Finite Group Databasebeta

← Group #115693

Character table — Group #115693

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11112222222222222222224444444444444444444444161616161616161616161616161616161616161616161616
order12222222222222444444442222222222444444444444224444448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ911111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ1011111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-1−i−iii−i−iii−i−iii−i−iii
χ1111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111ii−i−iii−i−i−i−iii−i−iii
χ1211111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111−i−iii−i−iiiii−i−iii−i−i
χ1311111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ1411111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ1511111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ1611111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1111-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222222-2-2-2-222222-2-2-2-2-2-20000000022-2-20000000022-2-200000000000000000000
χ18222222222-2-2-2-222222-2-2-2-2-2-20000000022-2-200000000-2-22200000000000000000000
χ19222222222-2-2-2-22-2-2-2-22222-2-200000000-2-222000000002-2-2200000000000000000000
χ20222222222-2-2-2-22-2-2-2-22222-2-200000000-2-22200000000-222-200000000000000000000
χ21222222-2-2-222-2-2-2222222-2-22-200000000-2-22-20000000000000000000000002-22-20000
χ22222222-2-2-222-2-2-2222222-2-22-200000000-2-22-2000000000000000000000000-22-220000
χ23222222-2-2-222-2-2-2-2-2-2-2-2-2222-20000000022-220000000000000000000000002i−2i−2i2i0000
χ24222222-2-2-222-2-2-2-2-2-2-2-2-2222-20000000022-22000000000000000000000000−2i2i2i−2i0000
χ25222222-2-2-2-2-222-22222-2-222-2200000000-2-2-2200000000000000002-22-2000000000000
χ26222222-2-2-2-2-222-22222-2-222-2200000000-2-2-220000000000000000-22-22000000000000
χ27222222-2-2-2-2-222-2-2-2-2-222-2-2-2200000000222-200000000000000002i−2i−2i2i000000000000
χ28222222-2-2-2-2-222-2-2-2-2-222-2-2-2200000000222-20000000000000000−2i2i2i−2i000000000000
χ292222-2-222-222-2-2-222-2-22222-22000000002-2-2-200000000000000000000000000002-22-2
χ302222-2-222-222-2-2-222-2-22222-22000000002-2-2-20000000000000000000000000000-22-22
χ312222-2-222-222-2-2-2-2-222-2-2-2-2-2200000000-222200000000000000000000000000002i−2i−2i2i
χ322222-2-222-222-2-2-2-2-222-2-2-2-2-2200000000-22220000000000000000000000000000−2i2i2i−2i
χ332222-2-222-2-2-222-222-2-2-2-2-2-22-2000000002-222000000000000000000002i−2i2i−2i00000000
χ342222-2-222-2-2-222-222-2-2-2-2-2-22-2000000002-22200000000000000000000−2i2i−2i2i00000000
χ352222-2-222-2-2-222-2-2-22222222-200000000-22-2-2000000000000000000002-2-2200000000
χ362222-2-222-2-2-222-2-2-22222222-200000000-22-2-200000000000000000000-222-200000000
χ372222-2-2-2-222222222-2-222-2-2-2-22222-2-2-2-2-22-222222-2-2-2-2000000000000000000000000
χ382222-2-2-2-222222222-2-222-2-2-2-2-2-2-2-22222-22-22-2-2-2-22222000000000000000000000000
χ392222-2-2-2-2222222-2-222-2-222-2-22222-2-2-2-22-22-2-2-2-2-22222000000000000000000000000
χ402222-2-2-2-2222222-2-222-2-222-2-2-2-2-2-222222-22-22222-2-2-2-2000000000000000000000000
χ412222-2-2-2-22-2-2-2-2222-2-2-2-2222200000000-222-20000000000002-22-20000000000000000
χ422222-2-2-2-22-2-2-2-2222-2-2-2-2222200000000-222-2000000000000-22-220000000000000000
χ432222-2-2-2-22-2-2-2-22-2-22222-2-222000000002-2-220000000000002-2-220000000000000000
χ442222-2-2-2-22-2-2-2-22-2-22222-2-222000000002-2-22000000000000-222-20000000000000000
χ4544-4-4004-400000000004i−4i4i−4i0022-2-222-2-200002i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ4644-4-4004-400000000004i−4i4i−4i00-2-222-2-2220000−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ4744-4-4004-40000000000−4i4i−4i4i0022-2-222-2-20000−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ4844-4-4004-40000000000−4i4i−4i4i00-2-222-2-22200002i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ4944-4-400-4400000000004i−4i−4i4i0022-2-2-2-22200002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ5044-4-400-4400000000004i−4i−4i4i00-2-22222-2-20000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ5144-4-400-440000000000−4i4i4i−4i0022-2-2-2-2220000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ5244-4-400-440000000000−4i4i4i−4i00-2-22222-2-200002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ534-44-4000044-44-4-4000000000000000000000000004i−4i4i−4i000000000000000000000000
χ544-44-4000044-44-4-400000000000000000000000000−4i4i−4i4i000000000000000000000000
χ554-44-400004-44-44-400000000000000000000004i−4i4i−4i0000000000000000000000000000
χ564-44-400004-44-44-40000000000000000000000−4i4i−4i4i0000000000000000000000000000
χ574-44-40000-44-4-444000000000000004-44-4000000000000000000000000000000000000
χ584-44-40000-44-4-44400000000000000-44-44000000000000000000000000000000000000
χ594-44-40000-4-444-4400000000004-44-40000000000000000000000000000000000000000
χ604-44-40000-4-444-440000000000-44-440000000000000000000000000000000000000000
χ614-4-444-4000000004-44-40000002-2-222-2-2200002-2-222-2-22000000000000000000000000
χ624-4-444-4000000004-44-4000000-222-2-222-20000-222-2-222-2000000000000000000000000
χ634-4-444-400000000-44-440000002-2-222-2-220000-222-2-222-2000000000000000000000000
χ644-4-444-400000000-44-44000000-222-2-222-200002-2-222-2-22000000000000000000000000
χ654-4-44-44000000004-4-440000002-2-22-222-200002-2-22-222-2000000000000000000000000
χ664-4-44-44000000004-4-44000000-222-22-2-220000-222-22-2-22000000000000000000000000
χ674-4-44-4400000000-444-40000002-2-22-222-20000-222-22-2-22000000000000000000000000
χ684-4-44-4400000000-444-4000000-222-22-2-2200002-2-22-222-2000000000000000000000000

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