Finite Group Databasebeta

← Group #276570

Character table — Group #276570

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222222244444488888888888888888888888881616161616161616161616163232
order12222222444444444444444444224444444888888888888888844448888888844
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ511111111111111111111111111-1-1-1-11-1-1-1-11111111111111111-1-1-1-111-1-1-1-111-1-1
χ611111111111111111111111111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ711111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-111
χ811111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ91111111111-1-1-1-1111111-1-111-1-11111-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11-1
χ101111111111-1-1-1-1111111-1-111-1-11111-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-1-111-11
χ111111111111-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11111-11
χ121111111111-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-111-1-11-1
χ131111111111-1-1-1-1111111-1-111-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1-11
χ141111111111-1-1-1-1111111-1-111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111-1
χ151111111111-1-1-1-1111111-1-111-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-111-1-1111-1
χ161111111111-1-1-1-1111111-1-111-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-1-11
χ17222222222-2222222-2-22-222-2-2-2-222-2-2-222-2-2000000000000000000000000000000
χ18222222222-2222222-2-22-222-2-2-2-2-2-222-2-2-222000000000000000000000000000000
χ19222222222-2-2-2-2-222-2-22-2-2-2-2-22222-2-22-2-222000000000000000000000000000000
χ20222222222-2-2-2-2-222-2-22-2-2-2-2-222-2-222222-2-2000000000000000000000000000000
χ2122222222-222222-2-222-22-2-2-2-2220000-2000022-2-222-2-20000000000000000000000
χ2222222222-222222-2-222-22-2-2-2-2220000-20000-2-222-2-2220000000000000000000000
χ2322222222-22-2-2-2-2-2-222-2222-2-2-2-200002000022-2-2-2-2220000000000000000000000
χ2422222222-22-2-2-2-2-2-222-2222-2-2-2-2000020000-2-22222-2-20000000000000000000000
χ2522222222-2-22222-2-2-2-2-2-2-2-222-2-200002000000000000000000000000002i−2i2i−2i0000
χ2622222222-2-22222-2-2-2-2-2-2-2-222-2-20000200000000000000000000000000−2i2i−2i2i0000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22222220000-2000000000000000000000000002i−2i−2i2i0000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22222220000-200000000000000000000000000−2i2i2i−2i0000
χ2922-222-2-2-2-2200002-2-2-222002-200000002i−2i2i−2i000000002i2i−2i−2i0000002-20000000000
χ3022-222-2-2-2-2200002-2-2-222002-200000002i−2i2i−2i00000000−2i−2i2i2i000000-220000000000
χ3122-222-2-2-2-2200002-2-2-222002-20000000−2i2i−2i2i000000002i2i−2i−2i000000-220000000000
χ3222-222-2-2-2-2200002-2-2-222002-20000000−2i2i−2i2i00000000−2i−2i2i2i0000002-20000000000
χ3322-222-2-2-2-2-200002-2222-200-2200000002i−2i−2i2i00000000000022-2-22i−2i000000000000
χ3422-222-2-2-2-2-200002-2222-200-2200000002i−2i−2i2i000000000000-2-222−2i2i000000000000
χ3522-222-2-2-2-2-200002-2222-200-220000000−2i2i2i−2i00000000000022-2-2−2i2i000000000000
χ3622-222-2-2-2-2-200002-2222-200-220000000−2i2i2i−2i000000000000-2-2222i−2i000000000000
χ372-2-22-2-2220222-2-2002-20-200002-2000000000002i−2i002i−2ii2−i2i2−i2i2−i2i2−i200002−200002−200
χ382-2-22-2-2220222-2-2002-20-200002-2000000000002i−2i002i−2i−i2i2−i2i2−i2i2−i2i20000−220000−2200
χ392-2-22-2-2220222-2-2002-20-200002-200000000000−2i2i00−2i2ii2−i2i2−i2i2−i2i2−i20000−220000−2200
χ402-2-22-2-2220222-2-2002-20-200002-200000000000−2i2i00−2i2i−i2i2−i2i2−i2i2−i2i200002−200002−200
χ412-2-22-2-22202-2-222002-20-20000-22000000000002i−2i00−2i2ii2−i2i2−i2−i2i2−i2i200002−20000−2200
χ422-2-22-2-22202-2-222002-20-20000-22000000000002i−2i00−2i2i−i2i2−i2i2i2−i2i2−i20000−2200002−200
χ432-2-22-2-22202-2-222002-20-20000-2200000000000−2i2i002i−2ii2−i2i2−i2−i2i2−i2i20000−2200002−200
χ442-2-22-2-22202-2-222002-20-20000-2200000000000−2i2i002i−2i−i2i2−i2i2i2−i2i2−i200002−20000−2200
χ45444-4-4-44-44000004-400-400000004-40000000000000000000000000000000000000
χ46444-4-4-44-44000004-400-40000000-440000000000000000000000000000000000000
χ47444-4-4-44-4-400000-440040000000004i−4i00000000000000000000000000000000000
χ48444-4-4-44-4-400000-44004000000000−4i4i00000000000000000000000000000000000
χ4944-444-4-4-4440000-44-4-4-4400-4400000000000000000000000000000000000000000
χ5044-444-4-4-44-40000-4444-4-4004-400000000000000000000000000000000000000000
χ5144-4-4-44-44404i−4i4i−4i-4-400404i−4i0000000000000000000000000000000000000000000
χ5244-4-4-44-4440−4i4i−4i4i-4-40040−4i4i0000000000000000000000000000000000000000000
χ5344-4-4-44-44-404i−4i4i−4i4400-40−4i4i0000000000000000000000000000000000000000000
χ5444-4-4-44-44-40−4i4i−4i4i4400-404i−4i0000000000000000000000000000000000000000000
χ554-444-44-4-404000000-440-40000000000000000000000022−22−2222000000000000000000
χ564-444-44-4-404000000-440-400000000000000000000000−222222−22000000000000000000
χ574-444-44-4-40-40000004-4040000000000000000000000000002i2−2i2−2i22i200000000000000
χ584-444-44-4-40-40000004-404000000000000000000000000000−2i22i22i2−2i200000000000000
χ594-44-44-4-44004i−4i−4i4i00000000000000000000022−22002i2−2i2000000000000000000000000
χ604-44-44-4-44004i−4i−4i4i000000000000000000000−222200−2i22i2000000000000000000000000
χ614-44-44-4-4400−4i4i4i−4i00000000000000000000022−2200−2i22i2000000000000000000000000
χ624-44-44-4-4400−4i4i4i−4i000000000000000000000−2222002i2−2i2000000000000000000000000
χ634-4-44-4-4440-444-4-400-44040000-44000000000000000000000000000000000000000
χ644-4-44-4-4440-4-4-44400-440400004-4000000000000000000000000000000000000000
χ658-8-8-8888-8000000000000000000000000000000000000000000000000000000000

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