Finite Group Databasebeta

← Group #316339

Character table — Group #316339

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222222222444444444444444444444444161616161616161616161616161616161616161616161616
order12222222444444444444224444448888888888888888224444444444888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-111-111-111-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-11-1-11-1-11-1-111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111-11111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-11-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-111111111-1-1-1-1
χ911111111111-1-1-1-111111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111111-1-1-11-1-1-1-1-11111-1-111-1-1
χ1011111111111-1-1-1-111111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1111-1-1-1-1-1111-1-1-1-111-1-111
χ1111111111111-1-1-1-111111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-11-1-1-111111-1-1-111-1-111-1-111
χ1211111111111-1-1-1-111111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1111-111111-1-111-1-111-1-1
χ1311111111111-1-1-1-111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111111-1-1-1111-1-1-111-1-111-1-1-1-111
χ1411111111111-1-1-1-111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1111-1-1-11-1-111-1-11111-1-1
χ1511111111111-1-1-1-111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1111-1-1-1111-111-1-1-1-11111-1-1
χ1611111111111-1-1-1-111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1111-1-1-1111-1-11111-1-1-1-111
χ17222222222-2-22222222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-22222000000000000000000000000
χ18222222222-2-22222222-2-2-2-2-2-2-2-222-2-2-2-222222222-2-2-2-2000000000000000000000000
χ19222222222-2-2-2-2-2-2222-2-22222-2-2-2-222222222-2-2-2-2-2-2-2-2000000000000000000000000
χ20222222222-2-2-2-2-2-2222-2-22222-2-2-2-2-2-2-2-2-2-2-2-222222222000000000000000000000000
χ2122222222-2222222-2-2-22222-2-2-2-2-2-2000000000000000000200-200-2002000000000000
χ2222222222-2222222-2-2-22222-2-2-2-2-2-2000000000000000000-200200200-2000000000000
χ2322222222-222-2-2-2-2-2-2-222-2-222-2-222000000000000000000200200-200-2000000000000
χ2422222222-222-2-2-2-2-2-2-222-2-222-2-222000000000000000000-200-2002002000000000000
χ2522222222-2-2-22222-2-2-2-2-2-2-22222-2-200000000000000000000000000002i−2i2i−2i00000000
χ2622222222-2-2-22222-2-2-2-2-2-2-22222-2-20000000000000000000000000000−2i2i−2i2i00000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2222200000000000000000000000000002i−2i−2i2i00000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222-2-222220000000000000000000000000000−2i2i2i−2i00000000
χ292-222-2-22-2-2002i2i−2i−2i22-2000000002i−2i000022-2-22i2i−2i−2i000000000000000000002−2i2−i2i2−i22−2
χ302-222-2-22-2-2002i2i−2i−2i22-2000000002i−2i000022-2-22i2i−2i−2i00000000000000000000−22−i2i2−i2i2−22
χ312-222-2-22-2-2002i2i−2i−2i22-2000000002i−2i0000-2-222−2i−2i2i2i000000000000000000002−2i2−i2−i2i2−22
χ322-222-2-22-2-2002i2i−2i−2i22-2000000002i−2i0000-2-222−2i−2i2i2i00000000000000000000−22−i2i2i2−i22−2
χ332-222-2-22-2-200−2i−2i2i2i22-200000000−2i2i000022-2-2−2i−2i2i2i000000000000000000002−2−i2i2−i2i22−2
χ342-222-2-22-2-200−2i−2i2i2i22-200000000−2i2i000022-2-2−2i−2i2i2i00000000000000000000−22i2−i2i2−i2−22
χ352-222-2-22-2-200−2i−2i2i2i22-200000000−2i2i0000-2-2222i2i−2i−2i000000000000000000002−2−i2i2i2−i2−22
χ362-222-2-22-2-200−2i−2i2i2i22-200000000−2i2i0000-2-2222i2i−2i−2i00000000000000000000−22i2−i2−i2i22−2
χ372-22-22-2-2222-200002-2-22-200002-20000002i−2i2i−2i00002i2i−2i−2i0002i−2i00002-20000000000000
χ382-22-22-2-2222-200002-2-22-200002-20000002i−2i2i−2i00002i2i−2i−2i000−2i2i0000-220000000000000
χ392-22-22-2-2222-200002-2-22-200002-2000000−2i2i−2i2i0000−2i−2i2i2i0002i−2i0000-220000000000000
χ402-22-22-2-2222-200002-2-22-200002-2000000−2i2i−2i2i0000−2i−2i2i2i000−2i2i00002-20000000000000
χ412-22-22-2-222-2200002-2-2-220000-220000002i−2i2i−2i0000−2i−2i2i2i2-200002i−2i0000000000000000
χ422-22-22-2-222-2200002-2-2-220000-220000002i−2i2i−2i0000−2i−2i2i2i-220000−2i2i0000000000000000
χ432-22-22-2-222-2200002-2-2-220000-22000000−2i2i−2i2i00002i2i−2i−2i2-20000−2i2i0000000000000000
χ442-22-22-2-222-2200002-2-2-220000-22000000−2i2i−2i2i00002i2i−2i−2i-2200002i−2i0000000000000000
χ45444-4-44-4-44000000-44-4000000000044-4-4000000000000000000000000000000000000
χ46444-4-44-4-44000000-44-40000000000-4-444000000000000000000000000000000000000
χ47444-4-44-4-4-40000004-44000000000000004i−4i−4i4i00000000000000000000000000000000
χ48444-4-44-4-4-40000004-4400000000000000−4i4i4i−4i00000000000000000000000000000000
χ4944-44-4-4-440444-44-4000-4-44-40000000000000000000000000000000000000000000000
χ5044-44-4-4-44044-44-44000-4-4-440000000000000000000000000000000000000000000000
χ5144-44-4-4-440-4-44-44-400044-440000000000000000000000000000000000000000000000
χ5244-44-4-4-440-4-4-44-44000444-40000000000000000000000000000000000000000000000
χ5344-4-44-44-4000000000000004i−4i0000000000002i2−2i22i2−2i222−2222−22000000000000000000000000
χ5444-4-44-44-4000000000000004i−4i000000000000−2i22i2−2i22i2−2222−2222000000000000000000000000
χ5544-4-44-44-400000000000000−4i4i0000000000002i2−2i22i2−2i2−2222−2222000000000000000000000000
χ5644-4-44-44-400000000000000−4i4i000000000000−2i22i2−2i22i222−2222−22000000000000000000000000
χ574-444-4-44-44004i4i−4i−4i-4-4400000000−4i4i0000000000000000000000000000000000000000
χ584-444-4-44-4400−4i−4i4i4i-4-44000000004i−4i0000000000000000000000000000000000000000
χ594-44-44-4-44-44-40000-4444-40000-44000000000000000000000000000000000000000000
χ604-44-44-4-44-4-440000-444-4400004-4000000000000000000000000000000000000000000
χ614-4-4444-4-40004i−4i−4i4i000000000000022−2222−22000000002i2−2i2−2i22i2000000000000000000000000
χ624-4-4444-4-40004i−4i−4i4i0000000000000−2222−222200000000−2i22i22i2−2i2000000000000000000000000
χ634-4-4444-4-4000−4i4i4i−4i000000000000022−2222−2200000000−2i22i22i2−2i2000000000000000000000000
χ644-4-4444-4-4000−4i4i4i−4i0000000000000−2222−2222000000002i2−2i2−2i22i2000000000000000000000000
χ654-4-4-4-444404-40000000-440000000022−22−2222000022−22−22220000000000000000000000000000
χ664-4-4-4-444404-40000000-4400000000−222222−220000−222222−220000000000000000000000000000
χ674-4-4-4-44440-4400000004-40000000022−22−22220000−222222−220000000000000000000000000000
χ684-4-4-4-44440-4400000004-400000000−222222−22000022−22−22220000000000000000000000000000

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