Finite Group Databasebeta

← Group #275993

Character table — Group #275993

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222222244444488888888888888888888888881616161616161616161616163232
order12222222444444444444444444224444444888888888888888844448888888824
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
χ511111111111111111111111111-1-11-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-111-1-1
χ611111111111111111111111111-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ711111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-111
χ811111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ911111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-11
χ1011111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1111-1
χ1111111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-111111-1
χ1211111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-11111-1-111-1-1-11
χ1311111111-1-1-1-11111111111-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-11-1
χ1411111111-1-1-1-11111111111-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-11
χ1511111111-1-1-1-11111111111-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111-1-111-11
χ1611111111-1-1-1-11111111111-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-11-1
χ172222222222222-222-2-22-2-2-2-2-22222-222-2-2-2-2000000000000000000000000000000
χ182222222222222-222-2-22-2-2-2-2-222-2-2-2-2-22222000000000000000000000000000000
χ19222222222222-22-2-222-22-2-222-2-200-200000022-2-222-2-20000000000000000000000
χ20222222222222-22-2-222-22-2-222-2-200-2000000-2-222-2-2220000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-222-2-2-2-200200000000000000000000000000002i−2i2i−2i0000
χ22222222222222-2-2-2-2-2-2-2-222-2-2-2-20020000000000000000000000000000−2i2i−2i2i0000
χ2322222222-2-2-2-22-222-2-22-2-2-222-2-2222-2-222-2-2000000000000000000000000000000
χ2422222222-2-2-2-22-222-2-22-2-2-222-2-2-2-2222-2-222000000000000000000000000000000
χ2522222222-2-2-2-2-22-2-222-22-2-2-2-22200200000022-2-2-2-2220000000000000000000000
χ2622222222-2-2-2-2-22-2-222-22-2-2-2-222002000000-2-22222-2-20000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-222222200-200000000000000000000000000002i−2i−2i2i0000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222222200-20000000000000000000000000000−2i2i2i−2i0000
χ2922-2-2-22-220000222-2-2-2-222-200000002i−2i2i−2i000000000022-2-20000002i−2i0000000000
χ3022-2-2-22-220000222-2-2-2-222-200000002i−2i2i−2i0000000000-2-222000000−2i2i0000000000
χ3122-2-2-22-220000222-2-2-2-222-20000000−2i2i−2i2i000000000022-2-2000000−2i2i0000000000
χ3222-2-2-22-220000222-2-2-2-222-20000000−2i2i−2i2i0000000000-2-2220000002i−2i0000000000
χ3322-2-2-22-2200002-22-222-2-2-2200000002i−2i−2i2i000000000000002i2i−2i−2i2-2000000000000
χ3422-2-2-22-2200002-22-222-2-2-2200000002i−2i−2i2i00000000000000−2i−2i2i2i-22000000000000
χ3522-2-2-22-2200002-22-222-2-2-220000000−2i2i2i−2i000000000000002i2i−2i−2i-22000000000000
χ3622-2-2-22-2200002-22-222-2-2-220000000−2i2i2i−2i00000000000000−2i−2i2i2i2-2000000000000
χ372-2-222-2-2222-2-202002-20-2002-200000000000002i−2i002i−2ii2−i2i2−i2i2−i2i2−i200002−200002−200
χ382-2-222-2-2222-2-202002-20-2002-200000000000002i−2i002i−2i−i2i2−i2i2−i2i2−i2i20000−220000−2200
χ392-2-222-2-2222-2-202002-20-2002-20000000000000−2i2i00−2i2ii2−i2i2−i2i2−i2i2−i20000−220000−2200
χ402-2-222-2-2222-2-202002-20-2002-20000000000000−2i2i00−2i2i−i2i2−i2i2−i2i2−i2i200002−200002−200
χ412-2-222-2-22-2-22202002-20-200-2200000000000002i−2i00−2i2ii2−i2i2−i2−i2i2−i2i200002−20000−2200
χ422-2-222-2-22-2-22202002-20-200-2200000000000002i−2i00−2i2i−i2i2−i2i2i2−i2i2−i20000−2200002−200
χ432-2-222-2-22-2-22202002-20-200-220000000000000−2i2i002i−2ii2−i2i2−i2−i2i2−i2i20000−2200002−200
χ442-2-222-2-22-2-22202002-20-200-220000000000000−2i2i002i−2i−i2i2−i2i2i2−i2i2−i200002−20000−2200
χ4544-44-4-44-44i−4i4i−4i0000000000000000000000022−22002i2−2i2000000000000000000000000
χ4644-44-4-44-44i−4i4i−4i00000000000000000000000−222200−2i22i2000000000000000000000000
χ4744-44-4-44-4−4i4i−4i4i0000000000000000000000022−2200−2i22i2000000000000000000000000
χ4844-44-4-44-4−4i4i−4i4i00000000000000000000000−2222002i2−2i2000000000000000000000000
χ4944-4-4-44-440000-44-44-4-444-440000000000000000000000000000000000000000000
χ5044-4-4-44-440000-4-4-44444-44-40000000000000000000000000000000000000000000
χ514-444-44-4-44i−4i−4i4i40-4-4004000004i−4i000000000000000000000000000000000000000
χ524-444-44-4-44i−4i−4i4i-404400-400000−4i4i000000000000000000000000000000000000000
χ534-444-44-4-4−4i4i4i−4i40-4-400400000−4i4i000000000000000000000000000000000000000
χ544-444-44-4-4−4i4i4i−4i-404400-4000004i−4i000000000000000000000000000000000000000
χ554-44-4-4-44400000400-440-4000000000000000000000002i2−2i2−2i22i2000000000000000000
χ564-44-4-4-44400000400-440-400000000000000000000000−2i22i22i2−2i2000000000000000000
χ574-44-4-4-44400000-4004-40400000000000000000000000000022−22−222200000000000000
χ584-44-4-4-44400000-4004-404000000000000000000000000000−222222−2200000000000000
χ594-4-444-4-4444-4-40-400-440400-4400000000000000000000000000000000000000000
χ604-4-444-4-44-4-4440-400-4404004-400000000000000000000000000000000000000000
χ614-4-4-4444-4000040-4400-4000000000000004i−4i000000000000000000000000000000
χ624-4-4-4444-4000040-4400-400000000000000−4i4i000000000000000000000000000000
χ634-4-4-4444-40000-404-400400000004-40000000000000000000000000000000000000
χ644-4-4-4444-40000-404-40040000000-440000000000000000000000000000000000000
χ65888-88-8-8-8000000000000000000000000000000000000000000000000000000000

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