Finite Group Databasebeta

← Group #275428

Character table — Group #275428

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222222244444488888888888888888888888881616161616161616161616163232
order12222222444444444444224444444444444888888888888888844448888888844
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
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
χ5111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-111-1-1
χ6111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111
χ7111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-111
χ8111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ9111111111-1-1-1-11111111-1-111-1-1-111-1-111-1-111-1-1111111-1-1-1-1-1-111-1-11111-1-1-1-1-11
χ10111111111-1-1-1-11111111-1-111-1-1-111-1-111-1-111-1-1-1-1-1-111-1-11111-1-111-1-111-1-1111-1
χ11111111111-1-1-1-11111111-1-111-1-1-111-1-111-1-1-1-1111111-1-111-1-1-1-111-1-1-1-1-1-111111-1
χ12111111111-1-1-1-11111111-1-111-1-1-111-1-111-1-1-1-111-1-1-1-1-1-1111111-1-11111-1-111-1-1-11
χ13111111111-1-1-1-11111111-1-111-1-1-1-1-111-1-11111-1-1111111-1-1-1-1-1-1-1-11111-1-111-1-11-1
χ14111111111-1-1-1-11111111-1-111-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-11111-11
χ15111111111-1-1-1-11111111-1-111-1-1-1-1-111-1-111-1-1111111-1-111-1-1-1-1-1-111-1-111-1-111-11
χ16111111111-1-1-1-11111111-1-111-1-1-1-1-111-1-111-1-111-1-1-1-1-1-111111111-1-11111-1-1-1-11-1
χ172222222222222-2-222-2-22-2-2-2-222-222-2-2-2-222000000000000000000000000000000
χ182222222222222-2-222-2-22-2-2-2-222-2-2-22222-2-2000000000000000000000000000000
χ19222222222-2-2-2-2-2-222-2-2222-2-2-2-222222-2-2-2-2000000000000000000000000000000
χ20222222222-2-2-2-2-2-222-2-2222-2-2-2-22-2-2-2-22222000000000000000000000000000000
χ2122222222-2222222-2-222-222-2-2-2-2-20000000022220000-2-2-2-2000000000000000000
χ2222222222-2222222-2-222-222-2-2-2-2-200000000-2-2-2-200002222000000000000000000
χ2322222222-22222-2-2-2-2-2-2-2-2-222-2-220000000000000000000000000000002i−2i2i−2i0000
χ2422222222-22222-2-2-2-2-2-2-2-2-222-2-22000000000000000000000000000000−2i2i−2i2i0000
χ2522222222-2-2-2-2-222-2-222-2-2-2-2-22220000000022-2-20000-2-222000000000000000000
χ2622222222-2-2-2-2-222-2-222-2-2-2-2-222200000000-2-222000022-2-2000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222222-20000000000000000000000000000002i−2i−2i2i0000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2000000000000000000000000000000−2i2i2i−2i0000
χ292222-2-2-2-2022-2-22200-2-202-200000000000002-22-222−2−2000022−2−200002−200002−200
χ302222-2-2-2-2022-2-22200-2-202-200000000000002-22-2−2−2220000−2−2220000−220000−2200
χ312222-2-2-2-2022-2-22200-2-202-20000000000000-22-2222−2−2000022−2−20000−220000−2200
χ322222-2-2-2-2022-2-22200-2-202-20000000000000-22-22−2−2220000−2−22200002−200002−200
χ332222-2-2-2-20-2-2222200-2-20-2200000000000002-2-2222−2−20000−2−22200002−20000−2200
χ342222-2-2-2-20-2-2222200-2-20-2200000000000002-2-22−2−222000022−2−20000−2200002−200
χ352222-2-2-2-20-2-2222200-2-20-220000000000000-222-222−2−20000−2−2220000−2200002−200
χ362222-2-2-2-20-2-2222200-2-20-220000000000000-222-2−2−222000022−2−200002−20000−2200
χ372-2-2222-2-2-200002-22-22-22002-2000002i−2i002i−2i0000000000002-22-22i−2i000000000000
χ382-2-2222-2-2-200002-22-22-22002-2000002i−2i002i−2i000000000000-22-22−2i2i000000000000
χ392-2-2222-2-2-200002-22-22-22002-200000−2i2i00−2i2i0000000000002-22-2−2i2i000000000000
χ402-2-2222-2-2-200002-22-22-22002-200000−2i2i00−2i2i000000000000-22-222i−2i000000000000
χ412-2-2222-2-2-20000-222-2-22200-22000002i−2i00−2i2i00002-22-200000000002i−2i0000000000
χ422-2-2222-2-2-20000-222-2-22200-22000002i−2i00−2i2i0000-22-220000000000−2i2i0000000000
χ432-2-2222-2-2-20000-222-2-22200-2200000−2i2i002i−2i00002-22-20000000000−2i2i0000000000
χ442-2-2222-2-2-20000-222-2-22200-2200000−2i2i002i−2i0000-22-2200000000002i−2i0000000000
χ454444-4-4-4-4044-4-4-4-400440-440000000000000000000000000000000000000000000
χ464444-4-4-4-40-4-444-4-4004404-40000000000000000000000000000000000000000000
χ4744-4-44-44-440000004-400-400000004-4000000000000000000000000000000000000
χ4844-4-44-44-440000004-400-40000000-44000000000000000000000000000000000000
χ4944-4-44-44-4-4000000-44004000000000004i−4i00000000000000000000000000000000
χ5044-4-44-44-4-4000000-4400400000000000−4i4i00000000000000000000000000000000
χ514-44-44-4-4444i−4i4i−4i00-4-400400004i−4i000000000000000000000000000000000000000
χ524-44-44-4-444−4i4i−4i4i00-4-40040000−4i4i000000000000000000000000000000000000000
χ534-44-44-4-44-44i−4i4i−4i004400-40000−4i4i000000000000000000000000000000000000000
χ544-44-44-4-44-4−4i4i−4i4i004400-400004i−4i000000000000000000000000000000000000000
χ554-44-4-444-404i−4i−4i4i0000000000000000000000000000002i2−2i222−22000000000000000000
χ564-44-4-444-404i−4i−4i4i000000000000000000000000000000−2i22i2−2222000000000000000000
χ574-44-4-444-40−4i4i4i−4i0000000000000000000000000000002i2−2i2−2222000000000000000000
χ584-44-4-444-40−4i4i4i−4i000000000000000000000000000000−2i22i222−22000000000000000000
χ594-4-4444-4-4400004-4-444-4-400-4400000000000000000000000000000000000000000
χ604-4-4444-4-440000-44-44-44-4004-400000000000000000000000000000000000000000
χ614-4-44-4-444000004-400-44000000000000000000000000000022−22−222200000000000000
χ624-4-44-4-444000004-400-440000000000000000000000000000−222222−2200000000000000
χ634-4-44-4-44400000-44004-40000000000000000000022−22−22220000000000000000000000
χ644-4-44-4-44400000-44004-400000000000000000000−222222−220000000000000000000000
χ6588-8-8-88-88000000000000000000000000000000000000000000000000000000000

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