Finite Group Databasebeta

← Group #316342

Character table — Group #316342

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222222222444444444444444444444444161616161616161616161616161616161616161616161616
order12222222444444444444224444448888888888888888444444444444888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-11-1-1-1-11-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-111-11111-111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-11-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-111111-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-1-11111-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11111111111-1-1-1-1
χ91111111111-1-1-1-1111111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11-1111-1-111-1-1-1-1-11111-1-111-1-1
χ101111111111-1-1-1-1111111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11-1-1-1111-1-1-111-1-111-1-111-1-111
χ111111111111-1-1-1-1111111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1111-1-1-1111-1-111-1-1-1-111-1-111
χ121111111111-1-1-1-1111111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-11-1-1-111-1-111111-1-111-1-111-1-1
χ131111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111111-1111-1-1-1-1-11111-1-111-1-1-1-111
χ141111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111111-1-1-111111-1-1-111-1-1-1-11111-1-1
χ151111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1111-1-1-1-1-1111-1-111-1-11111-1-1
χ161111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-11-1-1-111111-1-1-1-11111-1-1-1-111
χ1722222222222222-2-2-222-222-2-2-2-2-2-200000000000000002-200-20000200000000000000
χ1822222222222222-2-2-222-222-2-2-2-2-2-20000000000000000-220020000-200000000000000
χ192222222222-2-2-2-2-2-2-222-2-2-222-2-22200000000000000002200-20000-200000000000000
χ202222222222-2-2-2-2-2-2-222-2-2-222-2-2220000000000000000-2-20020000200000000000000
χ2122222222-2-22222222-2-22-2-2-2-2-2-2222222-2-2-2-2-2-2-2-22222000000000000000000000000
χ2222222222-2-22222222-2-22-2-2-2-2-2-222-2-2-2-222222222-2-2-2-2000000000000000000000000
χ2322222222-2-22222-2-2-2-2-2-2-2-22222-2-200000000000000000000000000002i−2i2i−2i00000000
χ2422222222-2-22222-2-2-2-2-2-2-2-22222-2-20000000000000000000000000000−2i2i−2i2i00000000
χ2522222222-2-2-2-2-2-2222-2-222222-2-2-2-222222222-2-2-2-2-2-2-2-2000000000000000000000000
χ2622222222-2-2-2-2-2-2222-2-222222-2-2-2-2-2-2-2-2-2-2-2-222222222000000000000000000000000
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
χ292-22-2-222-2002i2i−2i−2i-22200-20000002i−2i000022-2-22i2i−2i−2i00000000000000000000i2−i22−22−2i2−i2
χ302-22-2-222-2002i2i−2i−2i-22200-20000002i−2i000022-2-22i2i−2i−2i00000000000000000000−i2i2−22−22−i2i2
χ312-22-2-222-2002i2i−2i−2i-22200-20000002i−2i0000-2-222−2i−2i2i2i00000000000000000000i2−i22−2−22−i2i2
χ322-22-2-222-2002i2i−2i−2i-22200-20000002i−2i0000-2-222−2i−2i2i2i00000000000000000000−i2i2−222−2i2−i2
χ332-22-2-222-200−2i−2i2i2i-22200-2000000−2i2i000022-2-2−2i−2i2i2i00000000000000000000i2−i2−22−22i2−i2
χ342-22-2-222-200−2i−2i2i2i-22200-2000000−2i2i000022-2-2−2i−2i2i2i00000000000000000000−i2i22−22−2−i2i2
χ352-22-2-222-200−2i−2i2i2i-22200-2000000−2i2i0000-2-2222i2i−2i−2i00000000000000000000i2−i2−222−2−i2i2
χ362-22-2-222-200−2i−2i2i2i-22200-2000000−2i2i0000-2-2222i2i−2i−2i00000000000000000000−i2i22−2−22i2−i2
χ372-2-22-22-222-2000022-22-2-200002-20000002i−2i2i−2i00002i2i−2i−2i000002i−2i2-2000000000000000
χ382-2-22-22-222-2000022-22-2-200002-20000002i−2i2i−2i00002i2i−2i−2i00000−2i2i-22000000000000000
χ392-2-22-22-222-2000022-22-2-200002-2000000−2i2i−2i2i0000−2i−2i2i2i000002i−2i-22000000000000000
χ402-2-22-22-222-2000022-22-2-200002-2000000−2i2i−2i2i0000−2i−2i2i2i00000−2i2i2-2000000000000000
χ412-2-22-22-22-22000022-2-22-20000-220000002i−2i2i−2i0000−2i−2i2i2i002i−2i0000002-2000000000000
χ422-2-22-22-22-22000022-2-22-20000-220000002i−2i2i−2i0000−2i−2i2i2i00−2i2i000000-22000000000000
χ432-2-22-22-22-22000022-2-22-20000-22000000−2i2i−2i2i00002i2i−2i−2i002i−2i000000-22000000000000
χ442-2-22-22-22-22000022-2-22-20000-22000000−2i2i−2i2i00002i2i−2i−2i00−2i2i0000002-2000000000000
χ454444-4-4-4-44-40000000-440000000002222−22−22000022−2222−220000000000000000000000000000
χ464444-4-4-4-44-40000000-44000000000−22−2222220000−2222−22220000000000000000000000000000
χ474444-4-4-4-4-4400000004-40000000002222−22−220000−2222−22220000000000000000000000000000
χ484444-4-4-4-4-4400000004-4000000000−22−222222000022−2222−220000000000000000000000000000
χ4944-4-444-4-40000004-4400-4000000004-44-4000000000000000000000000000000000000
χ5044-4-444-4-40000004-4400-400000000-44-44000000000000000000000000000000000000
χ5144-4-444-4-4000000-44-40040000000000004i−4i−4i4i00000000000000000000000000000000
χ5244-4-444-4-4000000-44-4004000000000000−4i4i4i−4i00000000000000000000000000000000
χ5344-4-4-4-444004i−4i4i−4i0000000000000022−22−2222000000002i2−2i22i2−2i2000000000000000000000000
χ5444-4-4-4-444004i−4i4i−4i00000000000000−222222−2200000000−2i22i2−2i22i2000000000000000000000000
χ5544-4-4-4-44400−4i4i−4i4i0000000000000022−22−222200000000−2i22i2−2i22i2000000000000000000000000
χ5644-4-4-4-44400−4i4i−4i4i00000000000000−222222−22000000002i2−2i22i2−2i2000000000000000000000000
χ574-44-44-4-44000000000000004i−4i0000000000002i2−2i2−2i22i222−22−2222000000000000000000000000
χ584-44-44-4-44000000000000004i−4i000000000000−2i22i22i2−2i2−222222−22000000000000000000000000
χ594-44-44-4-4400000000000000−4i4i0000000000002i2−2i2−2i22i2−222222−22000000000000000000000000
χ604-44-44-4-4400000000000000−4i4i000000000000−2i22i22i2−2i222−22−2222000000000000000000000000
χ614-44-4-444-4004i4i−4i−4i4-4-4004000000−4i4i0000000000000000000000000000000000000000
χ624-44-4-444-400−4i−4i4i4i4-4-40040000004i−4i0000000000000000000000000000000000000000
χ634-4-444-44-4444-4-44000-4-404-40000000000000000000000000000000000000000000000
χ644-4-444-44-444-444-4000-4-40-440000000000000000000000000000000000000000000000
χ654-4-444-44-4-4-44-4-44000440-440000000000000000000000000000000000000000000000
χ664-4-444-44-4-4-4-444-40004404-40000000000000000000000000000000000000000000000
χ674-4-44-44-444-40000-4-444-440000-44000000000000000000000000000000000000000000
χ684-4-44-44-44-440000-4-44-44400004-4000000000000000000000000000000000000000000

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