Finite Group Databasebeta

← Group #288165

Character table — Group #288165

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111111112222222244444444448888888888888888888816161616161616161616161616163232
order12222222444444444444448888444444888888888888884444444488888824
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1111111-1-1-1-1-1-11-111111-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-111-1-111111111111111-11-1-1-1-1-1111-1-1-1-1-1-1
χ411111111111111111111111111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-111-1-1-1-1-111-1-1111-1-111-1-11-1
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11-1-111-111-1-111-11
χ71111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111-111-1-11-1-1-1-111-11
χ81111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111-1-111-1-1-11111-1-11-1
χ911111111111111111-1-1-1-11111111-1-11111-1-1-1-1111111111-11-1-1-1-1-1-1-11111-1-1
χ1011111111111111111-1-1-1-11111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1111-1-1-1-1111-1-1-1-111
χ1111111111111111111-1-1-1-111111-1-1-1-1-1-111-1-1-1-111111111-1-1-11111-1-1-1-1-1-1-111
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-11-111111111111-1-1
χ1311111111111111111-1-1-1-11-1-1-1-111-1-1-1-1111111-1-111-1-1-1-1-1-1111-1-1-11111-1-1-11
χ1411111111111111111-1-1-1-11-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-11111-1-11-1-1-1-1111-1
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11-1-1-1-111-111-1-1111-1
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-1-1111-1-111-1-1-11
χ17222222222-2-22-222-2-20000-22222220022000000-2-2000000-20-20000000000000
χ18222222222-2-22-222-2-20000-22222-2-200-2-2000000-2-20000002020000000000000
χ19222222222-2-22-222-2-20000-2-2-2-2-22200-2-20000002200000020-20000000000000
χ20222222222-2-22-222-2-20000-2-2-2-2-2-2-2002200000022000000-2020000000000000
χ2122222222-222-22-2-22-22222-2000000-2-20022000000-2-200000200000-200000000
χ2222222222-222-22-2-22-22222-2000000-2-200-2-20000002200000-200000200000000
χ2322222222-222-22-2-22-2-2-2-2-2-2000000220022000000-2-200000-200000200000000
χ2422222222-222-22-2-22-2-2-2-2-2-20000002200-2-20000002200000200000-200000000
χ252-2-22-2-222222-2-22-2-2-22i2i−2i−2i20000002i−2i00000000000022-2-2000000002i−2i000000
χ262-2-22-2-222222-2-22-2-2-22i2i−2i−2i20000002i−2i000000000000-2-22200000000−2i2i000000
χ272-2-22-2-222222-2-22-2-2-2−2i−2i2i2i2000000−2i2i00000000000022-2-200000000−2i2i000000
χ282-2-22-2-222222-2-22-2-2-2−2i−2i2i2i2000000−2i2i000000000000-2-222000000002i−2i000000
χ292-2-22-2-222-2222-2-22-222i2i−2i−2i-222-2-200−2i2i00002i2i−2i−2i2-20000000000000000000000
χ302-2-22-2-222-2222-2-22-222i2i−2i−2i-2-2-22200−2i2i0000−2i−2i2i2i-220000000000000000000000
χ312-2-22-2-222-2222-2-22-22−2i−2i2i2i-222-2-2002i−2i0000−2i−2i2i2i2-20000000000000000000000
χ322-2-22-2-222-2222-2-22-22−2i−2i2i2i-2-2-222002i−2i00002i2i−2i−2i-220000000000000000000000
χ332-2-22-2-222-2-2-222-222-20000222-2-2000000000000-220000000002-22-2000000000
χ342-2-22-2-222-2-2-222-222-20000222-2-2000000000000-22000000000-22-22000000000
χ352-2-22-2-222-2-2-222-222-200002-2-2220000000000002-20000000002-2-22000000000
χ362-2-22-2-222-2-2-222-222-200002-2-2220000000000002-2000000000-222-2000000000
χ372-2-2-2222-2200-20-2200000002i−2i2i−2i2i−2i002-2i2−i2000000i2−i22−22−200000000002−2i2−i200
χ382-2-2-2222-2200-20-2200000002i−2i2i−2i2i−2i002-2−i2i2000000−i2i2−22−220000000000−22−i2i200
χ392-2-2-2222-2200-20-2200000002i−2i2i−2i−2i2i00-22i2−i2000000i2−i22−22−20000000000−22−i2i200
χ402-2-2-2222-2200-20-2200000002i−2i2i−2i−2i2i00-22−i2i2000000−i2i2−22−2200000000002−2i2−i200
χ412-2-2-2222-2200-20-220000000−2i2i−2i2i2i−2i00-22i2−i2000000i2−i2−22−2200000000002−2−i2i200
χ422-2-2-2222-2200-20-220000000−2i2i−2i2i2i−2i00-22−i2i2000000−i2i22−22−20000000000−22i2−i200
χ432-2-2-2222-2200-20-220000000−2i2i−2i2i−2i2i002-2i2−i2000000i2−i2−22−220000000000−22i2−i200
χ442-2-2-2222-2200-20-220000000−2i2i−2i2i−2i2i002-2−i2i2000000−i2i22−22−200000000002−2−i2i200
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000
χ46444-4-4-44-440040-4-400000000000000000000000000022−22−22220000000000000000
χ47444-4-4-44-440040-4-4000000000000000000000000000−222222−220000000000000000
χ48444-4-4-44-4-400-404400000004i−4i−4i4i000000000000000000000000000000000000
χ49444-4-4-44-4-400-40440000000−4i4i4i−4i000000000000000000000000000000000000
χ5044-4-44-4-4404-40400-40000000000000000002i2−2i22i2−2i2000000000000000000000000
χ5144-4-44-4-4404-40400-4000000000000000000−2i22i2−2i22i2000000000000000000000000
χ5244-4-44-4-440-440-400404-44-400000000000000000000000000000000000000000
χ5344-4-44-4-440-440-40040-44-4400000000000000000000000000000000000000000
χ544-44-4-44-4404-40-400400000000000000000022−22−2222000000000000000000000000
χ554-44-4-44-4404-40-4004000000000000000000−222222−22000000000000000000000000
χ564-44-4-44-440-440400-404i−4i−4i4i00000000000000000000000000000000000000000
χ574-44-4-44-440-440400-40−4i4i4i−4i00000000000000000000000000000000000000000
χ584-4-44-4-4444-4-4-444-4440000-40000000000000000000000000000000000000000
χ594-4-4-4444-4-400404-4000000000000000002i2−2i2000000−2i22i200000000000000000000
χ604-4-4-4444-4-400404-400000000000000000−2i22i20000002i2−2i200000000000000000000
χ6188-88-88-8-8000000000000000000000000000000000000000000000000000000
χ628-8888-8-8-8000000000000000000000000000000000000000000000000000000

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