Finite Group Databasebeta

← Group #325178

Character table — Group #325178

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111111122222222444444444444448888888888888888888888888888881616161632323232
order12222222444444444444448888888844444444448888888888888888888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-11-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ9111111111111111111-1-1-1-111111111-111-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11-11-1
χ10111111111111111111-1-1-1-111111111-111-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-11-11
χ11111111111111111111-1-1-1-111111111-1-1-111-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-11-11
χ12111111111111111111-1-1-1-111111111-1-1-111-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1111-11-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1111-1-11
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-1-1-1-1-111111111-1-1-1-1111111-1-1-111-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111111-1-1-1-111111111-1-1-1-1-1-111-111-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-1-1-1111111111111-1-1-1-111-1-11-1-11
χ172222222222-2-2-2-222-2-222-2-22222-2-2-2-2-20000200000000000022-2-20000000000000000
χ182222222222-2-2-2-222-2-222-2-2-2-2-2-22222-200002000000000000-2-2220000000000000000
χ192222222222-2-2-2-222-2-2-2-2222222-2-2-2-220000-2000000000000-2-2220000000000000000
χ202222222222-2-2-2-222-2-2-2-222-2-2-2-2222220000-200000000000022-2-20000000000000000
χ2122222222-2-22222-2-2-2-2222200000000-222-2-2-2-2-2220000000000000000000000000000
χ2222222222-2-22222-2-2-2-2222200000000-2-2-222-222-2-20000000000000000000000000000
χ2322222222-2-22222-2-2-2-2-2-2-2-200000000222222-2-2-2-20000000000000000000000000000
χ2422222222-2-22222-2-2-2-2-2-2-2-2000000002-2-2-2-2222220000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-20000000020000-200000000000000002i2i−2i−2i2i2i−2i−2i00000000
χ2622222222-2-2-2-2-2-2-2-22222-2-20000000020000-20000000000000000−2i−2i2i2i−2i−2i2i2i00000000
χ2722222222-2-2-2-2-2-2-2-222-2-22200000000-20000200000000000000002i2i−2i−2i−2i−2i2i2i00000000
χ2822222222-2-2-2-2-2-2-2-222-2-22200000000-2000020000000000000000−2i−2i2i2i2i2i−2i−2i00000000
χ292222-2-2-2-22222-2-2-2-22-2000022-2-222-2-20000000000000022-2-2000000000000002-20000
χ302222-2-2-2-22222-2-2-2-22-2000022-2-222-2-200000000000000-2-22200000000000000-220000
χ312222-2-2-2-22222-2-2-2-22-20000-2-222-2-2220000000000000022-2-200000000000000-220000
χ322222-2-2-2-22222-2-2-2-22-20000-2-222-2-22200000000000000-2-222000000000000002-20000
χ332222-2-2-2-222-2-222-2-2-22000022-2-2-2-222000000000022-2-200000000000000002-2000000
χ342222-2-2-2-222-2-222-2-2-22000022-2-2-2-2220000000000-2-2220000000000000000-22000000
χ352222-2-2-2-222-2-222-2-2-220000-2-22222-2-2000000000022-2-20000000000000000-22000000
χ362222-2-2-2-222-2-222-2-2-220000-2-22222-2-20000000000-2-22200000000000000002-2000000
χ3722-2-22-22-2002-22-200002i−2i2i−2ii2−i2i2−i2i2−i2i2−i20002i−2i02-200000000002−22−2i2−i2i2−i22−22−200000000
χ3822-2-22-22-2002-22-200002i−2i2i−2ii2−i2i2−i2i2−i2i2−i2000−2i2i0-2200000000002−22−2−i2i2−i2i2−22−2200000000
χ3922-2-22-22-2002-22-200002i−2i2i−2i−i2i2−i2i2−i2i2−i2i20002i−2i02-20000000000−22−22−i2i2−i2i2−22−2200000000
χ4022-2-22-22-2002-22-200002i−2i2i−2i−i2i2−i2i2−i2i2−i2i2000−2i2i0-220000000000−22−22i2−i2i2−i22−22−200000000
χ4122-2-22-22-2002-22-20000−2i2i−2i2ii2−i2i2−i2i2−i2i2−i20002i−2i0-220000000000−22−22−i2i2−i2i22−22−200000000
χ4222-2-22-22-2002-22-20000−2i2i−2i2ii2−i2i2−i2i2−i2i2−i2000−2i2i02-20000000000−22−22i2−i2i2−i2−22−2200000000
χ4322-2-22-22-2002-22-20000−2i2i−2i2i−i2i2−i2i2−i2i2−i2i20002i−2i0-2200000000002−22−2i2−i2i2−i2−22−2200000000
χ4422-2-22-22-2002-22-20000−2i2i−2i2i−i2i2−i2i2−i2i2−i2i2000−2i2i02-200000000002−22−2−i2i2−i2i22−22−200000000
χ4522-2-22-22-200-22-2200002i−2i−2i2ii2−i2i2−i2−i2i2−i2i202i−2i000002-2000000002−2−222−2−22−i2i2i2−i200000000
χ4622-2-22-22-200-22-2200002i−2i−2i2ii2−i2i2−i2−i2i2−i2i20−2i2i00000-22000000002−2−22−222−2i2−i2−i2i200000000
χ4722-2-22-22-200-22-2200002i−2i−2i2i−i2i2−i2i2i2−i2i2−i202i−2i000002-200000000−222−2−222−2i2−i2−i2i200000000
χ4822-2-22-22-200-22-2200002i−2i−2i2i−i2i2−i2i2i2−i2i2−i20−2i2i00000-2200000000−222−22−2−22−i2i2i2−i200000000
χ4922-2-22-22-200-22-220000−2i2i2i−2ii2−i2i2−i2−i2i2−i2i202i−2i00000-2200000000−222−22−2−22i2−i2−i2i200000000
χ5022-2-22-22-200-22-220000−2i2i2i−2ii2−i2i2−i2−i2i2−i2i20−2i2i000002-200000000−222−2−222−2−i2i2i2−i200000000
χ5122-2-22-22-200-22-220000−2i2i2i−2i−i2i2−i2i2i2−i2i2−i202i−2i00000-22000000002−2−22−222−2−i2i2i2−i200000000
χ5222-2-22-22-200-22-220000−2i2i2i−2i−i2i2−i2i2i2−i2i2−i20−2i2i000002-2000000002−2−222−2−22i2−i2−i2i200000000
χ534444-4-4-4-4-4-444-4-444-4400000000000000000000000000000000000000000000000000
χ544444-4-4-4-4-4-4-4-444444-400000000000000000000000000000000000000000000000000
χ5544-4-4-44-44004-4-44000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000
χ5644-4-4-44-44004-4-4400000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000
χ5744-4-4-44-4400-444-4000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000000
χ5844-4-4-44-4400-444-400000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000000
χ594-44-44-4-444-400004-400000000000000000000000000002i2−2i22i2−2i200000000000000000000
χ604-44-44-4-444-400004-40000000000000000000000000000−2i22i2−2i22i200000000000000000000
χ614-44-44-4-44-440000-440000000000000000000000002i2−2i22i2−2i2000000000000000000000000
χ624-44-44-4-44-440000-44000000000000000000000000−2i22i2−2i22i2000000000000000000000000
χ634-44-4-444-44-40000-4400000000000000000000000000002i2−2i2−2i22i200000000000000000000
χ644-44-4-444-44-40000-440000000000000000000000000000−2i22i22i2−2i200000000000000000000
χ654-44-4-444-4-4400004-40000000000000000000000002i2−2i2−2i22i2000000000000000000000000
χ664-44-4-444-4-4400004-4000000000000000000000000−2i22i22i2−2i2000000000000000000000000
χ678-8-8888-8-8000000000000000000000000000000000000000000000000000000000000
χ688-8-88-8-888000000000000000000000000000000000000000000000000000000000000

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