Finite Group Databasebeta

← Group #167684

Character table — Group #167684

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222444444444444444422444444488888888888888884444444444448888
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-11111111111111111-1-11-1-1-1-1-11-1-1-1-1-1-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1111-1111111
χ5111111111111111111111111-1-11-1-1111111111111-1-1-1-1-1-1-1-11-1-11-1-111-1-111-1-1-1-1
χ6111111111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-1111111111-1-11-1-1-1-1-1-1-1-11111
χ7111111111111111111111111-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-111-1-1-11-1-11111
χ8111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1-11111-1111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-11-1-11111111-1-1-111-1-11111-1-1-1-11111-1-1-1-11-1-1-111111-1-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-11-1-11111111-1-1-111-1-1-1-1-1-11111-1-1-1-111111-1-1-111-1-11-111-1-111
χ1111111111-1-1-1-1-1-1-1-11-1-11111111-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-11-11-1-1-1-11111-1-111
χ1211111111-1-1-1-1-1-1-1-11-1-11111111-1-1-1-1-111-1-1-1-11111-1-1-1-11111-11-11-1-11111-1-111-1-1
χ1311111111-1-1-1-1-1-1-1-11-1-111111-1-1-11111-1-11111-1-1-1-1-1-1-1-11111111-1-1-111-11-1-1-1-111
χ1411111111-1-1-1-1-1-1-1-11-1-111111-1-1-11111-1-1-1-1-1-111111111-1-1-1-1111-1-1-1-1-1-111111-1-1
χ1511111111-1-1-1-1-1-1-1-11-1-111111-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1
χ1611111111-1-1-1-1-1-1-1-11-1-111111-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1-1-111
χ172222222222222222-2-2-222-2-2-200-20022220000000000000000-200-2000000000000
χ182222222222222222-2-2-222-2-2-200-200-2-2-2-200000000000000002002000000000000
χ19222222222222-2-2-2-22-2-2-2-2-2-2200200000000000000000000000200-22000-2000000
χ20222222222222-2-2-2-22-2-2-2-2-2-2200200000000000000000000000-2002-20002000000
χ21222222222222-2-2-2-2-222-2-222-222-2220000000000000000000000-200000-20000000
χ22222222222222-2-2-2-2-222-2-222-2-2-2-2-2-2000000000000000000000020000020000000
χ2322222222-2-2-2-22222222-2-2-2-2200-2000000000000000000000002002-2000-2000000
χ2422222222-2-2-2-22222222-2-2-2-2200-200000000000000000000000-200-220002000000
χ2522222222-2-2-2-22222-2-2-2-2-222-2222-2-20000000000000000000000200000-20000000
χ2622222222-2-2-2-22222-2-2-2-2-222-2-2-22220000000000000000000000-20000020000000
χ2722222222-2-2-2-2-2-2-2-2-22222-2-2-20020022-2-20000000000000000-2002000000000000
χ2822222222-2-2-2-2-2-2-2-2-22222-2-2-200200-2-2220000000000000000200-2000000000000
χ292-222-2-2-222i2i−2i−2i2i2i−2i−2i0002-2000000002i−2i2-20000000022−2−2i2i2−i2−i2000000000000i2−i22−2
χ302-222-2-2-222i2i−2i−2i2i2i−2i−2i0002-2000000002i−2i2-200000000−2−222−i2−i2i2i2000000000000−i2i2−22
χ312-222-2-2-222i2i−2i−2i2i2i−2i−2i0002-200000000−2i2i-220000000022−2−2i2i2−i2−i2000000000000−i2i2−22
χ322-222-2-2-222i2i−2i−2i2i2i−2i−2i0002-200000000−2i2i-2200000000−2−222−i2−i2i2i2000000000000i2−i22−2
χ332-222-2-2-22−2i−2i2i2i−2i−2i2i2i0002-2000000002i−2i-220000000022−2−2−i2−i2i2i2000000000000i2−i2−22
χ342-222-2-2-22−2i−2i2i2i−2i−2i2i2i0002-2000000002i−2i-2200000000−2−222i2i2−i2−i2000000000000−i2i22−2
χ352-222-2-2-22−2i−2i2i2i−2i−2i2i2i0002-200000000−2i2i2-20000000022−2−2−i2−i2i2i2000000000000−i2i22−2
χ362-222-2-2-22−2i−2i2i2i−2i−2i2i2i0002-200000000−2i2i2-200000000−2−222i2i2−i2−i2000000000000i2−i2−22
χ372-22-22-22-22i−2i2i−2i000002i−2i002-202-202i−2i000022−2−2i2i2−i2−i22−22−2i2−i2i2−i20000000000000000
χ382-22-22-22-22i−2i2i−2i000002i−2i002-202-202i−2i0000−2−222−i2−i2i2i2−22−22−i2i2−i2i20000000000000000
χ392-22-22-22-22i−2i2i−2i000002i−2i002-20-220−2i2i000022−2−2i2i2−i2−i2−22−22−i2i2−i2i20000000000000000
χ402-22-22-22-22i−2i2i−2i000002i−2i002-20-220−2i2i0000−2−222−i2−i2i2i22−22−2i2−i2i2−i20000000000000000
χ412-22-22-22-2−2i2i−2i2i00000−2i2i002-202-20−2i2i000022−2−2−i2−i2i2i22−22−2−i2i2−i2i20000000000000000
χ422-22-22-22-2−2i2i−2i2i00000−2i2i002-202-20−2i2i0000−2−222i2i2−i2−i2−22−22i2−i2i2−i20000000000000000
χ432-22-22-22-2−2i2i−2i2i00000−2i2i002-20-2202i−2i000022−2−2−i2−i2i2i2−22−22i2−i2i2−i20000000000000000
χ442-22-22-22-2−2i2i−2i2i00000−2i2i002-20-2202i−2i0000−2−222i2i2−i2−i22−22−2−i2i2−i2i20000000000000000
χ45444-4-44-4-44-4-44000000000000000000000000000002-2-222-2-220000000000000000
χ46444-4-44-4-44-4-4400000000000000000000000000000-222-2-222-20000000000000000
χ47444-4-44-4-4-444-4000000000000000000000000000002-2-22-222-20000000000000000
χ48444-4-44-4-4-444-400000000000000000000000000000-222-22-2-220000000000000000
χ4944-444-4-4-400004-44-4000000000000000002-22-22-22-2000000000000000000000000
χ5044-444-4-4-400004-44-400000000000000000-22-22-22-22000000000000000000000000
χ5144-444-4-4-40000-44-44000000000000000002-22-2-22-22000000000000000000000000
χ5244-444-4-4-40000-44-4400000000000000000-22-222-22-2000000000000000000000000
χ534-444-4-4-444i4i−4i−4i−4i−4i4i4i000-4400000000000000000000000000000000000000000000
χ544-444-4-4-44−4i−4i4i4i4i4i−4i−4i000-4400000000000000000000000000000000000000000000
χ554-44-44-44-44i−4i4i−4i00000−4i4i00-44000000000000000000000000000000000000000000
χ564-44-44-44-4−4i4i−4i4i000004i−4i00-44000000000000000000000000000000000000000000
χ574-4-44-444-400004i−4i−4i4i0000000000000000000000000000000000000002-2002i−2i0000
χ584-4-44-444-400004i−4i−4i4i000000000000000000000000000000000000000-2200−2i2i0000
χ594-4-44-444-40000−4i4i4i−4i0000000000000000000000000000000000000002-200−2i2i0000
χ604-4-44-444-40000−4i4i4i−4i000000000000000000000000000000000000000-22002i−2i0000
χ614-4-4-444-44000000004000000-400000000000002i2−2i2−2i22i2000000000000000000000000
χ624-4-4-444-44000000004000000-40000000000000−2i22i22i2−2i2000000000000000000000000
χ634-4-4-444-4400000000-4000000400000000022−22−22220000000000000000000000000000
χ644-4-4-444-4400000000-40000004000000000−222222−220000000000000000000000000000
χ6588-8-8-8-888000000000000000000000000000000000000000000000000000000000

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