Finite Group Databasebeta

← Group #255159

Character table — Group #255159

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222222244444444444422444444444444444888888884444444444448888
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-11-1-1-11-1-11111-1-1-1-1
χ311111111111111111111111111-1-1-1-111-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-111-1-1-1-1-1-11-1-111111111-11-1-1-11-1-1-1-1-1-11111
χ5111111111111111111111111-1-11111-1-111111111111111111-1-1-11-1-11-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-11111-1-11111-1-11-1-1-1-1-1-1-1-1-1-11-11-11-1-11-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-11-1-11-111111111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111111111-11-11-1-111111-1-1-1-1
χ9111111111111-1-1-1-1-1-11-1-1111111111-1-1-1-1-1-111-1111111-1-1-1-1-1-1-1-111-1111-1-111-1-1
χ10111111111111-1-1-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-111-111-111-1-1-1-111
χ11111111111111-1-1-1-1-1-11-1-111111-1-1-1-1-1-1111111-111-1-1-1-11111-1-1-1-111-11-1-111-1-111
χ12111111111111-1-1-1-1-1-11-1-111111-1-1-1-1-1-11111-1-1-1-1-11111-1-1-1-11-111-111-1-1-11111-1-1
χ13111111111111-1-1-1-1-1-11-1-1111-1-1111111-1-1-1-111-1111111-1-1-1-1111-1-1-1-1-1-1-111-1-111
χ14111111111111-1-1-1-1-1-11-1-1111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-111-111-1-11111-1-1
χ15111111111111-1-1-1-1-1-11-1-1111-1-1-1-1-1-111111111-111-1-1-1-11111111-1-1-1-1-111-1-111-1-1
χ16111111111111-1-1-1-1-1-11-1-1111-1-1-1-1-1-1111111-1-1-1-1-11111-1-1-1-1-11-111-11111-1-1-1-111
χ17222222222222222222-2-2-2-2-2-222000022000000-200000000000-2000-20000000000
χ18222222222222222222-2-2-2-2-2-2-2-20000-2-2000000-200000000000200020000000000
χ19222222222222-2-2-2-2-2-2-222-2-2-2220000-2-20000002000000000002000-20000000000
χ20222222222222-2-2-2-2-2-2-222-2-2-2-2-2000022000000200000000000-200020000000000
χ2122222222-2-2-2-22222-2-2222-2-2200000000000022-2-2-200000000000-2002000000000
χ2222222222-2-2-2-22222-2-2222-2-22000000000000-2-2-22200000000000200-2000000000
χ2322222222-2-2-2-22222-2-2-2-2-222-2000000000000002000000000020-20200-200000000
χ2422222222-2-2-2-22222-2-2-2-2-222-20000000000000020000000000-2020-200200000000
χ2522222222-2-2-2-2-2-2-2-2222-2-2-2-22000000000000222-2-200000000000200-2000000000
χ2622222222-2-2-2-2-2-2-2-2222-2-2-2-22000000000000-2-222200000000000-2002000000000
χ2722222222-2-2-2-2-2-2-2-222-22222-200000000000000-2000000000020-20-200200000000
χ2822222222-2-2-2-2-2-2-2-222-22222-200000000000000-20000000000-2020200-200000000
χ2922-22-22-2-2-2-22222-2-22-20000002-200002-2000000000i2i2−i2−i2i2i2−i2−i2000000000000i2−i2i2−i2
χ3022-22-22-2-2-2-22222-2-22-20000002-200002-2000000000−i2−i2i2i2−i2−i2i2i2000000000000−i2i2−i2i2
χ3122-22-22-2-2-2-22222-2-22-2000000-220000-22000000000i2i2−i2−i2i2i2−i2−i2000000000000−i2i2−i2i2
χ3222-22-22-2-2-2-22222-2-22-2000000-220000-22000000000−i2−i2i2i2−i2−i2i2i2000000000000i2−i2i2−i2
χ3322-22-22-2-2-2-222-2-222-220000002-20000-22000000000i2i2−i2−i2−i2−i2i2i2000000000000i2−i2−i2i2
χ3422-22-22-2-2-2-222-2-222-220000002-20000-22000000000−i2−i2i2i2i2i2−i2−i2000000000000−i2i2i2−i2
χ3522-22-22-2-2-2-222-2-222-22000000-2200002-2000000000i2i2−i2−i2−i2−i2i2i2000000000000−i2i2i2−i2
χ3622-22-22-2-2-2-222-2-222-22000000-2200002-2000000000−i2−i2i2i2i2i2−i2−i2000000000000i2−i2−i2i2
χ3722-2-2-2-2222-22-20000002002-2-2000000002i2i−2i−2i2-202-200002i−2i2i−2i0000000000000000
χ3822-2-2-2-2222-22-20000002002-2-2000000002i2i−2i−2i-220-220000−2i2i−2i2i0000000000000000
χ3922-2-2-2-2222-22-20000002002-2-200000000−2i−2i2i2i2-202-20000−2i2i−2i2i0000000000000000
χ4022-2-2-2-2222-22-20000002002-2-200000000−2i−2i2i2i-220-2200002i−2i2i−2i0000000000000000
χ4122-2-2-2-222-22-22000000200-22-2002i2i−2i−2i0000002-20-222i−2i2i−2i00000000000000000000
χ4222-2-2-2-222-22-22000000200-22-2002i2i−2i−2i000000-2202-2−2i2i−2i2i00000000000000000000
χ4322-2-2-2-222-22-22000000200-22-200−2i−2i2i2i0000002-20-22−2i2i−2i2i00000000000000000000
χ4422-2-2-2-222-22-22000000200-22-200−2i−2i2i2i000000-2202-22i−2i2i−2i00000000000000000000
χ45444-44-4-4-44-4-440000000000000000000000000000022−22−222200000000000000000000
χ46444-44-4-4-44-4-4400000000000000000000000000000−222222−2200000000000000000000
χ47444-44-4-4-4-444-400000000000000000000000000000000022−22−22220000000000000000
χ48444-44-4-4-4-444-4000000000000000000000000000000000−222222−220000000000000000
χ4944-44-44-4-444-4-444-4-4-4400000000000000000000000000000000000000000000000
χ5044-44-44-4-444-4-4-4-4444-400000000000000000000000000000000000000000000000
χ5144-4-4-4-4444-44-4000000-400-44400000000000000000000000000000000000000000
χ5244-4-4-4-444-44-44000000-4004-4400000000000000000000000000000000000000000
χ534-444-4-4-4400004i−4i4i−4i000000000000000000000000000000000000000002-22i−2i0000
χ544-444-4-4-4400004i−4i4i−4i00000000000000000000000000000000000000000-22−2i2i0000
χ554-444-4-4-440000−4i4i−4i4i000000000000000000000000000000000000000002-2−2i2i0000
χ564-444-4-4-440000−4i4i−4i4i00000000000000000000000000000000000000000-222i−2i0000
χ574-44-4-444-4000000000004i−4i000002i−2i2i−2i002-22-200000000000000000000000000000
χ584-44-4-444-4000000000004i−4i00000−2i2i−2i2i00-22-2200000000000000000000000000000
χ594-44-4-444-400000000000−4i4i000002i−2i2i−2i00-22-2200000000000000000000000000000
χ604-44-4-444-400000000000−4i4i00000−2i2i−2i2i002-22-200000000000000000000000000000
χ614-4-444-44-400004i−4i−4i4i00000000002-2-22002i−2i−2i2i00000000000000000000000000000
χ624-4-444-44-400004i−4i−4i4i0000000000-222-200−2i2i2i−2i00000000000000000000000000000
χ634-4-444-44-40000−4i4i4i−4i00000000002-2-2200−2i2i2i−2i00000000000000000000000000000
χ644-4-444-44-40000−4i4i4i−4i0000000000-222-2002i−2i−2i2i00000000000000000000000000000
χ658-8-8-888-88000000000000000000000000000000000000000000000000000000000

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