Finite Group Databasebeta

← Group #255924

Character table — Group #255924

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222444444442244444444444444488888888888888882222444444448888
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-11-1-1-1-1-1-1
χ3111111111111111111111111111-1-111-1-111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1
χ4111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1111111111
χ5111111111111111111111111-1-1111-1-11111111111-1-1-1-1-1-1-1-1-11-1-11-1-111-111-1-1-1-1
χ6111111111111111111111111-1-1111-1-111-1-1-1-1-1-1-1-111111111-11-1-11-1-1-1-1-1-1-11111
χ7111111111111111111111111-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-111-1-1-1-1-11111
χ8111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-11111-111-1-1-1-1
χ91111111111111111-1-1-1-1-1-11111-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-111111-1-111-1-1
χ101111111111111111-1-1-1-1-1-11111-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-111-1-1111-1-111
χ111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-11111-1-1-1-1111-1-111
χ121111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-11111-1-1111-1-111-1-1
χ131111111111111111-1-1-1-1-1-111-1-1-11111111111-1-1-1-1-1-1-1-111111-111-1-1-111-1-1-1-1-111
χ141111111111111111-1-1-1-1-1-111-1-1-1111111-1-1-1-111111111-1-1-1-11-111-1-1-1-1-1-11111-1-1
χ151111111111111111-1-1-1-1-1-111-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1111-1-1-11111-1-1
χ161111111111111111-1-1-1-1-1-111-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-111-1-111111-1-1-1-1-111
χ172222222222-2-2-222-222-2-2-2-2-2-222200-2-2000000000000000000200000000-2000000
χ182222222222-2-2-222-222-2-2-2-2-2-2-2-220022000000000000000000-2000000002000000
χ192222222222-2-2-222-2-2-22222-2-222-20022000000000000000000-200000000-2000000
χ202222222222-2-2-222-2-2-22222-2-2-2-2-200-2-20000000000000000002000000002000000
χ2122222222-2-2222-2-2222-2-222-2-200-22200-2-200000000000000000200-200000000000
χ2222222222-2-2222-2-2222-2-222-2-200-2-2-2002200000000000000000-200200000000000
χ2322222222-2-2222-2-22-2-222-2-2-2-20022200-2-200000000000000000-200200000000000
χ2422222222-2-2222-2-22-2-222-2-2-2-2002-2-2002200000000000000000200-200000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-22200-20000000000000000000000002-202-2000000000
χ2622222222-2-2-2-2-2-2-2-22222-2-22200-2000000000000000000000000-220-22000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-222220020000000000000000000000002-20-22000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22222002000000000000000000000000-2202-2000000000
χ292222-2-2-2-22-20002-20002i−2i2i−2i002-20002i−2i00i2i2−i2−i222−2−2i2i2−i2−i222−2−20000000000000000
χ302222-2-2-2-22-20002-20002i−2i2i−2i002-20002i−2i00−i2−i2i2i2−2−222−i2−i2i2i2−2−2220000000000000000
χ312222-2-2-2-22-20002-20002i−2i2i−2i00-22000−2i2i00i2i2−i2−i222−2−2−i2−i2i2i2−2−2220000000000000000
χ322222-2-2-2-22-20002-20002i−2i2i−2i00-22000−2i2i00−i2−i2i2i2−2−222i2i2−i2−i222−2−20000000000000000
χ332222-2-2-2-22-20002-2000−2i2i−2i2i002-2000−2i2i00i2i2−i2−i2−2−222i2i2−i2−i2−2−2220000000000000000
χ342222-2-2-2-22-20002-2000−2i2i−2i2i002-2000−2i2i00−i2−i2i2i222−2−2−i2−i2i2i222−2−20000000000000000
χ352222-2-2-2-22-20002-2000−2i2i−2i2i00-220002i−2i00i2i2−i2−i2−2−222−i2−i2i2i222−2−20000000000000000
χ362222-2-2-2-22-20002-2000−2i2i−2i2i00-220002i−2i00−i2−i2i2i222−2−2i2i2−i2−i2−2−2220000000000000000
χ372-22-22-22-22-222-2-22-20000002-20002-2002-200002i−2i2i−2i0000000000000000002i−2i0000
χ382-22-22-22-22-222-2-22-20000002-20002-2002-20000−2i2i−2i2i000000000000000000−2i2i0000
χ392-22-22-22-22-222-2-22-20000002-2000-2200-2200002i−2i2i−2i000000000000000000−2i2i0000
χ402-22-22-22-22-222-2-22-20000002-2000-2200-220000−2i2i−2i2i0000000000000000002i−2i0000
χ412-22-22-22-2-2222-22-2-2000000-220002-200-222i−2i2i−2i00000000000000000002i−2i0000000
χ422-22-22-22-2-2222-22-2-2000000-220002-200-22−2i2i−2i2i0000000000000000000−2i2i0000000
χ432-22-22-22-2-2222-22-2-2000000-22000-22002-22i−2i2i−2i0000000000000000000−2i2i0000000
χ442-22-22-22-2-2222-22-2-2000000-22000-22002-2−2i2i−2i2i00000000000000000002i−2i0000000
χ454444-4-4-4-4-44000-440004i−4i−4i4i0000000000000000000000000000000000000000000
χ464444-4-4-4-4-44000-44000−4i4i4i−4i0000000000000000000000000000000000000000000
χ4744-4-444-4-4000000004-4000000000000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ4844-4-444-4-4000000004-400000000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ4944-4-444-4-400000000-44000000000000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ5044-4-444-4-400000000-4400000000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ5144-4-4-4-444004-4400-4000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ5244-4-4-4-444004-4400-400000000000000000000000000000−2i22i22i2−2i20000000000000000
χ5344-4-4-4-44400-44-4004000000000000000000000000022−22−222200000000000000000000
χ5444-4-4-4-44400-44-40040000000000000000000000000−222222−2200000000000000000000
χ554-44-44-44-44-4-4-44-444000000-4400000000000000000000000000000000000000000
χ564-44-44-44-4-44-4-444-440000004-400000000000000000000000000000000000000000
χ574-44-4-44-4444000-4-400000000000000000000002i2−2i2−2i22i2000000000000000000000000
χ584-44-4-44-4444000-4-40000000000000000000000−2i22i22i2−2i2000000000000000000000000
χ594-44-4-44-44-4-40004400000000000000000022−22−22220000000000000000000000000000
χ604-44-4-44-44-4-400044000000000000000000−222222−220000000000000000000000000000
χ614-4-44-444-4004-4-40040000000000000000000000000000000000000000000000022−22
χ624-4-44-444-4004-4-400400000000000000000000000000000000000000000000000−2222
χ634-4-44-444-400-44400-40000000000000000000000000000000000000000000002i2−2i200
χ644-4-44-444-400-44400-4000000000000000000000000000000000000000000000−2i22i200
χ658-8-888-8-88000000000000000000000000000000000000000000000000000000000

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