Finite Group Databasebeta

← Group #311746

Character table — Group #311746

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444488888888888888888888888844444444444444448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1111-11-1-1-1-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-11111-1-1-11-11-1-1-1-1-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-11111-1-1-1-111-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111111111-1-111-1-1
χ9111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1111-1-111-1-111-1-1-1-11-1
χ10111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-111-1-1-1-1111111-11
χ11111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1111-1-111-1-1-1-1-1-1-11
χ12111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-11111-1-111111-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-11-1-1-11111-1-1-1-111-11
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-111111-1-111-1-111-1-11-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111111-1-1-111-1-1-1-111-1-1111-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-11-1-111-1-11111-1-1-11
χ17222222222-22-2-222-2-2-2000000002222-2-2-2-2000000000022-2-2000-20200000000000000
χ18222222222-22-2-222-2-2-2000000002222-2-2-2-20000000000-2-22200020-200000000000000
χ19222222222-22-2-222-2-2-200000000-2-2-2-22222000000000022-2-200020-200000000000000
χ20222222222-22-2-222-2-2-200000000-2-2-2-222220000000000-2-222000-20200000000000000
χ2122222222-22-222-2-22-2-22222-2-2-2-2000000000000000022000022-20-2000000000000000
χ2222222222-22-222-2-22-2-22222-2-2-2-20000000000000000-2-20000-2-2202000000000000000
χ2322222222-22-222-2-22-2-2-2-2-2-222220000000000000000220000-2-220-2000000000000000
χ2422222222-22-222-2-22-2-2-2-2-2-222220000000000000000-2-2000022-202000000000000000
χ2522-22-2-2-2222-2-2-22-22-222i2i−2i−2i2i2i−2i−2i00000000000000000000000000002i−2i2-20000000000
χ2622-22-2-2-2222-2-2-22-22-222i2i−2i−2i2i2i−2i−2i0000000000000000000000000000−2i2i-220000000000
χ2722-22-2-2-2222-2-2-22-22-22−2i−2i2i2i−2i−2i2i2i00000000000000000000000000002i−2i-220000000000
χ2822-22-2-2-2222-2-2-22-22-22−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000−2i2i2-20000000000
χ2922-22-2-2-22-222-2-2-2222-22i2i−2i−2i−2i−2i2i2i0000000000000000002i−2i2i−2i000000000000002-20000
χ3022-22-2-2-22-222-2-2-2222-22i2i−2i−2i−2i−2i2i2i000000000000000000−2i2i−2i2i00000000000000-220000
χ3122-22-2-2-22-222-2-2-2222-2−2i−2i2i2i2i2i−2i−2i0000000000000000002i−2i2i−2i00000000000000-220000
χ3222-22-2-2-22-222-2-2-2222-2−2i−2i2i2i2i2i−2i−2i000000000000000000−2i2i−2i2i000000000000002-20000
χ3322-22-2-2-22-2-2222-22-2-2200000000000000002222-2-2-2-2002i−2i−2i2i00000000000000002i−2i00
χ3422-22-2-2-22-2-2222-22-2-2200000000000000002222-2-2-2-200−2i2i2i−2i0000000000000000−2i2i00
χ3522-22-2-2-22-2-2222-22-2-220000000000000000-2-2-2-22222002i−2i−2i2i0000000000000000−2i2i00
χ3622-22-2-2-22-2-2222-22-2-220000000000000000-2-2-2-2222200−2i2i2i−2i00000000000000002i−2i00
χ372-2-2222-2-20-202-2002002-22-2000022−2−222−2−222−2−222−2−22i−2i00002i−2i00000000i2−i2i2−i2000000
χ382-2-2222-2-20-202-2002002-22-2000022−2−222−2−222−2−222−2−2−2i2i0000−2i2i00000000−i2i2−i2i2000000
χ392-2-2222-2-20-202-2002002-22-20000−2−222−2−222−2−222−2−2222i−2i00002i−2i00000000−i2i2−i2i2000000
χ402-2-2222-2-20-202-2002002-22-20000−2−222−2−222−2−222−2−222−2i2i0000−2i2i00000000i2−i2i2−i2000000
χ412-2-2222-2-20-202-200200-22-22000022−2−222−2−2−2−222−2−2222i−2i0000−2i2i00000000−i2i2i2−i2000000
χ422-2-2222-2-20-202-200200-22-22000022−2−222−2−2−2−222−2−222−2i2i00002i−2i00000000i2−i2−i2i2000000
χ432-2-2222-2-20-202-200200-22-220000−2−222−2−22222−2−222−2−22i−2i0000−2i2i00000000i2−i2−i2i2000000
χ442-2-2222-2-20-202-200200-22-220000−2−222−2−22222−2−222−2−2−2i2i00002i−2i00000000−i2i2i2−i2000000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ46444-4-44-4-440-400-440000000000000004-44-40000000000000000000000000000000000
χ47444-4-44-4-440-400-44000000000000000-44-440000000000000000000000000000000000
χ48444-4-44-4-4-404004-4000000000000000000022−2222−2222−2222−2200000000000000000000000000
χ49444-4-44-4-4-404004-40000000000000000000−2222−2222−2222−222200000000000000000000000000
χ5044-44-4-4-444-4-4444-4-44-400000000000000000000000000000000000000000000000000
χ5144-4-44-44-440400-4-4000000000000000000022−2222−22−2222−222200000000000000000000000000
χ5244-4-44-44-440400-4-40000000000000000000−2222−222222−2222−2200000000000000000000000000
χ5344-4-44-44-4-40-40044000000000004i−4i4i−4i00000000000000000000000000000000000000
χ5444-4-44-44-4-40-4004400000000000−4i4i−4i4i00000000000000000000000000000000000000
χ554-444-4-44-40404-400-40000000000000000002222−22−22−22−22222200000000000000000000000000
χ564-444-4-44-40404-400-4000000000000000000−22−2222222222−22−2200000000000000000000000000
χ574-444-4-44-40-40-44004004i−4i−4i4i0000000000000000000000000000000000000000000000
χ584-444-4-44-40-40-4400400−4i4i4i−4i0000000000000000000000000000000000000000000000
χ594-44-44-4-44000000000000002i2−2i22i2−2i22i2−2i2−2i22i200002-2-22-222-200000000000000000000000000
χ604-44-44-4-44000000000000002i2−2i22i2−2i2−2i22i22i2−2i20000-222-22-2-2200000000000000000000000000
χ614-44-44-4-4400000000000000−2i22i2−2i22i22i2−2i2−2i22i20000-222-22-2-2200000000000000000000000000
χ624-44-44-4-4400000000000000−2i22i2−2i22i2−2i22i22i2−2i200002-2-22-222-200000000000000000000000000
χ634-4-4444-4-4040-4400-400000000002222−22−22−22−2222220000000000000000000000000000000000
χ644-4-4444-4-4040-4400-40000000000−22−2222222222−22−220000000000000000000000000000000000
χ654-4-4-4-44440000000000000022−22−2222000022−22−22222-2-222-2-2200000000000000000000000000
χ664-4-4-4-44440000000000000022−22−22220000−222222−22-222-2-222-200000000000000000000000000
χ674-4-4-4-444400000000000000−222222−22000022−22−2222-222-2-222-200000000000000000000000000
χ684-4-4-4-444400000000000000−222222−220000−222222−222-2-222-2-2200000000000000000000000000

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