Finite Group Databasebeta

← Group #304331

Character table — Group #304331

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222222244444444444422444444444444444888888884444444444448888
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-11111111111111111-1-11-1-11-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-111111111
χ5111111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-11111
χ8111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-111-1111111-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-111111111-111-1-11111-1-1-1-11111-1-1-1-11-1-11-1-11-111-1-111-1-1
χ10111111111111-1-1-1-1-1-1-1-111111111-111-1-1-1-1-1-11111-1-1-1-111111-1-11-1-11-1-1-111-1-111
χ11111111111111-1-1-1-1-1-1-1-111111111-1-1-1111111-1-1-1-11111-1-1-1-1-11-1-11-1-11-1-111-1-111
χ12111111111111-1-1-1-1-1-1-1-111111111-1-1-111-1-1-1-11111-1-1-1-11111-11-1-11-1-1111-1-111-1-1
χ13111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111-11-111-1111-1-1-1-111
χ14111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-11-11-111-11-1-11111-1-1
χ15111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1111-111-1-1-11111-1-1
χ16111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1111-111-111-1-1-1-111
χ172222222222222222-2-222-2-2-2-20000-222220000000000000000-2-200000000000000
χ182222222222222222-2-222-2-2-2-20000-2-2-2-2-200000000000000002200000000000000
χ19222222222222-2-2-2-222-2-2-2-2-2-20000222-2-20000000000000000-2200000000000000
χ20222222222222-2-2-2-222-2-2-2-2-2-200002-2-22200000000000000002-200000000000000
χ2122222222-2-2-2-2222222-2-2-222-20000-200000000000000000000000220-2-200000000
χ2222222222-2-2-2-2222222-2-2-222-20000-200000000000000000000000-2-202200000000
χ2322222222-2-2-2-22222-2-2-2-22-2-2222-2-220000000000000000000000200-20000000000
χ2422222222-2-2-2-22222-2-2-2-22-2-22-2-22220000000000000000000000-20020000000000
χ2522222222-2-2-2-2-2-2-2-222222-2-2222-2-2-20000000000000000000000-20020000000000
χ2622222222-2-2-2-2-2-2-2-222222-2-22-2-222-20000000000000000000000200-20000000000
χ2722222222-2-2-2-2-2-2-2-2-2-222-222-200002000000000000000000000002-20-2200000000
χ2822222222-2-2-2-2-2-2-2-2-2-222-222-20000200000000000000000000000-2202-200000000
χ2922-22-2-22-22-22-200000000-22-222-22-20000000002i2i−2i−2i00002i2i−2i−2i0000000000000000
χ3022-22-2-22-22-22-200000000-22-222-22-2000000000−2i−2i2i2i0000−2i−2i2i2i0000000000000000
χ3122-22-2-22-22-22-200000000-22-22-22-220000000002i2i−2i−2i0000−2i−2i2i2i0000000000000000
χ3222-22-2-22-22-22-200000000-22-22-22-22000000000−2i−2i2i2i00002i2i−2i−2i0000000000000000
χ3322-22-2-22-2-22-2200000000-2-2222-2-22000002i2i−2i−2i00002i2i−2i−2i00000000000000000000
χ3422-22-2-22-2-22-2200000000-2-2222-2-2200000−2i−2i2i2i0000−2i−2i2i2i00000000000000000000
χ3522-22-2-22-2-22-2200000000-2-222-222-2000002i2i−2i−2i0000−2i−2i2i2i00000000000000000000
χ3622-22-2-22-2-22-2200000000-2-222-222-200000−2i−2i2i2i00002i2i−2i−2i00000000000000000000
χ372-2-22-22-2222-2-222-2-2002-20000000002-22-200000000i2−i2i2−i2i2−i2i2−i2000000000000i2−i2i2−i2
χ382-2-22-22-2222-2-222-2-2002-20000000002-22-200000000−i2i2−i2i2−i2i2−i2i2000000000000−i2i2−i2i2
χ392-2-22-22-2222-2-222-2-2002-2000000000-22-2200000000i2−i2i2−i2i2−i2i2−i2000000000000−i2i2−i2i2
χ402-2-22-22-2222-2-222-2-2002-2000000000-22-2200000000−i2i2−i2i2−i2i2−i2i2000000000000i2−i2i2−i2
χ412-2-22-22-2222-2-2-2-22200-220000000002-2-2200000000i2−i2i2−i2−i2i2−i2i2000000000000i2−i2−i2i2
χ422-2-22-22-2222-2-2-2-22200-220000000002-2-2200000000−i2i2−i2i2i2−i2i2−i2000000000000−i2i2i2−i2
χ432-2-22-22-2222-2-2-2-22200-22000000000-222-200000000i2−i2i2−i2−i2i2−i2i2000000000000−i2i2i2−i2
χ442-2-22-22-2222-2-2-2-22200-22000000000-222-200000000−i2i2−i2i2i2−i2i2−i2000000000000i2−i2−i2i2
χ45444-4-44-4-400004-44-4000000000000000002-22-22-22-2000000000000000000000000
χ46444-4-44-4-400004-44-400000000000000000-22-22-22-22000000000000000000000000
χ47444-4-44-4-40000-44-44000000000000000002-22-2-22-22000000000000000000000000
χ48444-4-44-4-40000-44-4400000000000000000-22-222-22-2000000000000000000000000
χ4944-44-4-44-44-44-4000000004-44-400000000000000000000000000000000000000000
χ5044-44-4-44-4-44-440000000044-4-400000000000000000000000000000000000000000
χ5144-4-44-4-44000000004-40000000000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ5244-4-44-4-44000000004-4000000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ5344-4-44-4-4400000000-440000000000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ5444-4-44-4-4400000000-44000000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ554-4444-4-4-44-4-4400000000000000000000000000000000022−22−22220000000000000000
χ564-4444-4-4-44-4-44000000000000000000000000000000000−222222−220000000000000000
χ574-4444-4-4-4-444-40000000000000000000000000000022−22−222200000000000000000000
χ584-4444-4-4-4-444-400000000000000000000000000000−222222−2200000000000000000000
χ594-4-44-44-44-4-44444-4-400-44000000000000000000000000000000000000000000000
χ604-4-44-44-44-4-444-4-444004-4000000000000000000000000000000000000000000000
χ614-4-4-4444-400004-4-44000000000000000000000000000000000000000002-22-20000
χ624-4-4-4444-400004-4-4400000000000000000000000000000000000000000-22-220000
χ634-4-4-4444-40000-444-4000000000000000000000000000000000000000002-2-220000
χ644-4-4-4444-40000-444-400000000000000000000000000000000000000000-222-20000
χ658-88-8-8-888000000000000000000000000000000000000000000000000000000000

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