Finite Group Databasebeta

← Group #258576

Character table — Group #258576

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444448888888888888888888161616161616161616161616161616161616
order12222222444444444444444444444444444444488888888244444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1
χ511111111111111111111-1-1-1-11111-1-1-1-111111-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-11111
χ711111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11-1-111111111-1-111111111-1-1-1-1-1-1-1-1
χ811111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111
χ91111111111111111-1-1-1-111111-1-11-1-1-1-111-1-1-1111111-1-1-1-11-11111-1-1-1-111-1-111-1-1
χ101111111111111111-1-1-1-111111-1-11-1-1-1-111-1-1-111-1-1-1-111111-111-1-1-1-111-1-111-1-111
χ111111111111111111-1-1-1-111111-1-11-1-1-1-1-1-111-1111111-1-1-1-1-11-1-1-1-11111-1-11111-1-1
χ121111111111111111-1-1-1-111111-1-11-1-1-1-1-1-111-111-1-1-1-11111-11-1-11111-1-111-1-1-1-111
χ131111111111111111-1-1-1-1-1-1-1-11-1-11111111-1-1-1-1-11111-1-1-1-11-1-1-1-1-1111111-1-1-1-111
χ141111111111111111-1-1-1-1-1-1-1-11-1-11111111-1-1-1-1-1-1-1-1-111111-1-1-11111-1-1-1-11111-1-1
χ151111111111111111-1-1-1-1-1-1-1-11-1-111111-1-111-1-1-11111-1-1-1-1-111111-1-1-1-1-1-111-1-111
χ161111111111111111-1-1-1-1-1-1-1-11-1-111111-1-111-1-1-1-1-1-1-11111-1111-1-1-1-11111-1-111-1-1
χ172222222222-2-2-222-222-2-22222-2-2-2-222-2-200002-2-200000000000000000000000000
χ182222222222-2-2-222-222-2-2-2-2-2-2-2-2-2-2-2-222000022200000000000000000000000000
χ192222222222-2-2-222-2-2-2222222-222-2-2-2220000-2-2-200000000000000000000000000
χ202222222222-2-2-222-2-2-222-2-2-2-2-222-222-2-20000-22200000000000000000000000000
χ2122222222-2-2222-2-2222-2-20000-222-200002222-20000000000-2-20000000000000000
χ2222222222-2-2222-2-2222-2-20000-222-20000-2-2-2-2-20000000000220000000000000000
χ2322222222-2-2222-2-22-2-2220000-2-2-2-2000022-2-220000000000-220000000000000000
χ2422222222-2-2222-2-22-2-2220000-2-2-2-20000-2-222200000000002-20000000000000000
χ2522222222-2-2-2-2-2-2-2-2222200002-2-2200000000-20000000000002-2002-20000000000
χ2622222222-2-2-2-2-2-2-2-2222200002-2-2200000000-2000000000000-2200-220000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2000022220000000020000000000002-200-220000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-200002222000000002000000000000-22002-20000000000
χ2922-22-2-2-222-20002-20002i−2i2i2i−2i−2i02i−2i0002-2000000022−2−2i2i2−i2−i200000000000000i2−i22−2
χ3022-22-2-2-222-20002-20002i−2i2i2i−2i−2i02i−2i0002-20000000−2−222−i2−i2i2i200000000000000−i2i2−22
χ3122-22-2-2-222-20002-20002i−2i−2i−2i2i2i02i−2i000-22000000022−2−2i2i2−i2−i200000000000000−i2i2−22
χ3222-22-2-2-222-20002-20002i−2i−2i−2i2i2i02i−2i000-220000000−2−222−i2−i2i2i200000000000000i2−i22−2
χ3322-22-2-2-222-20002-2000−2i2i2i2i−2i−2i0−2i2i000-22000000022−2−2−i2−i2i2i200000000000000i2−i2−22
χ3422-22-2-2-222-20002-2000−2i2i2i2i−2i−2i0−2i2i000-220000000−2−222i2i2−i2−i200000000000000−i2i22−2
χ3522-22-2-2-222-20002-2000−2i2i−2i−2i2i2i0−2i2i0002-2000000022−2−2−i2−i2i2i200000000000000−i2i22−2
χ3622-22-2-2-222-20002-2000−2i2i−2i−2i2i2i0−2i2i0002-20000000−2−222i2i2−i2−i200000000000000i2−i2−22
χ372-2-222-22-22-222-2-22-200002i−2i2i−2i-20020000000002i−2i00000000000000002i−2i002-20000
χ382-2-222-22-22-222-2-22-200002i−2i2i−2i-20020000000002i−2i0000000000000000−2i2i00-220000
χ392-2-222-22-22-222-2-22-20000−2i2i−2i2i-2002000000000−2i2i00000000000000002i−2i00-220000
χ402-2-222-22-22-222-2-22-20000−2i2i−2i2i-2002000000000−2i2i0000000000000000−2i2i002-20000
χ412-2-222-22-22-2-2-22-22200002i−2i2i−2i200-2000000000−2i2i0000000000002-200002i−2i000000
χ422-2-222-22-22-2-2-22-22200002i−2i2i−2i200-2000000000−2i2i000000000000-220000−2i2i000000
χ432-2-222-22-22-2-2-22-2220000−2i2i−2i2i200-20000000002i−2i0000000000002-20000−2i2i000000
χ442-2-222-22-22-2-2-22-2220000−2i2i−2i2i200-20000000002i−2i000000000000-2200002i−2i000000
χ45444-44-4-4-4000000004-40000000000000000000002-22-22-22-2000000000000000000
χ46444-44-4-4-4000000004-4000000000000000000000-22-22-22-22000000000000000000
χ47444-44-4-4-400000000-440000000000000000000002-22-2-22-22000000000000000000
χ48444-44-4-4-400000000-44000000000000000000000-22-222-22-2000000000000000000
χ4944-44-4-4-44-44000-440004i−4i00000−4i4i00000000000000000000000000000000000000
χ5044-44-4-4-44-44000-44000−4i4i000004i−4i00000000000000000000000000000000000000
χ5144-4-4-444-4004-4400-40000000000000000000000022−22−22220000000000000000000000
χ5244-4-4-444-4004-4400-400000000000000000000000−222222−220000000000000000000000
χ5344-4-4-444-400-44-40040000000000000000000000000002i2−2i2−2i22i2000000000000000000
χ5444-4-4-444-400-44-4004000000000000000000000000000−2i22i22i2−2i2000000000000000000
χ554-444-44-4-444000-4-4000004-4-4400000000000000000000000000000000000000000
χ564-444-44-4-444000-4-400000-444-400000000000000000000000000000000000000000
χ574-444-44-4-4-4-40004400000000000004i−4i00000000000000000000000000000000000
χ584-444-44-4-4-4-4000440000000000000−4i4i00000000000000000000000000000000000
χ594-44-4-4-444004-4-40040000000000000000004-400000000000000000000000000000
χ604-44-4-4-444004-4-4004000000000000000000-4400000000000000000000000000000
χ614-44-4-4-44400-44400-400000000000000004i−4i0000000000000000000000000000000
χ624-44-4-4-44400-44400-40000000000000000−4i4i0000000000000000000000000000000
χ634-4-444-44-4-4444-44-4-400000000400-40000000000000000000000000000000000000
χ644-4-444-44-4-44-4-444-4400000000-40040000000000000000000000000000000000000
χ658-8-8-888-88000000000000000000000000000000000000000000000000000000000

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