Finite Group Databasebeta

← Group #349058

Character table — Group #349058

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11112222222222224444444444444444444444488888888888888888161616161616161632323232
order12222244444488882222444444488888888888822244444888888888888888884488
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111-1-11111-1-1111111111-1-1-1-11-1-1-1-11-1-11-1-111-1-1-1-11111-1-1-1-111-1-1
χ4111111111111111111-1-11111-1-1111111111-1-1-1-11-1-1-1-11-1-11-1-111-1-1-1-1-1-1-1-11111-1-111
χ51111111111111111-1-11111-1-11111111-1-1-1-11111-1-1-111-1-1-1111-1-1-1-1-1-111111111-1-1-1-1
χ61111111111111111-1-11111-1-11111111-1-1-1-11111-1-1-111-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111-1-1-1-111-1-1-1-111111-1-1-1-1-1-1-1-1-111-1-1-1111-1-1-1-111111111-1-1-1-1-1-111
χ81111111111111111-1-1-1-111-1-1-1-111111-1-1-1-1-1-1-1-1-111-1-1-1111-1-1-1-11111-1-1-1-1111111-1-1
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
χ11111111111111-1-1-1-111-1-11111-1-11-1-1-1-1-1-1-1-111111-1-1-1-11-1-1-111-1-1111111-1-1-1-1111-1-11
χ12111111111111-1-1-1-111-1-11111-1-11-1-1-1-1-1-1-1-111111-1-1-1-11-1-1-111-1-11111-1-11111-1-1-111-1
χ13111111111111-1-1-1-1-1-11111-1-1111-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-111-1-1-11-11
χ14111111111111-1-1-1-1-1-11111-1-1111-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-111-1-1111-11-1
χ15111111111111-1-1-1-1-1-1-1-111-1-1-1-11-1-1-1-111111111-111-1-1-111-11111-1-1-1-111-1-1-1-111-111-1
χ16111111111111-1-1-1-1-1-1-1-111-1-1-1-11-1-1-1-111111111-111-1-1-111-11111-1-1-1-1-1-11111-1-11-1-11
χ1722222222-2-2-2-200002200-22-2-200-2000000002i2i−2i−2i20000-20002i−2i002i2i−2i−2i000000000000
χ1822222222-2-2-2-200002200-22-2-200-200000000−2i−2i2i2i20000-2000−2i2i00−2i−2i2i2i000000000000
χ1922222222-2-2-2-20000-2-200-222200-2000000002i2i−2i−2i-2000020002i−2i00−2i−2i2i2i000000000000
χ2022222222-2-2-2-20000-2-200-222200-200000000−2i−2i2i2i-200002000−2i2i002i2i−2i−2i000000000000
χ21222222-2-2222222220022-2-20022-2-2-22200002222000-2-2000-2-2-2000000000000000000
χ22222222-2-22222222200-2-2-2-200-2-2-2-2-2220000-2-2-2-200022000-222000000000000000000
χ23222222-2-22222-2-2-2-20022-2-20022-222-2-20000-2-2-2-2000-2-2000222000000000000000000
χ24222222-2-22222-2-2-2-200-2-2-2-200-2-2-222-2-200002222000220002-2-2000000000000000000
χ25222222-2-2-2-2-2-2000000002-20000200002i2i−2i−2i2i2i−2i−2i02-20002-20−2i2i2i−2i0000000000000000
χ26222222-2-2-2-2-2-2000000002-20000200002i2i−2i−2i−2i−2i2i2i0-22000-2202i−2i2i−2i0000000000000000
χ27222222-2-2-2-2-2-2000000002-2000020000−2i−2i2i2i2i2i−2i−2i0-22000-220−2i2i−2i2i0000000000000000
χ28222222-2-2-2-2-2-2000000002-2000020000−2i−2i2i2i−2i−2i2i2i02-20002-202i−2i−2i2i0000000000000000
χ292222-2-22222-2-200002222-2-2-2-2-2-22000000000000-222-222-2-2000000000000000000000
χ302222-2-22222-2-2000022-2-2-2-2-2-2222000000000000-2-2-22-2222000000000000000000000
χ312222-2-22222-2-20000-2-222-2-222-2-220000000000002-2-2-22-222000000000000000000000
χ322222-2-22222-2-20000-2-2-2-2-2-2222220000000000002222-2-2-2-2000000000000000000000
χ332222-2-222-2-222222222002-22200-222-2-222220000-20000-200-200-2-20000000000000000
χ342222-2-222-2-2222222-2-2002-2-2-200-222-2-2-2-2-2-2000020000200-200220000000000000000
χ352222-2-222-2-222-2-2-2-222002-22200-2-2-222-2-2-2-20000-20000-200200220000000000000000
χ362222-2-222-2-222-2-2-2-2-2-2002-2-2-200-2-2-2222222000020000200200-2-20000000000000000
χ372222-2-2-2-222-2-2000000222200-2-2-200002i2i−2i−2i00000002-2000000−2i2i2i−2i2i−2i000000000000
χ382222-2-2-2-222-2-2000000222200-2-2-20000−2i−2i2i2i00000002-20000002i−2i−2i2i−2i2i000000000000
χ392222-2-2-2-222-2-2000000-2-2220022-200002i2i−2i−2i0000000-22000000−2i2i−2i2i−2i2i000000000000
χ402222-2-2-2-222-2-2000000-2-2220022-20000−2i−2i2i2i0000000-220000002i−2i2i−2i2i−2i000000000000
χ412222-2-2-2-2-2-22222220000-2200002-2-2-2-20000000002-2000-22200002-2-22000000000000
χ422222-2-2-2-2-2-22222220000-2200002-2-2-2-2000000000-220002-220000-222-2000000000000
χ432222-2-2-2-2-2-222-2-2-2-20000-220000222220000000002-2000-22-20000-222-2000000000000
χ442222-2-2-2-2-2-222-2-2-2-20000-22000022222000000000-220002-2-200002-2-22000000000000
χ452-2-222-2002-22-22i2i−2i−2i002-200002-20002i−2i00002i−2i2i−2i00000000000000000i2−i22−2i2−i22−20000
χ462-2-222-2002-22-22i2i−2i−2i002-200002-20002i−2i00002i−2i2i−2i00000000000000000−i2i2−22−i2i2−220000
χ472-2-222-2002-22-22i2i−2i−2i00-220000-220002i−2i0000−2i2i−2i2i00000000000000000i2−i22−2−i2i2−220000
χ482-2-222-2002-22-22i2i−2i−2i00-220000-220002i−2i0000−2i2i−2i2i00000000000000000−i2i2−22i2−i22−20000
χ492-2-222-2002-22-2−2i−2i2i2i002-200002-2000−2i2i0000−2i2i−2i2i00000000000000000i2−i2−22i2−i2−220000
χ502-2-222-2002-22-2−2i−2i2i2i002-200002-2000−2i2i0000−2i2i−2i2i00000000000000000−i2i22−2−i2i22−20000
χ512-2-222-2002-22-2−2i−2i2i2i00-220000-22000−2i2i00002i−2i2i−2i00000000000000000i2−i2−22−i2i22−20000
χ522-2-222-2002-22-2−2i−2i2i2i00-220000-22000−2i2i00002i−2i2i−2i00000000000000000−i2i22−2i2−i2−220000
χ534-44-4004-400002i2−2i22i2−2i20000004i−4i0002i2−2i20022−2222−22000000000000000000000000000000000
χ544-44-4004-400002i2−2i22i2−2i2000000−4i4i0002i2−2i200−2222−2222000000000000000000000000000000000
χ554-44-4004-40000−2i22i2−2i22i20000004i−4i000−2i22i200−2222−2222000000000000000000000000000000000
χ564-44-4004-40000−2i22i2−2i22i2000000−4i4i000−2i22i20022−2222−22000000000000000000000000000000000
χ574-44-400-4400002i2−2i22i2−2i24-4000000000−2i22i2002i2−2i2−2i22i2000000000000000000000000000000000
χ584-44-400-4400002i2−2i22i2−2i2-44000000000−2i22i200−2i22i22i2−2i2000000000000000000000000000000000
χ594-44-400-440000−2i22i2−2i22i24-40000000002i2−2i200−2i22i22i2−2i2000000000000000000000000000000000
χ604-44-400-440000−2i22i2−2i22i2-440000000002i2−2i2002i2−2i2−2i22i2000000000000000000000000000000000
χ614-4-444-400-44-44000000000000000000000004-4-4400000000000000000000000000000
χ624-4-444-400-44-4400000000000000000000000-444-400000000000000000000000000000
χ634-4-44-44004-4-440000004-40000-44000000000000000000000000000000000000000000
χ644-4-44-44004-4-44000000-4400004-4000000000000000000000000000000000000000000
χ654-4-44-4400-444-44i4i−4i−4i0000000000000−4i4i0000000000000000000000000000000000000
χ664-4-44-4400-444-4−4i−4i4i4i00000000000004i−4i0000000000000000000000000000000000000
χ6788-8-80000000042−42−42420000000000000000000000000000000000000000000000000000
χ6888-8-800000000−424242−420000000000000000000000000000000000000000000000000000

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