Finite Group Databasebeta

← Group #252877

Character table — Group #252877

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444448888888888888888888161616161616161616161616161616161616
order12222222444444442244444444444444444444488888888222444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111-1-1-1-11111
χ5111111111111111111-1-1-1-11111111-1-1-1-1-1-11111111111111-1-11-1-1-1-1-1-1-1-1-1-11111
χ6111111111111111111-1-1-1-11111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1
χ7111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111111111-111-1111111-1-1-1-1-1-1-1-1
χ8111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111
χ91111111111111111-1-11111-1-1-1-111-1-1-111-1-111-1-11111-1-1-1-1-1111-1-111-1-111-1-111-1-1
χ101111111111111111-1-11111-1-1-1-111-1-1-111-1-111-1-1-1-1-1-11111-1-1-11-1-11111-1-111-1-111
χ111111111111111111-1-11111-1-1-1-111-1-1-111-1-1-1-1111111-1-1-1-11-1-1-111-1-11111-1-1-1-111
χ121111111111111111-1-11111-1-1-1-111-1-1-111-1-1-1-111-1-1-1-11111111-111-1-1-1-1-1-11111-1-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-111-111-1-11111-1-11111-1-1-1-1-1-1-1111-1-111-1-11111-1-1
χ141111111111111111-1-1-1-1-1-1-1-1-1-111-111-1-11111-1-1-1-1-1-11111-111111-1-1-1-111-1-1-1-111
χ151111111111111111-1-1-1-1-1-1-1-1-1-111-111-1-111-1-1111111-1-1-1-1111-1-1-111-1-1-1-111-1-111
χ161111111111111111-1-1-1-1-1-1-1-1-1-111-111-1-111-1-111-1-1-1-111111-1-1-1-1-1111111-1-111-1-1
χ172222222222-2-2-222-222000022-2-2-2-2-2000000222200000000-200-200000000000000
χ182222222222-2-2-222-222000022-2-2-2-2-2000000-2-2-2-200000000200200000000000000
χ192222222222-2-2-222-2-2-20000-2-222-2-2200000022-2-200000000200-200000000000000
χ202222222222-2-2-222-2-2-20000-2-222-2-22000000-2-22200000000-200200000000000000
χ2122222222-2-2222-2-22222222-2-222-2-2-222-2-2-2-2000000000000000000000000000000
χ2222222222-2-2222-2-2222-2-2-2-2-2-222-2-2-2-2-22222000000000000000000000000000000
χ2322222222-2-2222-2-22-2-2222222-2-2-2-22-2-2-2-222000000000000000000000000000000
χ2422222222-2-2222-2-22-2-2-2-2-2-222-2-2-2-222222-2-2000000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-2220000-2-2-2-222200000000000000000000002-22-20000000000
χ2622222222-2-2-2-2-2-2-2-2220000-2-2-2-22220000000000000000000000-22-220000000000
χ2722222222-2-2-2-2-2-2-2-2-2-20000222222-200000000000000000000002-2-220000000000
χ2822222222-2-2-2-2-2-2-2-2-2-20000222222-20000000000000000000000-222-20000000000
χ2922-2-2-22-220022-200-22-22i2i−2i−2i002-20002i−2i00000000i2i2−i2−i2i2i2−i2−i200000000002−22−20000
χ3022-2-2-22-220022-200-22-22i2i−2i−2i002-20002i−2i00000000−i2−i2i2i2−i2−i2i2i20000000000−22−220000
χ3122-2-2-22-220022-200-22-2−2i−2i2i2i002-2000−2i2i00000000i2i2−i2−i2i2i2−i2−i20000000000−22−220000
χ3222-2-2-22-220022-200-22-2−2i−2i2i2i002-2000−2i2i00000000−i2−i2i2i2−i2−i2i2i200000000002−22−20000
χ3322-2-2-22-220022-200-2-222i2i−2i−2i00-22000−2i2i00000000i2i2−i2−i2−i2−i2i2i200000000002−2−220000
χ3422-2-2-22-220022-200-2-222i2i−2i−2i00-22000−2i2i00000000−i2−i2i2i2i2i2−i2−i20000000000−222−20000
χ3522-2-2-22-220022-200-2-22−2i−2i2i2i00-220002i−2i00000000i2i2−i2−i2−i2−i2i2i20000000000−222−20000
χ3622-2-2-22-220022-200-2-22−2i−2i2i2i00-220002i−2i00000000−i2−i2i2i2i2i2−i2−i200000000002−2−220000
χ372-22-2-2-2222-22-222-2-2002i−2i2i−2i00002-20002i−2i0000000000000002-2000000000002i−2i00
χ382-22-2-2-2222-22-222-2-2002i−2i2i−2i00002-20002i−2i000000000000000-2200000000000−2i2i00
χ392-22-2-2-2222-22-222-2-200−2i2i−2i2i00002-2000−2i2i0000000000000002-200000000000−2i2i00
χ402-22-2-2-2222-22-222-2-200−2i2i−2i2i00002-2000−2i2i000000000000000-22000000000002i−2i00
χ412-22-2-2-222-222-22-22-2002i−2i2i−2i0000-22000−2i2i00000000000000000000002-20000002i−2i
χ422-22-2-2-222-222-22-22-2002i−2i2i−2i0000-22000−2i2i0000000000000000000000-22000000−2i2i
χ432-22-2-2-222-222-22-22-200−2i2i−2i2i0000-220002i−2i00000000000000000000002-2000000−2i2i
χ442-22-2-2-222-222-22-22-200−2i2i−2i2i0000-220002i−2i0000000000000000000000-220000002i−2i
χ4544-44-4-44-44-4000-4400000000000000000000004i−4i00000000000000000000000000
χ4644-44-4-44-44-4000-440000000000000000000000−4i4i00000000000000000000000000
χ4744-44-4-44-4-440004-4000000000000000000004i−4i0000000000000000000000000000
χ4844-44-4-44-4-440004-400000000000000000000−4i4i0000000000000000000000000000
χ4944-4-4-44-4400-4-440044-4000000-44000000000000000000000000000000000000000
χ5044-4-4-44-4400-4-44004-440000004-4000000000000000000000000000000000000000
χ514-444-44-4-4000000000000004i−4i0000000000000002i−2i2i−2i2-22-2000000000000000000
χ524-444-44-4-4000000000000004i−4i000000000000000−2i2i−2i2i-22-22000000000000000000
χ534-444-44-4-400000000000000−4i4i0000000000000002i−2i2i−2i-22-22000000000000000000
χ544-444-44-4-400000000000000−4i4i000000000000000−2i2i−2i2i2-22-2000000000000000000
χ554-44-4-4-4444-4-44-44-440000000000-440000000000000000000000000000000000000
χ564-44-4-4-444-44-44-4-44400000000004-40000000000000000000000000000000000000
χ574-4-444-4-44004-4-4004004-4-440000000000000000000000000000000000000000000
χ584-4-444-4-44004-4-400400-444-40000000000000000000000000000000000000000000
χ594-4-444-4-4400-44400-4000000000000000004i−4i000000000000000000000000000000
χ604-4-444-4-4400-44400-400000000000000000−4i4i000000000000000000000000000000
χ614-4-4-4444-444000-4-400000000000000000000000000002i2−2i2−2i22i2000000000000000000
χ624-4-4-4444-444000-4-40000000000000000000000000000−2i22i22i2−2i2000000000000000000
χ634-4-4-4444-4-4-40004400000000000000000000000022−22−22220000000000000000000000
χ644-4-4-4444-4-4-400044000000000000000000000000−222222−220000000000000000000000
χ65888-88-8-8-8000000000000000000000000000000000000000000000000000000000

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