Finite Group Databasebeta

← Group #305730

Character table — Group #305730

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888224444444488888888888888444444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-111-1-111-1-1111111111111111-1-1-1-1-1-1-111-1-1-1-1-1
χ411111111111111111111111111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111111
χ51111111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-1111-1-1-111-1-111-1-1-1
χ61111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1111
χ71111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11-1-1111-1-1-1-1-1-1111
χ81111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111111-1-11111-1-1-1
χ911111111111111111-1-1-1-11111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11
χ1011111111111111111-1-1-1-11111111-1-111-1-11111-1-1-1-111111111-1-1-11-1-1-1-1-1-11111-1
χ1111111111111111111-1-1-1-111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111111111-1
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-111-11111-1-1-1-1-1-11
χ1311111111111111111-1-1-1-11-1-1-1-111-1-1-1-11111-1-11111-1-1-1-11111111-111-1-1-1-1-1-111-1
χ1411111111111111111-1-1-1-11-1-1-1-111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-11
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111-1-11-1-111-1-111-1-11
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1111-1-11111-1-111-1
χ172222222222-2-222-2-2-20000-2222222002200-2-2-2-2000000000000000-200000000000
χ182222222222-2-222-2-2-20000-22222-2-200-2-20022-2-2000000000000000200000000000
χ192222222222-2-222-2-2-20000-2-2-2-2-22200-2-200-2-222000000000000000200000000000
χ202222222222-2-222-2-2-20000-2-2-2-2-2-2-20022002222000000000000000-200000000000
χ2122222222-2-222-2-222-22222-2000000-2-200220000000022-2-20000-200000000000000
χ2222222222-2-222-2-222-22222-2000000-2-200-2-200000000-2-2220000200000000000000
χ2322222222-2-222-2-222-2-2-2-2-2-200000022002200000000-2-2220000-200000000000000
χ2422222222-2-222-2-222-2-2-2-2-2-20000002200-2-20000000022-2-20000200000000000000
χ2522-2-22-2-22002-2002-2022-2-20i2i2−i2−i20000002i−2i00i2−i2i2i2−i2−i22i−2i0022−2−2000000002−200000
χ2622-2-22-2-22002-2002-2022-2-20i2i2−i2−i2000000−2i2i00i2−i2i2i2−i2−i2−2i2i00−2−22200000000−2200000
χ2722-2-22-2-22002-2002-2022-2-20−i2−i2i2i20000002i−2i00−i2i2−i2−i2i2i22i−2i00−2−22200000000−2200000
χ2822-2-22-2-22002-2002-2022-2-20−i2−i2i2i2000000−2i2i00−i2i2−i2−i2i2i2−2i2i0022−2−2000000002−200000
χ2922-2-22-2-22002-2002-20-2-2220i2i2−i2−i20000002i−2i00i2−i2−i2−i2i2i2−2i2i00−2−222000000002−200000
χ3022-2-22-2-22002-2002-20-2-2220i2i2−i2−i2000000−2i2i00i2−i2−i2−i2i2i22i−2i0022−2−200000000−2200000
χ3122-2-22-2-22002-2002-20-2-2220−i2−i2i2i20000002i−2i00−i2i2i2i2−i2−i2−2i2i0022−2−200000000−2200000
χ3222-2-22-2-22002-2002-20-2-2220−i2−i2i2i2000000−2i2i00−i2i2i2i2−i2−i22i−2i00−2−222000000002−200000
χ332-222-2-2-222222-2-2-2-222-22-2-200002-22-200002-2000000000000000000002-20000000
χ342-222-2-2-222222-2-2-2-222-22-2-20000-222-20000-2200000000000000000000-220000000
χ352-222-2-2-222222-2-2-2-22-22-22-200002-2-2200002-200000000000000000000-220000000
χ362-222-2-2-222222-2-2-2-22-22-22-20000-22-220000-22000000000000000000002-20000000
χ372-222-2-2-2222-2-2-2-222-20000200002-2000000-22002i−2i2i−2i0000000000002i−2i000000000
χ382-222-2-2-2222-2-2-2-222-20000200002-2000000-2200−2i2i−2i2i000000000000−2i2i000000000
χ392-222-2-2-2222-2-2-2-222-2000020000-220000002-2002i−2i2i−2i000000000000−2i2i000000000
χ402-222-2-2-2222-2-2-2-222-2000020000-220000002-200−2i2i−2i2i0000000000002i−2i000000000
χ412-222-2-2-22-2-22222-2-2-22-22-22000000-220000000000000000000002i−2i00000002i−2i000
χ422-222-2-2-22-2-22222-2-2-22-22-22000000-22000000000000000000000−2i2i0000000−2i2i000
χ432-222-2-2-22-2-22222-2-2-2-22-2220000002-20000000000000000000002i−2i0000000−2i2i000
χ442-222-2-2-22-2-22222-2-2-2-22-2220000002-2000000000000000000000−2i2i00000002i−2i000
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000
χ46444-4-44-4-44-4004-400000000000000004-4000000000000000000000000000000000
χ47444-4-44-4-44-4004-40000000000000000-44000000000000000000000000000000000
χ48444-4-44-4-4-4400-4400000000000000000000000000000000000000000000000022−220
χ49444-4-44-4-4-4400-44000000000000000000000000000000000000000000000000−22220
χ5044-4-44-4-4400-4400-440000002i22i2−2i2−2i20000000000−2i22i2000000000000000000000000000
χ5144-4-44-4-4400-4400-44000000−2i2−2i22i22i200000000002i2−2i2000000000000000000000000000
χ524-444-4-4-44-4-4-4-4444440000-40000000000000000000000000000000000000000000
χ534-44-44-44-44-400-44000000004i−4i4i−4i000000000000000000000000000000000000000
χ544-44-44-44-44-400-4400000000−4i4i−4i4i000000000000000000000000000000000000000
χ554-44-44-44-4-44004-4000000000000000000000000000000002i2−2i22i2−2i2000000000000000
χ564-44-44-44-4-44004-400000000000000000000000000000000−2i22i2−2i22i2000000000000000
χ574-4-4444-4-40000000000000022−22−22220000000000000000002i2−2i22i−2i−2i2i000000000000000
χ584-4-4444-4-40000000000000022−22−2222000000000000000000−2i22i2−2i2i2i−2i000000000000000
χ594-4-4444-4-400000000000000−222222−220000000000000000002i2−2i2−2i2i2i−2i000000000000000
χ604-4-4444-4-400000000000000−222222−22000000000000000000−2i22i22i−2i−2i2i000000000000000
χ614-4-4-4-4444004-400-4404-4-4400000000000000000000000000000000000000000000
χ624-4-4-4-4444004-400-440-444-400000000000000000000000000000000000000000000
χ634-4-4-4-444400-44004-4000000000000000000000022−22−222200000000000000000000000
χ644-4-4-4-444400-44004-40000000000000000000000−222222−2200000000000000000000000
χ6588-88-8-88-8000000000000000000000000000000000000000000000000000000000

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