-440000000000000000000000000002i2−2i2−2i22i20000000000000000000
χ4944-4-4-444-44-4000-44000000000000000000000000000−2i22i22i2−2i20000000000000000000
χ5044-4-4-444-4-440004-40000000000000004i−4i000000000000000000000000000000000
χ5144-4-4-444-4-440004-4000000000000000−4i4i000000000000000000000000000000000
χ524-444-4-44-4000000000022−22−22222i2−2i2−2i22i2000000000000000000000000−2i2i2i−2i00000000000
χ534-444-4-44-4000000000022−22−2222−2i22i22i2−2i20000000000000000000000002i−2i−2i2i00000000000
χ544-444-4-44-40000000000−222222−222i2−2i2−2i22i20000000000000000000000002i−2i−2i2i00000000000
χ554-444-4-44-40000000000−222222−22−2i22i22i2−2i2000000000000000000000000−2i2i2i−2i00000000000
χ564-44-4-44-44444-44-4-4-44-400000000000000000000000000000000000000000000000
χ574-44-4-44-44-4-44-4444-4-4400000000000000000000000000000000000000000000000
χ584-44-4-44-44-4-4-44-44444-400000000000000000000000000000000000000000000000
χ594-4-4444-4-4-44000-440002i2−2i22i2−2i20000000000000000−2i22i20000000000000000000000000
χ604-4-4444-4-4-44000-44000−2i22i2−2i22i200000000000000002i2−2i20000000000000000000000000
χ614-4-4-44-4440044-400-40000000000000000004i−4i00000000000000000000000000000
χ624-4-4-44-4440044-400-4000000000000000000−4i4i00000000000000000000000000000
χ634-4-4-44-44400-4-4400400000000000000000000000000000022−22−2222000000000000000
χ644-4-4-44-44400-4-44004000000000000000000000000000000−222222−22000000000000000
χ65888-88-8-8-8000000000000000000000000000000000000000000000000000000000

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