Finite Group Databasebeta

← Group #349059

Character table — Group #349059

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11112222222222224444444444444444444444488888888888888888161616161616161632323232
order12222244444488882244444444488888888888822444444888888888888888884488
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111-1-1111-1-1111111111-1-1-1-11-1-1-11-1-1-1111-1-1-1-1-1-11111-1-1-1-111-1-1
χ41111111111111111111-1-1111-1-1111111111-1-1-1-11-1-1-11-1-1-1111-1-1-1-1-1-1-1-1-1-11111-1-111
χ51111111111111111-1-11111-1-11111111-1-1-1-11111-11-1-1-11-1-11-1-111-1-1-1-111111111-1-1-1-1
χ61111111111111111-1-11111-1-11111111-1-1-1-11111-11-1-1-11-1-11-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111-1-11-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-1111-1-1-1-111111111-1-1-1-1-1-111
χ81111111111111111-1-11-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-1111-1-1-1-11111-1-1-1-1111111-1-1
χ9111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-111-1-11-11-1
χ10111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111-1-111-11-11
χ11111111111111-1-1-1-1111-1-1111-1-11-1-1-1-1-1-1-1-111111-1-1-11-1-1-1-1-1-111111111-1-1-1-1111-1-11
χ12111111111111-1-1-1-1111-1-1111-1-11-1-1-1-1-1-1-1-111111-1-1-11-1-1-1-1-1-1111111-1-11111-1-1-111-1
χ13111111111111-1-1-1-1-1-11111-1-1111-1-1-1-11111-1-1-1-1-11-1-1-11-1-1-111-1-1111111-1-111-1-1-11-11
χ14111111111111-1-1-1-1-1-11111-1-1111-1-1-1-11111-1-1-1-1-11-1-1-11-1-1-111-1-11111-1-111-1-1111-11-1
χ15111111111111-1-1-1-1-1-11-1-11-1-1-1-11-1-1-1-111111111-1-111-1-111-11111-1-1-1-111-1-1-1-111-111-1
χ16111111111111-1-1-1-1-1-11-1-11-1-1-1-11-1-1-1-111111111-1-111-1-111-11111-1-1-1-1-1-11111-1-11-1-11
χ1722222222-2-222222200-222-20022-222-2-2000022220-2000-200-200-2-20000000000000000
χ1822222222-2-222222200-2-2-2-200-2-2-222-2-20000-2-2-2-202000200-200220000000000000000
χ1922222222-2-222-2-2-2-200-222-20022-2-2-2220000-2-2-2-20-2000-200200220000000000000000
χ2022222222-2-222-2-2-2-200-2-2-2-200-2-2-2-2-2220000222202000200200-2-20000000000000000
χ21222222-2-222-2-2000022-2002-2-200-2000000002i2i−2i−2i2000-20000002i−2i2i2i−2i−2i000000000000
χ22222222-2-222-2-2000022-2002-2-200-200000000−2i−2i2i2i2000-2000000−2i2i−2i−2i2i2i000000000000
χ23222222-2-222-2-20000-2-2-20022200-2000000002i2i−2i−2i-200020000002i−2i−2i−2i2i2i000000000000
χ24222222-2-222-2-20000-2-2-20022200-200000000−2i−2i2i2i-20002000000−2i2i2i2i−2i−2i000000000000
χ25222222-2-2-2-2-2-2000000200-20000200002i2i−2i−2i2i2i−2i−2i002-2002-202i−2i−2i2i0000000000000000
χ26222222-2-2-2-2-2-2000000200-20000200002i2i−2i−2i−2i−2i2i2i00-2200-2202i−2i2i−2i0000000000000000
χ27222222-2-2-2-2-2-2000000200-2000020000−2i−2i2i2i2i2i−2i−2i00-2200-220−2i2i−2i2i0000000000000000
χ28222222-2-2-2-2-2-2000000200-2000020000−2i−2i2i2i−2i−2i2i2i002-2002-20−2i2i2i−2i0000000000000000
χ292222-2-22222-2-2000022-222-2-2-2-2-22000000000000-2-22222-2-2000000000000000000000
χ302222-2-22222-2-2000022-2-2-2-2-2-2222000000000000-22-2-22-222000000000000000000000
χ312222-2-22222-2-20000-2-2-222-222-2-220000000000002-2-2-2-2222000000000000000000000
χ322222-2-22222-2-20000-2-2-2-2-2-2222220000000000002222-2-2-2-2000000000000000000000
χ332222-2-222-2-2-2-2000000222200-2-2-200002i2i−2i−2i000002000-2000−2i2i002i−2i2i−2i000000000000
χ342222-2-222-2-2-2-2000000222200-2-2-20000−2i−2i2i2i000002000-20002i−2i00−2i2i−2i2i000000000000
χ352222-2-222-2-2-2-20000002-2-220022-200002i2i−2i−2i00000-20002000−2i2i00−2i2i−2i2i000000000000
χ362222-2-222-2-2-2-20000002-2-220022-20000−2i−2i2i2i00000-200020002i−2i002i−2i2i−2i000000000000
χ372222-2-2-2-22222222222200-22200-2-2-22222220000-2000-2000-2-2-2000000000000000000
χ382222-2-2-2-222222222-2-2200-2-2-200-2-2-222-2-2-2-2000020002000-222000000000000000000
χ392222-2-2-2-22222-2-2-2-222200-22200-222-2-2-2-2-2-20000-2000-2000222000000000000000000
χ402222-2-2-2-22222-2-2-2-2-2-2200-2-2-200-222-2-222220000200020002-2-2000000000000000000
χ412222-2-2-2-2-2-222222200-200200002-2-2-2-200000000002-200-22200002-2-22000000000000
χ422222-2-2-2-2-2-222222200-200200002-2-2-2-20000000000-22002-220000-222-2000000000000
χ432222-2-2-2-2-2-222-2-2-2-200-200200002222200000000002-200-22-20000-222-2000000000000
χ442222-2-2-2-2-2-222-2-2-2-200-20020000222220000000000-22002-2-200002-2-22000000000000
χ452-22-22-22-2002-22i2i−2i−2i0002i−2i0002i−2i02i−2i0000002-22-200000000000000000i2−i22−22−2i2−i20000
χ462-22-22-22-2002-22i2i−2i−2i0002i−2i0002i−2i02i−2i0000002-22-200000000000000000−i2i2−22−22−i2i20000
χ472-22-22-22-2002-22i2i−2i−2i000−2i2i000−2i2i02i−2i000000-22-2200000000000000000i2−i22−2−22−i2i20000
χ482-22-22-22-2002-22i2i−2i−2i000−2i2i000−2i2i02i−2i000000-22-2200000000000000000−i2i2−222−2i2−i20000
χ492-22-22-22-2002-2−2i−2i2i2i0002i−2i0002i−2i0−2i2i000000-22-2200000000000000000i2−i2−222−2−i2i20000
χ502-22-22-22-2002-2−2i−2i2i2i0002i−2i0002i−2i0−2i2i000000-22-2200000000000000000−i2i22−2−22i2−i20000
χ512-22-22-22-2002-2−2i−2i2i2i000−2i2i000−2i2i0−2i2i0000002-22-200000000000000000i2−i2−22−22i2−i20000
χ522-22-22-22-2002-2−2i−2i2i2i000−2i2i000−2i2i0−2i2i0000002-22-200000000000000000−i2i22−22−2−i2i20000
χ534-44-44-4-4400-44000000000000000000000004i−4i−4i4i00000000000000000000000000000
χ544-44-44-4-4400-4400000000000000000000000−4i4i4i−4i00000000000000000000000000000
χ554-44-4-444-400-4400000004i−4i000−4i4i000000000000000000000000000000000000000000
χ564-44-4-444-400-440000000−4i4i0004i−4i000000000000000000000000000000000000000000
χ574-44-4-44-44004-44i4i−4i−4i00000000000−4i4i000000000000000000000000000000000000000
χ584-44-4-44-44004-4−4i−4i4i4i000000000004i−4i000000000000000000000000000000000000000
χ594-4-4400004-4002i2−2i22i2−2i20000004i−4i000002i2−2i222−2222−22000000000000000000000000000000000
χ604-4-4400004-4002i2−2i22i2−2i2000000−4i4i000002i2−2i2−2222−2222000000000000000000000000000000000
χ614-4-4400004-400−2i22i2−2i22i20000004i−4i00000−2i22i2−2222−2222000000000000000000000000000000000
χ624-4-4400004-400−2i22i2−2i22i2000000−4i4i00000−2i22i222−2222−22000000000000000000000000000000000
χ634-4-440000-44002i2−2i22i2−2i24-400000000000−2i22i22i2−2i2−2i22i2000000000000000000000000000000000
χ644-4-440000-44002i2−2i22i2−2i2-4400000000000−2i22i2−2i22i22i2−2i2000000000000000000000000000000000
χ654-4-440000-4400−2i22i2−2i22i24-4000000000002i2−2i2−2i22i22i2−2i2000000000000000000000000000000000
χ664-4-440000-4400−2i22i2−2i22i2-44000000000002i2−2i22i2−2i2−2i22i2000000000000000000000000000000000
χ6788-8-80000000042−42−42420000000000000000000000000000000000000000000000000000
χ6888-8-800000000−424242−420000000000000000000000000000000000000000000000000000

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