Finite Group Databasebeta

← Group #120992

Character table — Group #120992

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11112222222222222222224444444444444444444444161616161616161616161616161616161616161616161616
order12222244444444444444442244448888888888888888444444448888888888888888
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
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ91111-1-1111111-1-11111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-1ii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i
χ101111-1-1111111-1-11111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-1ii−i−iii−i−i-1-111-1-111−i−iii−i−iii
χ111111-1-1111111-1-11111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-1−i−iii−i−iii11-1-111-1-1−i−iii−i−iii
χ121111-1-1111111-1-11111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-1−i−iii−i−iii-1-111-1-111ii−i−iii−i−i
χ131111-1-1111111-1-11111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-111111111ii−i−i−i−iii11-1-1-1-111ii−i−i−i−iii
χ141111-1-1111111-1-11111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-111111111ii−i−i−i−iii-1-11111-1-1−i−iiiii−i−i
χ151111-1-1111111-1-11111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-111111111−i−iiiii−i−i11-1-1-1-111−i−iiiii−i−i
χ161111-1-1111111-1-11111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-111111111−i−iiiii−i−i-1-11111-1-1ii−i−i−i−iii
χ172222222222-2-22222-2-2-2-2-2-2-2-222-2-200000000000000000000000000002i−2i2i−2i00000000
χ182222222222-2-22222-2-2-2-2-2-2-2-222-2-20000000000000000000000000000−2i2i−2i2i00000000
χ1922222222-2-22222-2-2-2-222-2-222-2-2-2-20000000000000000000000000000000000002i−2i2i−2i
χ2022222222-2-22222-2-2-2-222-2-222-2-2-2-2000000000000000000000000000000000000−2i2i−2i2i
χ2122222222-2-2-2-222-2-222-2-222-2-2-2-22200000000000000002-22-200000000000000000000
χ2222222222-2-2-2-222-2-222-2-222-2-2-2-2220000000000000000-22-2200000000000000000000
χ23222222-2-22222-2-2-2-2-2-22222-2-22-2-222222-2-2-2-22222-2-2-2-2000000000000000000000000
χ24222222-2-22222-2-2-2-2-2-22222-2-22-2-22-2-2-2-22222-2-2-2-22222000000000000000000000000
χ25222222-2-222-2-2-2-2-2-222-2-2-2-2222-22-20000000000000000000000002i−2i2i−2i000000000000
χ26222222-2-222-2-2-2-2-2-222-2-2-2-2222-22-2000000000000000000000000−2i2i−2i2i000000000000
χ27222222-2-2-2-222-2-2222222-2-2-2-2-222-2000000000000000000000000000000002-22-20000
χ28222222-2-2-2-222-2-2222222-2-2-2-2-222-200000000000000000000000000000000-22-220000
χ29222222-2-2-2-2-2-2-2-222-2-2-2-22222-22-22000000000000000000002-22-20000000000000000
χ30222222-2-2-2-2-2-2-2-222-2-2-2-22222-22-2200000000000000000000-22-220000000000000000
χ312222-2-22222-2-2-2-222-2-22222-22-2-22-200000000000000000000000000002i−2i−2i2i00000000
χ322222-2-22222-2-2-2-222-2-22222-22-2-22-20000000000000000000000000000−2i2i2i−2i00000000
χ332222-2-222-2-222-2-2-2-2-2-2-2-2222-2222-20000000000000000000000000000000000002-2-22
χ342222-2-222-2-222-2-2-2-2-2-2-2-2222-2222-2000000000000000000000000000000000000-222-2
χ352222-2-222-2-2-2-2-2-2-2-22222-2-2-2222-2200000000000000002i−2i−2i2i00000000000000000000
χ362222-2-222-2-2-2-2-2-2-2-22222-2-2-2222-220000000000000000−2i2i2i−2i00000000000000000000
χ372222-2-2-2-2222222-2-2-2-2-2-2-2-2-22-22222222-2-2-2-2-2-2-2-22222000000000000000000000000
χ382222-2-2-2-2222222-2-2-2-2-2-2-2-2-22-2222-2-2-2-222222222-2-2-2-2000000000000000000000000
χ392222-2-2-2-222-2-222-2-22222222-2-22-2-20000000000000000000000002i−2i−2i2i000000000000
χ402222-2-2-2-222-2-222-2-22222222-2-22-2-2000000000000000000000000−2i2i2i−2i000000000000
χ412222-2-2-2-2-2-222222222-2-222-222-2-2-2000000000000000000000000000000002i−2i−2i2i0000
χ422222-2-2-2-2-2-222222222-2-222-222-2-2-200000000000000000000000000000000−2i2i2i−2i0000
χ432222-2-2-2-2-2-2-2-22222-2-222-2-22-22-222000000000000000000002i−2i−2i2i0000000000000000
χ442222-2-2-2-2-2-2-2-22222-2-222-2-22-22-22200000000000000000000−2i2i2i−2i0000000000000000
χ4544-4-4000000004i−4i004i−4i004-400000022-2-22i2i−2i−2i22-2-22i2i−2i−2i000000000000000000000000
χ4644-4-4000000004i−4i004i−4i004-4000000-2-222−2i−2i2i2i-2-222−2i−2i2i2i000000000000000000000000
χ4744-4-4000000004i−4i00−4i4i00-4400000022-2-2−2i−2i2i2i-2-2222i2i−2i−2i000000000000000000000000
χ4844-4-4000000004i−4i00−4i4i00-44000000-2-2222i2i−2i−2i22-2-2−2i−2i2i2i000000000000000000000000
χ4944-4-400000000−4i4i004i−4i00-4400000022-2-22i2i−2i−2i-2-222−2i−2i2i2i000000000000000000000000
χ5044-4-400000000−4i4i004i−4i00-44000000-2-222−2i−2i2i2i22-2-22i2i−2i−2i000000000000000000000000
χ5144-4-400000000−4i4i00−4i4i004-400000022-2-2−2i−2i2i2i22-2-2−2i−2i2i2i000000000000000000000000
χ5244-4-400000000−4i4i00−4i4i004-4000000-2-2222i2i−2i−2i-2-2222i2i−2i−2i000000000000000000000000
χ534-44-4004i−4i4-400004i−4i000000000000000000002i2−2i22i2−2i222−2222−22000000000000000000000000
χ544-44-4004i−4i4-400004i−4i00000000000000000000−2i22i2−2i22i2−2222−2222000000000000000000000000
χ554-44-4004i−4i-440000−4i4i0000000000002i2−2i22i2−2i222−2222−2200000000000000000000000000000000
χ564-44-4004i−4i-440000−4i4i000000000000−2i22i2−2i22i2−2222−222200000000000000000000000000000000
χ574-44-400−4i4i4-40000−4i4i000000000000000000002i2−2i22i2−2i2−2222−2222000000000000000000000000
χ584-44-400−4i4i4-40000−4i4i00000000000000000000−2i22i2−2i22i222−2222−22000000000000000000000000
χ594-44-400−4i4i-4400004i−4i0000000000002i2−2i22i2−2i2−2222−222200000000000000000000000000000000
χ604-44-400−4i4i-4400004i−4i000000000000−2i22i2−2i22i222−2222−2200000000000000000000000000000000
χ614-4-444-400004-40000004-40000000000002i2−2i2−2i22i200002i2−2i2−2i22i2000000000000000000000000
χ624-4-444-400004-40000004-4000000000000−2i22i22i2−2i20000−2i22i22i2−2i2000000000000000000000000
χ634-4-444-40000-44000000-44000000002i2−2i2−2i22i200002i2−2i2−2i22i20000000000000000000000000000
χ644-4-444-40000-44000000-4400000000−2i22i22i2−2i20000−2i22i22i2−2i20000000000000000000000000000
χ654-4-44-4400004-4000000-440000000000002i2−2i2−2i22i20000−2i22i22i2−2i2000000000000000000000000
χ664-4-44-4400004-4000000-44000000000000−2i22i22i2−2i200002i2−2i2−2i22i2000000000000000000000000
χ674-4-44-440000-440000004-4000000002i2−2i2−2i22i20000−2i22i22i2−2i20000000000000000000000000000
χ684-4-44-440000-440000004-400000000−2i22i22i2−2i200002i2−2i2−2i22i20000000000000000000000000000

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