Finite Group Databasebeta

← Group #300720

Character table — Group #300720

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111111112222222244444444448888888888888888888816161616161616161616161616163232
order12222222444444444444448888224444888888888888884444444488888844
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-111-1-11111111111111111-1-1-1-1-1-111-1-1-1-1-1-1
χ411111111111111111111111111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-111-1-11-1
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111-1-1-111-1-111-11
χ71111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1111-1-1-1-111-11
χ81111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111111-1-11-1
χ911111111111111111-1-1-1-11111111-1-111111111-1-1-1-11111-1-11-1-11-1-1-1-11111-1-1
χ1011111111111111111-1-1-1-11111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1111-1-11-1-111-1-1-1-111
χ1111111111111111111-1-1-1-111111-1-1-1-1-1-1111111-1-1-1-11111-1-1-111-111-1-1-1-1-1-111
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-111-111111111-1-1
χ1311111111111111111-1-1-1-11-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1-1-11-1-1-1111111-1-1-11
χ1411111111111111111-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111111-1-1-111-1-1-1-1111-1
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1111-1-111-1-1111-1
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111-1111-1-1-1-111-1-1-11
χ17222222222-222-2-2-22-22222-2000000-2-20022-2-200000000002-200000000000000
χ18222222222-222-2-2-22-22222-2000000-2-200-2-2220000000000-2200000000000000
χ19222222222-222-2-2-22-2-2-2-2-2-2000000220022-2-20000000000-2200000000000000
χ20222222222-222-2-2-22-2-2-2-2-2-20000002200-2-22200000000002-200000000000000
χ2122222222-22-2-2222-2-20000-222222200220000-2-20000000000-200-20000000000
χ2222222222-22-2-2222-2-20000-22222-2-200-2-20000-2-2000000000020020000000000
χ2322222222-22-2-2222-2-20000-2-2-2-2-22200-2-20000220000000000-20020000000000
χ2422222222-22-2-2222-2-20000-2-2-2-2-2-2-200220000220000000000200-20000000000
χ252-2-222-2-220-20022-2000000022-2-22-2002-2i2−i2i2−i2000000i2i2−i2−i20000000000i2−i2i2−i200
χ262-2-222-2-220-20022-2000000022-2-22-2002-2−i2i2−i2i2000000−i2−i2i2i20000000000−i2i2−i2i200
χ272-2-222-2-220-20022-2000000022-2-2-2200-22i2−i2i2−i2000000i2i2−i2−i20000000000−i2i2−i2i200
χ282-2-222-2-220-20022-2000000022-2-2-2200-22−i2i2−i2i2000000−i2−i2i2i20000000000i2−i2i2−i200
χ292-2-222-2-220-20022-20000000-2-2222-200-22i2−i2i2−i2000000−i2−i2i2i20000000000i2−i2−i2i200
χ302-2-222-2-220-20022-20000000-2-2222-200-22−i2i2−i2i2000000i2i2−i2−i20000000000−i2i2i2−i200
χ312-2-222-2-220-20022-20000000-2-222-22002-2i2−i2i2−i2000000−i2−i2i2i20000000000−i2i2i2−i200
χ322-2-222-2-220-20022-20000000-2-222-22002-2−i2i2−i2i2000000i2i2−i2−i20000000000i2−i2−i2i200
χ332-2-2-2-222222-2-2-22-22-222-2-220000002-20000000000002-22-2000000002-2000000
χ342-2-2-2-222222-2-2-22-22-222-2-220000002-2000000000000-22-2200000000-22000000
χ352-2-2-2-222222-2-2-22-22-2-2-2222000000-220000000000002-22-200000000-22000000
χ362-2-2-2-222222-2-2-22-22-2-2-2222000000-22000000000000-22-22000000002-2000000
χ372-2-2-2-22222-2-2-22-222222-2-2-22-22-200-220000002-222-2-200000000000000000000
χ382-2-2-2-22222-2-2-22-222222-2-2-2-22-2200-22000000-22-2-22200000000000000000000
χ392-2-2-2-22222-2-2-22-2222-2-222-22-22-2002-20000002-2-2-22200000000000000000000
χ402-2-2-2-22222-2-2-22-2222-2-222-2-22-22002-2000000-2222-2-200000000000000000000
χ412-2-2-2-2222-2-2222-22-2-2000022-22-20000000000-22000000000002-202-200000000
χ422-2-2-2-2222-2-2222-22-2-2000022-22-20000000000-2200000000000-220-2200000000
χ432-2-2-2-2222-2-2222-22-2-200002-22-2200000000002-2000000000002-20-2200000000
χ442-2-2-2-2222-2-2222-22-2-200002-22-2200000000002-200000000000-2202-200000000
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000
χ46444-4-4-4-4404004-4-400000004-4-44000000000000000000000000000000000000
χ47444-4-4-4-4404004-4-40000000-444-4000000000000000000000000000000000000
χ48444-4-4-4-440-400-4440000000000000000000000000002i2−2i2−2i22i20000000000000000
χ49444-4-4-4-440-400-444000000000000000000000000000−2i22i22i2−2i20000000000000000
χ5044-44-44-4-4404-4000-4000000000000000000000022−2222−2200000000000000000000
χ5144-44-44-4-4404-4000-40000000000000000000000−2222−222200000000000000000000
χ5244-44-44-4-4-40-44000404i−4i4i−4i00000000000000000000000000000000000000000
χ5344-44-44-4-4-40-4400040−4i4i−4i4i00000000000000000000000000000000000000000
χ544-44-444-4-440-44000-4000000000000000000000022−22−222200000000000000000000
χ554-44-444-4-440-44000-40000000000000000000000−222222−2200000000000000000000
χ564-44-444-4-4-404-4000404i−4i−4i4i00000000000000000000000000000000000000000
χ574-44-444-4-4-404-400040−4i4i4i−4i00000000000000000000000000000000000000000
χ584-4-444-4-440400-4-44000000000000000002i2−2i2−2i22i200000000000000000000000000
χ594-4-444-4-440400-4-4400000000000000000−2i22i22i2−2i200000000000000000000000000
χ604-4-4-4-4444-4444-44-4-440000-40000000000000000000000000000000000000000
χ6188-8-88-88-8000000000000000000000000000000000000000000000000000000
χ628-888-8-88-8000000000000000000000000000000000000000000000000000000

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