Finite Group Databasebeta

← Group #238913

Character table — Group #238913

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11112222222222222222224444444444444444444444161616161616161616161616161616161616161616161616
order12222222444444444444442444444444444444444444222444448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-111-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-11111-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-1-1-1-11111-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ91111-1-11111-1-1-1-11-1-111111-111-1-1-111111111-1-1-1-1-1-1-1-11-11-1-11-1111-1-111-1-111-1-111-1-1
χ101111-1-11111-1-1-1-11-1-111111-111-1-1-111111111-1-1-1-1-1-1-1-11-1-1111-1-1-1-11111-1-1-1-111-1-111
χ111111-1-11111-1-1-1-11-1-111111-111-1-1-111111111-1-1-1-1-1-1-1-1-111-1-1-11111-1-1-1-111-1-111-1-111
χ121111-1-11111-1-1-1-11-1-111111-111-1-1-111111111-1-1-1-1-1-1-1-1-11-111-11-1-1-111-1-11111-1-111-1-1
χ131111-1-11111-1-1-1-11-1-111111-111-1-1-1-1-1-1-1-1-1-1-1111111111-11-1-11-11-1-111-1-11111-1-1-1-111
χ141111-1-11111-1-1-1-11-1-111111-111-1-1-1-1-1-1-1-1-1-1-1111111111-1-1111-1-111-1-1-1-111-1-11111-1-1
χ151111-1-11111-1-1-1-11-1-111111-111-1-1-1-1-1-1-1-1-1-1-111111111-111-1-1-111-1-11111-1-1-1-11111-1-1
χ161111-1-11111-1-1-1-11-1-111111-111-1-1-1-1-1-1-1-1-1-1-111111111-11-111-11-111-1-111-1-111-1-1-1-111
χ17222222222222-2-2-2-2-2-2-222-22-2-22-2-2000000000000000000000000000000002-22-20000
χ18222222222222-2-2-2-2-2-2-222-22-2-22-2-200000000000000000000000000000000-22-220000
χ1922222222-2-2-2-222-2-2-2-2-2-2-2-2222-22-20000000000000000000000000000000000002i−2i2i−2i
χ2022222222-2-2-2-222-2-2-2-2-2-2-2-2222-22-2000000000000000000000000000000000000−2i2i−2i2i
χ2122222222-2-2-2-2-2-222222-2-222-2-2-2-222222-2-2-2-22222-2-2-2-2000000000000000000000000
χ2222222222-2-2-2-2-2-222222-2-222-2-2-2-22-2-2-2-22222-2-2-2-22222000000000000000000000000
χ23222222-2-222-2-222222-2-2-2-22-22-22-2-20000000000000000000000002i−2i2i−2i000000000000
χ24222222-2-222-2-222222-2-2-2-22-22-22-2-2000000000000000000000000−2i2i−2i2i000000000000
χ25222222-2-222-2-2-2-2-2-2-222-2-2-2-2-2222200000000000000000000000000002i−2i2i−2i00000000
χ26222222-2-222-2-2-2-2-2-2-222-2-2-2-2-222220000000000000000000000000000−2i2i−2i2i00000000
χ27222222-2-2-2-22222-2-2-22222-2-22-2-2-22000000000000000022000-2-200000000000000000
χ28222222-2-2-2-22222-2-2-22222-2-22-2-2-220000000000000000-2-20002200000000000000000
χ29222222-2-2-2-222-2-2222-2-2222-2-22-22-200000000000000000022-200-20000000000000000
χ30222222-2-2-2-222-2-2222-2-2222-2-22-22-2000000000000000000-2-220020000000000000000
χ312222-2-22222-2-222-222-2-222-2-2-2-2-222000000000000000000000000000000002-2-220000
χ322222-2-22222-2-222-222-2-222-2-2-2-2-22200000000000000000000000000000000-222-20000
χ332222-2-222-2-222222-2-222-2-22-2-2-222-22222-2-2-2-2-2-2-2-22222000000000000000000000000
χ342222-2-222-2-222222-2-222-2-22-2-2-222-2-2-2-2-222222222-2-2-2-2000000000000000000000000
χ352222-2-222-2-222-2-2-222-2-2-2-2-2-2222-220000000000000000000000000000000000002i−2i−2i2i
χ362222-2-222-2-222-2-2-222-2-2-2-2-2-2222-22000000000000000000000000000000000000−2i2i2i−2i
χ372222-2-2-2-2222222-22222-2-2-22-22-2-2-200000000000000000000000000002i−2i−2i2i00000000
χ382222-2-2-2-2222222-22222-2-2-22-22-2-2-20000000000000000000000000000−2i2i2i−2i00000000
χ392222-2-2-2-22222-2-22-2-2-2-2-2-2222-2-2220000000000000000000000002i−2i−2i2i000000000000
χ402222-2-2-2-22222-2-22-2-2-2-2-2-2222-2-222000000000000000000000000−2i2i2i−2i000000000000
χ412222-2-2-2-2-2-2-2-2222-2-2-2-22222-222-220000000000000000002-2200-20000000000000000
χ422222-2-2-2-2-2-2-2-2222-2-2-2-22222-222-22000000000000000000-22-20020000000000000000
χ432222-2-2-2-2-2-2-2-2-2-2-2222222-222-222-200000000000000002-2000-2200000000000000000
χ442222-2-2-2-2-2-2-2-2-2-2-2222222-222-222-20000000000000000-220002-200000000000000000
χ4544-4-400004i−4i004-404i−4i0000000000022-2-22i2i−2i−2i2i2i−2i−2i22-2-2000000000000000000000000
χ4644-4-400004i−4i004-404i−4i00000000000-2-222−2i−2i2i2i−2i−2i2i2i-2-222000000000000000000000000
χ4744-4-400004i−4i00-440−4i4i0000000000022-2-22i2i−2i−2i−2i−2i2i2i-2-222000000000000000000000000
χ4844-4-400004i−4i00-440−4i4i00000000000-2-222−2i−2i2i2i2i2i−2i−2i22-2-2000000000000000000000000
χ4944-4-40000−4i4i004-40−4i4i0000000000022-2-2−2i−2i2i2i−2i−2i2i2i22-2-2000000000000000000000000
χ5044-4-40000−4i4i004-40−4i4i00000000000-2-2222i2i−2i−2i2i2i−2i−2i-2-222000000000000000000000000
χ5144-4-40000−4i4i00-4404i−4i0000000000022-2-2−2i−2i2i2i2i2i−2i−2i-2-222000000000000000000000000
χ5244-4-40000−4i4i00-4404i−4i00000000000-2-2222i2i−2i−2i−2i−2i2i2i22-2-2000000000000000000000000
χ534-44-44-400004-400000004-400000002i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ544-44-44-400004-400000004-40000000−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ554-44-44-40000-440000000-4400000002i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ564-44-44-40000-440000000-440000000−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ574-44-4-4400004-40000000-4400000002i−2i2i−2i−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ584-44-4-4400004-40000000-440000000−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ594-44-4-440000-4400000004-400000002i−2i2i−2i2i−2i2i−2i−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ604-44-4-440000-4400000004-40000000−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ614-4-44004-40000004004-400-40000000000000000004i−4i−4i4i000000000000000000000000
χ624-4-44004-40000004004-400-4000000000000000000−4i4i4i−4i000000000000000000000000
χ634-4-44004-4000000-400-44004000000000000004-4-440000000000000000000000000000
χ644-4-44004-4000000-400-4400400000000000000-444-40000000000000000000000000000
χ654-4-4400-44000000400-4400-40000004i−4i−4i4i000000000000000000000000000000000000
χ664-4-4400-44000000400-4400-4000000−4i4i4i−4i000000000000000000000000000000000000
χ674-4-4400-44000000-4004-400400000000004-4-4400000000000000000000000000000000
χ684-4-4400-44000000-4004-40040000000000-444-400000000000000000000000000000000

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