Finite Group Databasebeta

← Group #305733

Character table — Group #305733

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444442222448888224444444488888888888888444444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-11-11111-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-111-1-1-1-11111111111111111-11-1-1-1-1-1-1-1-1-1-111-1
χ411111111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-11
χ51111111111111111111111-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-1-1111-1-11111-1-1-1-1-1
χ61111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111111
χ71111111111111111111111-1-1-1-1-1-111-1-11111-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-11
χ81111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1111111-1-111-1
χ91111111111111111-1-1-1-111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1111
χ101111111111111111-1-1-1-111111111-1-11111-1-1111111-1-1-1-111111-1-1-1-1-1-1-11111-1-1-1
χ111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1111111-1
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1111111-1-1-1-1-1-11
χ131111111111111111-1-1-1-111-1-1-1-111-1-111-1-111-1-1-1-1-1-111111111-11-1-11111-1-111-1-1-1
χ141111111111111111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1111
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-11
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11-111-1-111-1-11111-1
χ172222222222-2-22-2-220000-2-222222200-2-2-2-200-2-2000000000000200000000000000
χ182222222222-2-22-2-220000-2-22222-2-200222200-2-2000000000000-200000000000000
χ192222222222-2-22-2-220000-2-2-2-2-2-22200-2-2220022000000000000-200000000000000
χ202222222222-2-22-2-220000-2-2-2-2-2-2-2-20022-2-20022000000000000200000000000000
χ2122222222-2-222-222-22222-2-2000000-2-20000220022-2-2000000000-20000000000000
χ2222222222-2-222-222-22222-2-2000000-2-20000-2-200-2-22200000000020000000000000
χ2322222222-2-222-222-2-2-2-2-2-2-20000002200002200-2-222000000000-20000000000000
χ2422222222-2-222-222-2-2-2-2-2-2-2000000220000-2-20022-2-200000000020000000000000
χ2522-2-22-22-22222-2-2-2-222-2-22-200002-22-22-2000000000000000000002-200000000000
χ2622-2-22-22-22222-2-2-2-222-2-22-20000-222-2-2200000000000000000000-2200000000000
χ2722-2-22-22-22222-2-2-2-2-2-2222-200002-2-222-200000000000000000000-2200000000000
χ2822-2-22-22-22222-2-2-2-2-2-2222-20000-22-22-22000000000000000000002-200000000000
χ2922-2-22-22-222-2-2-222-20000-2200002-200-2200000000002i2i−2i−2i000000002i−2i000000000
χ3022-2-22-22-222-2-2-222-20000-2200002-200-220000000000−2i−2i2i2i00000000−2i2i000000000
χ3122-2-22-22-222-2-2-222-20000-220000-22002-200000000002i2i−2i−2i00000000−2i2i000000000
χ3222-2-22-22-222-2-2-222-20000-220000-22002-20000000000−2i−2i2i2i000000002i−2i000000000
χ3322-2-22-22-2-2-2222-2-2222-2-2-22000000-22000000000000000000000000002i−2i2i−2i00000
χ3422-2-22-22-2-2-2222-2-2222-2-2-22000000-2200000000000000000000000000−2i2i−2i2i00000
χ3522-2-22-22-2-2-2222-2-22-2-222-220000002-2000000000000000000000000002i−2i−2i2i00000
χ3622-2-22-22-2-2-2222-2-22-2-222-220000002-200000000000000000000000000−2i2i2i−2i00000
χ372-22-2-222-2002-202-202-22-200i2i2−i2−i2000000002i−2ii2−i22i−2i00i2−i2i2−i222−2−20000000000002−20
χ382-22-2-222-2002-202-202-22-200i2i2−i2−i200000000−2i2ii2−i2−2i2i00i2−i2i2−i2−2−222000000000000−220
χ392-22-2-222-2002-202-202-22-200−i2−i2i2i2000000002i−2i−i2i22i−2i00−i2i2−i2i2−2−222000000000000−220
χ402-22-2-222-2002-202-202-22-200−i2−i2i2i200000000−2i2i−i2i2−2i2i00−i2i2−i2i222−2−20000000000002−20
χ412-22-2-222-2002-202-20-22-2200i2i2−i2−i2000000002i−2ii2−i2−2i2i00−i2i2−i2i2−2−2220000000000002−20
χ422-22-2-222-2002-202-20-22-2200i2i2−i2−i200000000−2i2ii2−i22i−2i00−i2i2−i2i222−2−2000000000000−220
χ432-22-2-222-2002-202-20-22-2200−i2−i2i2i2000000002i−2i−i2i2−2i2i00i2−i2i2−i222−2−2000000000000−220
χ442-22-2-222-2002-202-20-22-2200−i2−i2i2i200000000−2i2i−i2i22i−2i00i2−i2i2−i2−2−2220000000000002−20
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000
χ464444-4-4-4-40000000000000022−2222−220000000000000022−2200002-22-2000000000000000
χ474444-4-4-4-40000000000000022−2222−2200000000000000−22220000-22-22000000000000000
χ484444-4-4-4-400000000000000−2222−22220000000000000022−220000-22-22000000000000000
χ494444-4-4-4-400000000000000−2222−222200000000000000−222200002-22-2000000000000000
χ5044-4-44-44-4-4-4-4-4444400004-40000000000000000000000000000000000000000000
χ514-44-44-4-444-400400-40000004i−4i−4i4i000000000000000000000000000000000000000
χ524-44-44-4-444-400400-4000000−4i4i4i−4i000000000000000000000000000000000000000
χ534-44-44-4-44-4400-400400000000000000000000000000000022−22−2222000000000000000
χ544-44-44-4-44-4400-4004000000000000000000000000000000−222222−22000000000000000
χ554-44-4-444-400-440-4400000002i22i2−2i2−2i20000000000−2i22i2000000000000000000000000000
χ564-44-4-444-400-440-440000000−2i2−2i22i22i200000000002i2−2i2000000000000000000000000000
χ574-4-4444-4-44-400-400400000000000000004i−4i0000000000000000000000000000000
χ584-4-4444-4-44-400-40040000000000000000−4i4i0000000000000000000000000000000
χ594-4-4444-4-4-4400400-40000000000000000000000000000000000000000000022−22000
χ604-4-4444-4-4-4400400-400000000000000000000000000000000000000000000−2222000
χ614-4-44-4-444004-40-4404-4-44000000000000000000000000000000000000000000000
χ624-4-44-4-444004-40-440-444-4000000000000000000000000000000000000000000000
χ634-4-44-4-44400-4404-400000000000000000000000000022−22−22220000000000000000000
χ644-4-44-4-44400-4404-4000000000000000000000000000−222222−220000000000000000000
χ6588-8-8-88-88000000000000000000000000000000000000000000000000000000000

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