Finite Group Databasebeta

← Group #167504

Character table — Group #167504

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222444444444444444444444444488888888888888882244444444448888
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
χ311111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-11-1-111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111
χ7111111111111111111111111-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111
χ8111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-1-1-111111111-1-1-111-1-11111-1-1-1-11111-1-1-1-11-11-11-11-111-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-1-1-111111111-1-1-111-1-1-1-1-1-11111-1-1-1-111111-11-11-11-1-1-111-1-111
χ1111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-111-1-11-1111-1-1-1-111
χ1211111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-1-1-111111111-1-1-1-1-111-1-11-11-1-11111-1-1
χ1311111111-1-1-1-1-1-1-1-1-1-1111111-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-11-111-1-11-1-111-1-111
χ1411111111-1-1-1-1-1-1-1-1-1-1111111-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-11-111-1-1111-1-111-1-1
χ1511111111-1-1-1-1-1-1-1-1-1-1111111-1-1-111-1-1111111-1-1-1-1-1-1-1-111111-1-11-111-1-1-11111-1-1
χ1611111111-1-1-1-1-1-1-1-1-1-1111111-1-1-111-1-111-1-1-1-111111111-1-1-1-11-1-11-111-111-1-1-1-111
χ172222222222222222-2-22-2-22-2-222-2220000000000000000000000-2-2000000000000
χ182222222222222222-2-22-2-22-2-2-2-2-2-2-2000000000000000000000022000000000000
χ19222222222222-2-2-2-222-2-22-2-2200-200000000000000000000002-20000-2200000000
χ20222222222222-2-2-2-222-2-22-2-2200-20000000000000000000000-2200002-200000000
χ21222222222222-2-2-2-2-2-2-22-2-22-20020022-2-200000000000000000000-220000000000
χ22222222222222-2-2-2-2-2-2-22-2-22-200200-2-222000000000000000000002-20000000000
χ2322222222-2-2-2-2222222-22-2-22-200-200222200000000000000000000-2-20000000000
χ2422222222-2-2-2-2222222-22-2-22-200-200-2-2-2-200000000000000000000220000000000
χ2522222222-2-2-2-22222-2-2-2-22-2-220020000000000000000000000220000-2-200000000
χ2622222222-2-2-2-22222-2-2-2-22-2-220020000000000000000000000-2-200002200000000
χ2722222222-2-2-2-2-2-2-2-2222-2-22-2-2222-2-20000000000000000000000-22000000000000
χ2822222222-2-2-2-2-2-2-2-2222-2-22-2-2-2-222200000000000000000000002-2000000000000
χ2922-2-222-2-2000022-2-22-20-20020000002i−2i2i−2i22−2−222−2−2i2i2−i2−i2i2i2−i2−i20000000000000000
χ3022-2-222-2-2000022-2-22-20-20020000002i−2i2i−2i−2−222−2−222−i2−i2i2i2−i2−i2i2i20000000000000000
χ3122-2-222-2-2000022-2-22-20-2002000000−2i2i−2i2i22−2−222−2−2−i2−i2i2i2−i2−i2i2i20000000000000000
χ3222-2-222-2-2000022-2-22-20-2002000000−2i2i−2i2i−2−222−2−222i2i2−i2−i2i2i2−i2−i20000000000000000
χ3322-2-222-2-20000-2-222-220-20020000002i−2i−2i2i22−2−2−2−222i2i2−i2−i2−i2−i2i2i20000000000000000
χ3422-2-222-2-20000-2-222-220-20020000002i−2i−2i2i−2−22222−2−2−i2−i2i2i2i2i2−i2−i20000000000000000
χ3522-2-222-2-20000-2-222-220-2002000000−2i2i2i−2i22−2−2−2−222−i2−i2i2i2i2i2−i2−i20000000000000000
χ3622-2-222-2-20000-2-222-220-2002000000−2i2i2i−2i−2−22222−2−2i2i2−i2−i2−i2−i2i2i20000000000000000
χ372-2222-2-2-222-2-22-22-200-2002002i−2i02i−2i000000000000i2−i2i2−i2i2−i2i2−i20000000000002−22−2
χ382-2222-2-2-222-2-22-22-200-2002002i−2i02i−2i000000000000−i2i2−i2i2−i2i2−i2i2000000000000−22−22
χ392-2222-2-2-222-2-22-22-200-200200−2i2i0−2i2i000000000000i2−i2i2−i2i2−i2i2−i2000000000000−22−22
χ402-2222-2-2-222-2-22-22-200-200200−2i2i0−2i2i000000000000−i2i2−i2i2−i2i2−i2i20000000000002−22−2
χ412-2222-2-2-2-2-222-22-2200-2002002i−2i0−2i2i000000000000i2−i2i2−i2−i2i2−i2i20000000000002−2−22
χ422-2222-2-2-2-2-222-22-2200-2002002i−2i0−2i2i000000000000−i2i2−i2i2i2−i2i2−i2000000000000−222−2
χ432-2222-2-2-2-2-222-22-2200-200200−2i2i02i−2i000000000000i2−i2i2−i2−i2i2−i2i2000000000000−222−2
χ442-2222-2-2-2-2-222-22-2200-200200−2i2i02i−2i000000000000−i2i2−i2i2i2−i2i2−i20000000000002−2−22
χ45444-4-4-44-4000000000000400-400000000022−2222−220000000000000000000000000000
χ46444-4-4-44-4000000000000400-4000000000−2222−22220000000000000000000000000000
χ47444-4-4-44-4000000000000-400400000000000002i2−2i22i2−2i2000000000000000000000000
χ48444-4-4-44-4000000000000-40040000000000000−2i22i2−2i22i2000000000000000000000000
χ4944-44-4-4-444i−4i4i−4i0000000000000000000002-2-222i−2i−2i2i000000000000000000000000
χ5044-44-4-4-444i−4i4i−4i000000000000000000000-222-2−2i2i2i−2i000000000000000000000000
χ5144-44-4-4-44−4i4i−4i4i0000000000000000000002-2-22−2i2i2i−2i000000000000000000000000
χ5244-44-4-4-44−4i4i−4i4i000000000000000000000-222-22i−2i−2i2i000000000000000000000000
χ5344-4-444-4-4000044-4-4-440400-4000000000000000000000000000000000000000000
χ5444-4-444-4-40000-4-4444-40400-4000000000000000000000000000000000000000000
χ554-4444-4-4-444-4-4-44-4400400-40000000000000000000000000000000000000000000
χ564-4444-4-4-4-4-4444-44-400400-40000000000000000000000000000000000000000000
χ574-4-44-444-44i−4i−4i4i0000000000000000000000000000000000000000000002-22i−2i0000
χ584-4-44-444-44i−4i−4i4i000000000000000000000000000000000000000000000-22−2i2i0000
χ594-4-44-444-4−4i4i4i−4i0000000000000000000000000000000000000000000002-2−2i2i0000
χ604-4-44-444-4−4i4i4i−4i000000000000000000000000000000000000000000000-222i−2i0000
χ614-4-4-44-44400004-4-4400000000000000000000000002-2-222-2-220000000000000000
χ624-4-4-44-44400004-4-440000000000000000000000000-222-2-222-20000000000000000
χ634-4-4-44-4440000-444-400000000000000000000000002-2-22-222-20000000000000000
χ644-4-4-44-4440000-444-40000000000000000000000000-222-22-2-220000000000000000
χ658-88-8-88-88000000000000000000000000000000000000000000000000000000000

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