Finite Group Databasebeta

← Group #344179

Character table — Group #344179

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444488888888888888888888888844444444444444448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-11-1-1-11-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-11111-1-1-11-1-1-11-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111
χ51111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-11111111-1-1-1-1-1-11-1
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-11-111-1-11111-11
χ71111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-11-1-111-1-1-1-1-11
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11-111-1-1-1-11111111-1
χ9111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1111-1-1-111-1-1-1-111-1-11-1
χ10111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111111-1-1-1-1-1-1-111-11
χ11111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-11111111-1-1-11
χ12111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-1-1-11111-1-1111-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-111-1-111-1-11111
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-11111-1-1-11111-1-1-1-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1111-111-1111-1-1-1-111-1-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-111-1-1-1-111-1-111-1-111
χ17222222222-2-22-222-2-2-222220000-2-2-2-2000000000000000022-2-20002000-20000000000
χ18222222222-2-22-222-2-2-222220000-2-2-2-20000000000000000-2-222000-200020000000000
χ19222222222-2-22-222-2-2-2-2-2-2-20000222200000000000000002222000-2000-20000000000
χ20222222222-2-22-222-2-2-2-2-2-2-2000022220000000000000000-2-2-2-2000200020000000000
χ2122222222-222-22-2-22-2-2000022220000-2-2-2-2000000002222000000-2000-200000000000
χ2222222222-222-22-2-22-2-2000022220000-2-2-2-200000000-2-2-2-20000002000200000000000
χ2322222222-222-22-2-22-2-20000-2-2-2-2000022220000000022-2-20000002000-200000000000
χ2422222222-222-22-2-22-2-20000-2-2-2-20000222200000000-2-222000000-2000200000000000
χ2522-2-22-22-202-20-20020022−2−22i2i−2i−2i22−2−20000i2i2i2i2−i2−i2−i2−i22i−2i2-2000000000000i2−i22−2000000
χ2622-2-22-22-202-20-20020022−2−22i2i−2i−2i22−2−20000i2i2i2i2−i2−i2−i2−i2−2i2i-22000000000000−i2i2−22000000
χ2722-2-22-22-202-20-20020022−2−2−2i−2i2i2i22−2−20000−i2−i2−i2−i2i2i2i2i22i−2i-22000000000000i2−i2−22000000
χ2822-2-22-22-202-20-20020022−2−2−2i−2i2i2i22−2−20000−i2−i2−i2−i2i2i2i2i2−2i2i2-2000000000000−i2i22−2000000
χ2922-2-22-22-202-20-200200−2−2222i2i−2i−2i−2−2220000−i2−i2−i2−i2i2i2i2i22i−2i2-2000000000000−i2i2−22000000
χ3022-2-22-22-202-20-200200−2−2222i2i−2i−2i−2−2220000−i2−i2−i2−i2i2i2i2i2−2i2i-22000000000000i2−i22−2000000
χ3122-2-22-22-202-20-200200−2−222−2i−2i2i2i−2−2220000i2i2i2i2−i2−i2−i2−i22i−2i-22000000000000−i2i22−2000000
χ3222-2-22-22-202-20-200200−2−222−2i−2i2i2i−2−2220000i2i2i2i2−i2−i2−i2−i2−2i2i2-2000000000000i2−i2−22000000
χ332-222-2-22-22-2-2-222-222-200000000000000002i2i−2i−2i2i2i−2i−2i000000002-2002i−2i000000000000
χ342-222-2-22-22-2-2-222-222-200000000000000002i2i−2i−2i2i2i−2i−2i00000000-2200−2i2i000000000000
χ352-222-2-22-22-2-2-222-222-20000000000000000−2i−2i2i2i−2i−2i2i2i000000002-200−2i2i000000000000
χ362-222-2-22-22-2-2-222-222-20000000000000000−2i−2i2i2i−2i−2i2i2i00000000-22002i−2i000000000000
χ372-2-2222-2-2-200202-20000000i2−i2i2−i22i−2i2i−2ii2i2−i2−i22−22−22−22−200002-22i−2i000000000000i2−i22−200
χ382-2-2222-2-2-200202-20000000i2−i2i2−i22i−2i2i−2ii2i2−i2−i22−22−22−22−20000-22−2i2i000000000000−i2i2−2200
χ392-2-2222-2-2-200202-20000000i2−i2i2−i2−2i2i−2i2ii2i2−i2−i2−22−22−22−2200002-2−2i2i000000000000i2−i2−2200
χ402-2-2222-2-2-200202-20000000i2−i2i2−i2−2i2i−2i2ii2i2−i2−i2−22−22−22−220000-222i−2i000000000000−i2i22−200
χ412-2-2222-2-2-200202-20000000−i2i2−i2i22i−2i2i−2i−i2−i2i2i2−22−22−22−2200002-22i−2i000000000000−i2i2−2200
χ422-2-2222-2-2-200202-20000000−i2i2−i2i22i−2i2i−2i−i2−i2i2i2−22−22−22−220000-22−2i2i000000000000i2−i22−200
χ432-2-2222-2-2-200202-20000000−i2i2−i2i2−2i2i−2i2i−i2−i2i2i22−22−22−22−200002-2−2i2i000000000000−i2i22−200
χ442-2-2222-2-2-200202-20000000−i2i2−i2i2−2i2i−2i2i−i2−i2i2i22−22−22−22−20000-222i−2i000000000000i2−i2−2200
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ46444-4-44-4-4000000000022−2222−220000000022−2222−222-2-22-222-200000000000000000000000000
χ47444-4-44-4-4000000000022−2222−2200000000−2222−2222-222-22-2-2200000000000000000000000000
χ48444-4-44-4-40000000000−2222−22220000000022−2222−22-222-22-2-2200000000000000000000000000
χ49444-4-44-4-40000000000−2222−222200000000−2222−22222-2-22-222-200000000000000000000000000
χ5044-44-4-4-4440040-4-40004-4-440000000000000000000000000000000000000000000000
χ5144-44-4-4-4440040-4-4000-444-40000000000000000000000000000000000000000000000
χ5244-44-4-4-44-400-404400000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000
χ5344-44-4-4-44-400-40440000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000
χ5444-4-44-44-40-440400-4002222−22−220000−22−22222200000000000000000000000000000000000000
χ5544-4-44-44-40-440400-400−22−22222200002222−22−2200000000000000000000000000000000000000
χ564-444-4-44-4444-4-44-4-4-4400000000000000000000000000000000000000000000000000
χ574-444-4-44-4-4444-4-44-44-400000000000000000000000000000000000000000000000000
χ584-444-4-44-4-4-4-444-444-4400000000000000000000000000000000000000000000000000
χ594-44-44-4-440000000000000022−22−22222i2−2i2−2i22i20000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000
χ604-44-44-4-440000000000000022−22−2222−2i22i22i2−2i200002i−2i2i−2i−2i2i−2i2i00000000000000000000000000
χ614-44-44-4-4400000000000000−222222−222i2−2i2−2i22i200002i−2i2i−2i−2i2i−2i2i00000000000000000000000000
χ624-44-44-4-4400000000000000−222222−22−2i22i22i2−2i20000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000
χ634-4-4444-4-4400-40-4400000002i2−2i22i2−2i20000−2i2−2i22i22i20000000000000000000000000000000000
χ644-4-4444-4-4400-40-440000000−2i22i2−2i22i200002i22i2−2i2−2i20000000000000000000000000000000000
χ654-4-4-4-444404-40400-4000000000000004i−4i−4i4i0000000000000000000000000000000000
χ664-4-4-4-444404-40400-400000000000000−4i4i4i−4i0000000000000000000000000000000000
χ674-4-4-4-44440-440-40040000000000000000002222−22−22−22−22222200000000000000000000000000
χ684-4-4-4-44440-440-4004000000000000000000−22−2222222222−22−2200000000000000000000000000

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