Finite Group Databasebeta

← Group #314752

Character table — Group #314752

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222222222444444444444444444444444161616161616161616161616161616161616161616161616
order12222222222244444444444444448888888888888888244444444444888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-111
χ311111111111111111111111111111111111111111111-1-1-11111-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111111-1-1-1-1-1-11111-1-1
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-1-1-1111111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ911111111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-1111-1-1-111-1-11111-1-111-1-1-1-1
χ1011111111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-11-1-111-1-1-11111-1-111-1-111-1-1
χ1111111111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-11-111-1-1111-1-1-1-1-1-111-1-11111
χ1211111111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-11-1-1-1111-1-111-1-111-1-111-1-111
χ1311111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1111-1-1-1-1-111-1-111-1-1-1-11111
χ1411111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-11-1-111-111-1-1-1-1-1-11111-1-111
χ1511111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-11-111-1-11-1-11111-1-11111-1-1-1-1
χ1611111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-11-1-1-111111-1-11111-1-1-1-111-1-1
χ172222222222222-2-2-2-2222-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2000000000000000000000000
χ182222222222222-2-2-2-2222-2-2-2-2-2-222-2-2-2-2-2-2-2-222222222000000000000000000000000
χ19222222222222-22222-2-2-2-2-222-2-2-2-200000000000000002-2-2000020000000000000000
χ20222222222222-22222-2-2-2-2-222-2-2-2-20000000000000000-2220000-20000000000000000
χ21222222222222-2-2-2-2-2-2-2-222-2-222-2-200000000000000000000000000002i−2i000000002i−2i
χ22222222222222-2-2-2-2-2-2-2-222-2-222-2-20000000000000000000000000000−2i2i00000000−2i2i
χ2322222222-2-2-2-22-2-2-2-2222-2-22222-2-22222-2-2-2-2-2-2-2-22222000000000000000000000000
χ2422222222-2-2-2-22-2-2-2-2222-2-22222-2-2-2-2-2-222222222-2-2-2-2000000000000000000000000
χ2522222222-2-2-2-2-22222-2-2-2-2-2-2-22222000000000000000022-20000-20000000000000000
χ2622222222-2-2-2-2-22222-2-2-2-2-2-2-222220000000000000000-2-22000020000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-22200000000000000000000000000002i−2i00000000−2i2i
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2220000000000000000000000000000−2i2i000000002i−2i
χ292-222-22-2-20000-222-2-22-222-2000000000022-2-2000022-2-2000002i−2i02i−2i00000000000000
χ302-222-22-2-20000-222-2-22-222-2000000000022-2-2000022-2-200000−2i2i0−2i2i00000000000000
χ312-222-22-2-20000-222-2-22-222-20000000000-2-2220000-2-222000002i−2i0−2i2i00000000000000
χ322-222-22-2-20000-222-2-22-222-20000000000-2-2220000-2-22200000−2i2i02i−2i00000000000000
χ332-222-22-2-20000-2-2-2222-22-22000000000022-2-20000-2-2220002i−2i000002i−2i000000000000
χ342-222-22-2-20000-2-2-2222-22-22000000000022-2-20000-2-222000−2i2i00000−2i2i000000000000
χ352-222-22-2-20000-2-2-2222-22-220000000000-2-222000022-2-20002i−2i00000−2i2i000000000000
χ362-222-22-2-20000-2-2-2222-22-220000000000-2-222000022-2-2000−2i2i000002i−2i000000000000
χ372-2-2-222-2222-2-2200002-2-20000002-2000000002i2i−2i−2i2i−2i2i−2i00000000000000i2−i2i2−i22−22−200
χ382-2-2-222-2222-2-2200002-2-20000002-2000000002i2i−2i−2i2i−2i2i−2i00000000000000−i2i2−i2i2−22−2200
χ392-2-2-222-2222-2-2200002-2-20000002-200000000−2i−2i2i2i−2i2i−2i2i00000000000000i2−i2i2−i2−22−2200
χ402-2-2-222-2222-2-2200002-2-20000002-200000000−2i−2i2i2i−2i2i−2i2i00000000000000−i2i2−i2i22−22−200
χ412-2-2-222-22-2-222200002-2-2000000-22000000002i2i−2i−2i−2i2i−2i2i00000000000000i2−i2−i2i22−2−2200
χ422-2-2-222-22-2-222200002-2-2000000-22000000002i2i−2i−2i−2i2i−2i2i00000000000000−i2i2i2−i2−222−200
χ432-2-2-222-22-2-222200002-2-2000000-2200000000−2i−2i2i2i2i−2i2i−2i00000000000000i2−i2−i2i2−222−200
χ442-2-2-222-22-2-222200002-2-2000000-2200000000−2i−2i2i2i2i−2i2i−2i00000000000000−i2i2i2−i22−2−2200
χ45444-44-4-4-4000004-44-4000000000002222−22−22000022−2222−220000000000000000000000000000
χ46444-44-4-4-4000004-44-400000000000−22−2222220000−2222−22220000000000000000000000000000
χ47444-44-4-4-400000-44-44000000000002222−22−220000−2222−22220000000000000000000000000000
χ48444-44-4-4-400000-44-4400000000000−22−222222000022−2222−220000000000000000000000000000
χ4944-44-4-4-444-44-400000000000000002i2−2i22i2−2i22i2−2i22i2−2i200000000000000000000000000000000
χ5044-44-4-4-444-44-40000000000000000−2i22i2−2i22i2−2i22i2−2i22i200000000000000000000000000000000
χ5144-44-4-4-44-44-4400000000000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000000000
χ5244-44-4-4-44-44-440000000000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000000000
χ5344-4-4-444-4000040000-4-44000000004i−4i−4i4i000000000000000000000000000000000000
χ5444-4-4-444-4000040000-4-4400000000−4i4i4i−4i000000000000000000000000000000000000
χ5544-4-4-444-40000-4000044-4000000000000000000004i−4i−4i4i000000000000000000000000
χ5644-4-4-444-40000-4000044-400000000000000000000−4i4i4i−4i000000000000000000000000
χ574-444-44-4-40000444-4-4-44-4-440000000000000000000000000000000000000000000000
χ584-444-44-4-400004-4-444-44-44-40000000000000000000000000000000000000000000000
χ594-44-4-4-4444-4-4404-4-44000004-400000000000000000000000000000000000000000000
χ604-44-4-4-4444-4-440-444-400000-4400000000000000000000000000000000000000000000
χ614-44-4-4-444-444-404-4-4400000-4400000000000000000000000000000000000000000000
χ624-44-4-4-444-444-40-444-4000004-400000000000000000000000000000000000000000000
χ634-4-444-44-400000000000000004-40000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000
χ644-4-444-44-400000000000000004-4000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000
χ654-4-444-44-40000000000000000-440000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000
χ664-4-444-44-40000000000000000-44000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000
χ674-4-4-444-4444-4-4-40000-444000000-440000000000000000000000000000000000000000
χ684-4-4-444-44-4-444-40000-4440000004-40000000000000000000000000000000000000000

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