Finite Group Databasebeta

← Group #457247

Character table — Group #457247

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222222222444444444444444444444444161616161616161616161616161616161616161616161616
order12222222222244444444444444448888888888888888224444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-111-1-1-1-1-1-11-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111111111-11-1-111-1-1-1-1-11-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111111111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-111-1-1-1-111
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111-1-1111-1-1-11111-1-111-1-1
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-11-1-111-1-111-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-1
χ911111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-111-1-1-1-1
χ1011111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-11-11111-1-1111111
χ1111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111111-1-1-1-1-11111111-1-1-1-1-1-1
χ1211111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-11111
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-111-1-111-1-1-1-111-1-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11111-1-1111-111-1-1-1-1-1-1-1-111
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1-1-1-1-1-111-1111-1-1111111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1111111-1-111
χ1722222222-2-2-2-222-22-2-2-2200000000000000002222-2-2-2-2202-2000000-20000000000000
χ1822222222-2-2-2-222-22-2-2-2200000000000000002222-2-2-2-2-20-2200000020000000000000
χ1922222222-2-2-2-222-22-2-2-220000000000000000-2-2-2-2222220-22000000-20000000000000
χ2022222222-2-2-2-222-22-2-2-220000000000000000-2-2-2-22222-202-200000020000000000000
χ2122222222-2-2-2-2-2-22-2222-2000000002222-2-2-2-20000000002002-200000-2000000000000
χ2222222222-2-2-2-2-2-22-2222-2000000002222-2-2-2-2000000000-200-22000002000000000000
χ2322222222-2-2-2-2-2-22-2222-200000000-2-2-2-22222000000000200-2200000-2000000000000
χ2422222222-2-2-2-2-2-22-2222-200000000-2-2-2-22222000000000-2002-2000002000000000000
χ2522-2-2-2-2222-2-222-2-2-222-222222-2-2-2-200000000000000000000002-200002-20000000000
χ2622-2-2-2-2222-2-222-2-2-222-222222-2-2-2-20000000000000000000000-220000-220000000000
χ2722-2-2-2-2222-2-222-2-2-222-22-2-2-2-2222200000000000000000000002-20000-220000000000
χ2822-2-2-2-2222-2-222-2-2-222-22-2-2-2-222220000000000000000000000-2200002-20000000000
χ292-222-2-2-2222-2-222-2-22-22-22i2i−2i−2i2i2i−2i−2i22-2-222-2-22i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ302-222-2-2-2222-2-222-2-22-22-22i2i−2i−2i2i2i−2i−2i-2-222-2-222−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ312-222-2-2-2222-2-222-2-22-22-2−2i−2i2i2i−2i−2i2i2i22-2-222-2-2−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ322-222-2-2-2222-2-222-2-22-22-2−2i−2i2i2i−2i−2i2i2i-2-222-2-2222i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ332-222-2-2-22-2-222222-2-22-2-200000000000000002i2i−2i−2i−2i−2i2i2i00000000000000002-22i−2i0000
χ342-222-2-2-22-2-222222-2-22-2-200000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000-22−2i2i0000
χ352-222-2-2-22-2-222222-2-22-2-20000000000000000−2i−2i2i2i2i2i−2i−2i00000000000000002-2−2i2i0000
χ362-222-2-2-22-2-222222-2-22-2-20000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000-222i−2i0000
χ372-222-2-2-22-2-222-2-2-222-2220000000022-2-2-2-22200000000000000000000000000002-22-2
χ382-222-2-2-22-2-222-2-2-222-2220000000022-2-2-2-2220000000000000000000000000000-22-22
χ392-222-2-2-22-2-222-2-2-222-22200000000-2-22222-2-200000000000000000000000000002-2-22
χ402-222-2-2-22-2-222-2-2-222-22200000000-2-22222-2-20000000000000000000000000000-222-2
χ412-2-2-222-222-22-22-2222-2-2-22i2i−2i−2i−2i−2i2i2i0000000000000000000000002i−2i00002-200000000
χ422-2-2-222-222-22-22-2222-2-2-22i2i−2i−2i−2i−2i2i2i000000000000000000000000−2i2i0000-2200000000
χ432-2-2-222-222-22-22-2222-2-2-2−2i−2i2i2i2i2i−2i−2i0000000000000000000000002i−2i0000-2200000000
χ442-2-2-222-222-22-22-2222-2-2-2−2i−2i2i2i2i2i−2i−2i000000000000000000000000−2i2i00002-200000000
χ45444444444444-4-4-4-4-4-4-4-4000000000000000000000000000000000000000000000000
χ46444-44-4-4-40000000000002-22-22-22-2000022−2222−22000022−2222−22000000000000000000000000
χ47444-44-4-4-40000000000002-22-22-22-20000−2222−22220000−2222−2222000000000000000000000000
χ48444-44-4-4-4000000000000-22-22-22-22000022−2222−220000−2222−2222000000000000000000000000
χ49444-44-4-4-4000000000000-22-22-22-220000−2222−2222000022−2222−22000000000000000000000000
χ5044-44-44-4-40000000000002-22-2-22-2222−2222−22000022−2222−220000000000000000000000000000
χ5144-44-44-4-40000000000002-22-2-22-22−2222−22220000−2222−22220000000000000000000000000000
χ5244-44-44-4-4000000000000-22-222-22-222−2222−220000−2222−22220000000000000000000000000000
χ5344-44-44-4-4000000000000-22-222-22-2−2222−2222000022−2222−220000000000000000000000000000
χ5444-4-4-4-4444-4-44-4444-4-44-4000000000000000000000000000000000000000000000000
χ5544-4-4-4-444-444-44-44-4-4-444000000000000000000000000000000000000000000000000
χ5644-4-4-4-444-444-4-44-4444-4-4000000000000000000000000000000000000000000000000
χ574-444-4-4-4444-4-4-4-444-44-44000000000000000000000000000000000000000000000000
χ584-44-4-444-40000000000002i−2i−2i2i2i−2i−2i2i000022−22−222200002i2−2i2−2i22i2000000000000000000000000
χ594-44-4-444-40000000000002i−2i−2i2i2i−2i−2i2i0000−222222−220000−2i22i22i2−2i2000000000000000000000000
χ604-44-4-444-4000000000000−2i2i2i−2i−2i2i2i−2i000022−22−22220000−2i22i22i2−2i2000000000000000000000000
χ614-44-4-444-4000000000000−2i2i2i−2i−2i2i2i−2i0000−222222−2200002i2−2i2−2i22i2000000000000000000000000
χ624-4-444-44-40000000000002i−2i−2i2i−2i2i2i−2i22−22−222200002i2−2i2−2i22i20000000000000000000000000000
χ634-4-444-44-40000000000002i−2i−2i2i−2i2i2i−2i−222222−220000−2i22i22i2−2i20000000000000000000000000000
χ644-4-444-44-4000000000000−2i2i2i−2i2i−2i−2i2i22−22−22220000−2i22i22i2−2i20000000000000000000000000000
χ654-4-444-44-4000000000000−2i2i2i−2i2i−2i−2i2i−222222−2200002i2−2i2−2i22i20000000000000000000000000000
χ664-4-4-444-444-44-4-44-4-4-4444000000000000000000000000000000000000000000000000
χ674-4-4-444-44-44-444-4-44-444-4000000000000000000000000000000000000000000000000
χ684-4-4-444-44-44-44-444-44-4-44000000000000000000000000000000000000000000000000

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