Finite Group Databasebeta

← Group #284368

Character table — Group #284368

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111111112222222244444444448888888888888888888816161616161616161616161616163232
order12222222444444444444448888444444888888888888882222444488888844
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1111111-1-1-1-1-1-1111-1-1111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-111-1-111111111111111-1-1-111-1-1-1-1-111-1-1-1-1
χ411111111111111111111111111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111
χ51111111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-111111-1-1-1-111-11
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111111-1-11-1
χ71111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111111-1-1-111-1-1-1-11-1
χ81111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-11111-11
χ911111111111111111-1-1-1-11111111-1-1111111-1-1-1-11111111-1-1-1-11-1-111-1-111-1-1
χ1011111111111111111-1-1-1-11111111-1-111-1-111-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-111-1-111
χ1111111111111111111-1-1-1-111111-1-1-1-1-1-11111-1-1-1-1111111-111-1-1-111-1-1-1-1-1-111
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11111-111111111-1-1
χ1311111111111111111-1-1-1-11-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1-111-1-11-1-1-1-111111-1
χ1411111111111111111-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-111111-1-111-1-1-1-1-11
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-11-1-1-1-1-1111111-1-1-11
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-11111-1-111111-1-111-111-1-1-1-1111-1
χ172222222222-2-2-222-2-20000-2222222002200-2-20000000000-20000-20000000000
χ182222222222-2-2-222-2-20000-22222-2-200-2-200-2-200000000002000020000000000
χ192222222222-2-2-222-2-20000-2-2-2-2-22200-2-20022000000000020000-20000000000
χ202222222222-2-2-222-2-20000-2-2-2-2-2-2-2002200220000000000-2000020000000000
χ2122222222-2-2222-2-22-22222-2000000-2-20022000000-2-20000000-2200000000000
χ2222222222-2-2222-2-22-22222-2000000-2-200-2-20000002200000002-200000000000
χ2322222222-2-2222-2-22-2-2-2-2-2-2000000220022000000-2-200000002-200000000000
χ2422222222-2-2222-2-22-2-2-2-2-2-20000002200-2-2000000220000000-2200000000000
χ2522-22-2-22-22-20002-2000000022-2-22i−2i002i−2ii2−i2000000i2−i2i2i2−i2−i2000000002−2002−200
χ2622-22-2-22-22-20002-2000000022-2-22i−2i002i−2i−i2i2000000−i2i2−i2−i2i2i200000000−2200−2200
χ2722-22-2-22-22-20002-2000000022-2-2−2i2i00−2i2ii2−i2000000i2−i2i2i2−i2−i200000000−2200−2200
χ2822-22-2-22-22-20002-2000000022-2-2−2i2i00−2i2i−i2i2000000−i2i2−i2−i2i2i2000000002−2002−200
χ2922-22-2-22-22-20002-20000000-2-2222i−2i00−2i2ii2−i2000000i2−i2−i2−i2i2i200000000−22002−200
χ3022-22-2-22-22-20002-20000000-2-2222i−2i00−2i2i−i2i2000000−i2i2i2i2−i2−i2000000002−200−2200
χ3122-22-2-22-22-20002-20000000-2-222−2i2i002i−2ii2−i2000000i2−i2−i2−i2i2i2000000002−200−2200
χ3222-22-2-22-22-20002-20000000-2-222−2i2i002i−2i−i2i2000000−i2i2i2i2−i2−i200000000−22002−200
χ332-2-222-2-22222-22-2-2-2-2000022i−2i2i−2i000000002i−2i000000000002-20002i−2i00000000
χ342-2-222-2-22222-22-2-2-2-2000022i−2i2i−2i000000002i−2i00000000000-22000−2i2i00000000
χ352-2-222-2-22222-22-2-2-2-200002−2i2i−2i2i00000000−2i2i000000000002-2000−2i2i00000000
χ362-2-222-2-22222-22-2-2-2-200002−2i2i−2i2i00000000−2i2i00000000000-220002i−2i00000000
χ372-2-222-2-2222-22-2-2-22222-2-2-22i−2i2i−2i002-20000−2i2i2i2i−2i−2i0000000000000000000000
χ382-2-222-2-2222-22-2-2-22222-2-2-2−2i2i−2i2i002-200002i−2i−2i−2i2i2i0000000000000000000000
χ392-2-222-2-2222-22-2-2-222-2-222-22i−2i2i−2i00-220000−2i2i−2i−2i2i2i0000000000000000000000
χ402-2-222-2-2222-22-2-2-222-2-222-2−2i2i−2i2i00-2200002i−2i2i2i−2i−2i0000000000000000000000
χ412-2-222-2-22-2-2-22-2222-222-2-22000000-220000000000002-22-200000000002-20000
χ422-2-222-2-22-2-2-22-2222-222-2-22000000-22000000000000-22-220000000000-220000
χ432-2-222-2-22-2-2-22-2222-2-2-22220000002-20000000000002-22-20000000000-220000
χ442-2-222-2-22-2-2-22-2222-2-2-22220000002-2000000000000-22-2200000000002-20000
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000
χ4644-44-4-44-4-44000-44000000000000000002i2−2i2000000−2i22i200000000000000000000
χ4744-44-4-44-4-44000-4400000000000000000−2i22i20000002i2−2i200000000000000000000
χ4844-4-4-44-440044-400-4000000000000000000002i2−2i22i2−2i20000000000000000000000
χ4944-4-4-44-440044-400-400000000000000000000−2i22i2−2i22i20000000000000000000000
χ5044-4-4-44-4400-4-4400404-44-400000000000000000000000000000000000000000
χ5144-4-4-44-4400-4-440040-44-4400000000000000000000000000000000000000000
χ524-444-44-4-44-4000-4400000004i−4i−4i4i000000000000000000000000000000000000
χ534-444-44-4-44-4000-440000000−4i4i4i−4i000000000000000000000000000000000000
χ544-444-44-4-4-440004-40000000000000000000000000002i2−2i2−2i22i20000000000000000
χ554-444-44-4-4-440004-4000000000000000000000000000−2i22i22i2−2i20000000000000000
χ564-44-4-4-444004-4-400404-4-4400000000000000000000000000000000000000000
χ574-44-4-4-444004-4-40040-444-400000000000000000000000000000000000000000
χ584-44-4-4-44400-44400-40000000000000000000022−22−22220000000000000000000000
χ594-44-4-4-44400-44400-400000000000000000000−222222−220000000000000000000000
χ604-4-444-4-44-4-44-4444-440000-40000000000000000000000000000000000000000
χ61888-88-8-8-8000000000000000000000000000000000000000000000000000000
χ628-8-8-8888-8000000000000000000000000000000000000000000000000000000

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