Finite Group Databasebeta

← Group #325155

Character table — Group #325155

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444444444444444444448888888888888888161616161616161632323232
order12222222444444448888888844444444448888888888884444444488888888888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11-11-1
χ611111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111-11-11
χ711111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-11-11
χ811111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111-11-1
χ91111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11-1-11
χ101111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-111-1
χ111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-111-1
χ121111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111-1-11
χ131111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ141111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111-1-11111-1-1-1-111
χ151111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-111-1-1-1-111-1-111
χ161111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1-1-11111-1-111-1-1
χ1722222222222-2-2-2-2222222222-2-222-2-222-2-2-2-2-2-22222-2-2-2-20000000000000000000000000000
χ1822222222222-2-2-2-2222222222-2-2-2-222-2-222-2-2-2-2-2-2-2-222220000000000000000000000000000
χ1922222222222-2-2-2-22-2-2-2-2-2-2-2-2-2-222-2-222-2-22222-2-2-2-222220000000000000000000000000000
χ2022222222222-2-2-2-22-2-2-2-2-2-2-2-2-2-2-2-222-2-22222222222-2-2-2-20000000000000000000000000000
χ2122222222-2-2-22222-200000000-2-222-2-2-2-22200000000000022-2-2-2-22200000000000000000000
χ2222222222-2-2-22222-200000000-2-222-2-2-2-222000000000000-2-22222-2-200000000000000000000
χ2322222222-2-2-22222-200000000-2-2-2-22222-2-20000000000002222-2-2-2-200000000000000000000
χ2422222222-2-2-22222-200000000-2-2-2-22222-2-2000000000000-2-2-2-2222200000000000000000000
χ2522222222-2-2-2-2-2-2-2-200000000222222-2-2-2-2000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ2622222222-2-2-2-2-2-2-2-200000000222222-2-2-2-200000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ2722222222-2-2-2-2-2-2-2-20000000022-2-2-2-22222000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ2822222222-2-2-2-2-2-2-2-20000000022-2-2-2-2222200000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ292222-2-2-2-222-222-2-2-22222-2-2-2-22-20000000022-2-200000000000000000000000000002-22-20000
χ302222-2-2-2-222-222-2-2-22222-2-2-2-22-20000000022-2-20000000000000000000000000000-22-220000
χ312222-2-2-2-222-222-2-2-2-2-2-2-222222-200000000-2-22200000000000000000000000000002-2-220000
χ322222-2-2-2-222-222-2-2-2-2-2-2-222222-200000000-2-2220000000000000000000000000000-222-20000
χ332222-2-2-2-222-2-2-222-22222-2-2-2-2-2200000000-2-2220000000000000000000000002-22-200000000
χ342222-2-2-2-222-2-2-222-22222-2-2-2-2-2200000000-2-222000000000000000000000000-22-2200000000
χ352222-2-2-2-222-2-2-222-2-2-2-2-22222-220000000022-2-20000000000000000000000002-2-2200000000
χ362222-2-2-2-222-2-2-222-2-2-2-2-22222-220000000022-2-2000000000000000000000000-222-200000000
χ3722-2-2-222-20002-22-20i2i2−i2−i2i2i2−i2−i2002i−2i00002i−2ii2−i2i2−i222−2−222−2−2002-22i−2i002−22−2i2−i2i2−i2000000000000
χ3822-2-2-222-20002-22-20i2i2−i2−i2i2i2−i2−i2002i−2i00002i−2ii2−i2i2−i222−2−222−2−200-22−2i2i00−22−22−i2i2−i2i2000000000000
χ3922-2-2-222-20002-22-20i2i2−i2−i2i2i2−i2−i200−2i2i0000−2i2ii2−i2i2−i2−2−222−2−222002-2−2i2i00−22−22i2−i2i2−i2000000000000
χ4022-2-2-222-20002-22-20i2i2−i2−i2i2i2−i2−i200−2i2i0000−2i2ii2−i2i2−i2−2−222−2−22200-222i−2i002−22−2−i2i2−i2i2000000000000
χ4122-2-2-222-20002-22-20−i2−i2i2i2−i2−i2i2i2002i−2i00002i−2i−i2i2−i2i2−2−222−2−222002-22i−2i00−22−22−i2i2−i2i2000000000000
χ4222-2-2-222-20002-22-20−i2−i2i2i2−i2−i2i2i2002i−2i00002i−2i−i2i2−i2i2−2−222−2−22200-22−2i2i002−22−2i2−i2i2−i2000000000000
χ4322-2-2-222-20002-22-20−i2−i2i2i2−i2−i2i2i200−2i2i0000−2i2i−i2i2−i2i222−2−222−2−2002-2−2i2i002−22−2−i2i2−i2i2000000000000
χ4422-2-2-222-20002-22-20−i2−i2i2i2−i2−i2i2i200−2i2i0000−2i2i−i2i2−i2i222−2−222−2−200-222i−2i00−22−22i2−i2i2−i2000000000000
χ4522-2-2-222-2000-22-220i2i2−i2−i2i2i2−i2−i2002i−2i0000−2i2i−i2i2−i2i222−2−2−2−2222-200002i−2ii2−i2−i2i2−222−2000000000000
χ4622-2-2-222-2000-22-220i2i2−i2−i2i2i2−i2−i2002i−2i0000−2i2i−i2i2−i2i222−2−2−2−222-220000−2i2i−i2i2i2−i22−2−22000000000000
χ4722-2-2-222-2000-22-220i2i2−i2−i2i2i2−i2−i200−2i2i00002i−2i−i2i2−i2i2−2−22222−2−22-20000−2i2ii2−i2−i2i22−2−22000000000000
χ4822-2-2-222-2000-22-220i2i2−i2−i2i2i2−i2−i200−2i2i00002i−2i−i2i2−i2i2−2−22222−2−2-2200002i−2i−i2i2i2−i2−222−2000000000000
χ4922-2-2-222-2000-22-220−i2−i2i2i2−i2−i2i2i2002i−2i0000−2i2ii2−i2i2−i2−2−22222−2−22-200002i−2i−i2i2i2−i22−2−22000000000000
χ5022-2-2-222-2000-22-220−i2−i2i2i2−i2−i2i2i2002i−2i0000−2i2ii2−i2i2−i2−2−22222−2−2-220000−2i2ii2−i2−i2i2−222−2000000000000
χ5122-2-2-222-2000-22-220−i2−i2i2i2−i2−i2i2i200−2i2i00002i−2ii2−i2i2−i222−2−2−2−2222-20000−2i2i−i2i2i2−i2−222−2000000000000
χ5222-2-2-222-2000-22-220−i2−i2i2i2−i2−i2i2i200−2i2i00002i−2ii2−i2i2−i222−2−2−2−222-2200002i−2ii2−i2−i2i22−2−22000000000000
χ534444-4-4-4-4-4-4444-4-4400000000-44000000000000000000000000000000000000000000000000
χ544444-4-4-4-4-4-44-4-4444000000004-4000000000000000000000000000000000000000000000000
χ5544-4-44-4-440004-4-4402i22i2−2i2−2i2−2i2−2i22i22i200000000002i2−2i2−2i22i2000000000000000000000000000000000000
χ5644-4-44-4-440004-4-440−2i2−2i22i22i22i22i2−2i2−2i20000000000−2i22i22i2−2i2000000000000000000000000000000000000
χ5744-4-44-4-44000-444-402i22i2−2i2−2i2−2i2−2i22i22i20000000000−2i22i22i2−2i2000000000000000000000000000000000000
χ5844-4-44-4-44000-444-40−2i2−2i22i22i22i22i2−2i2−2i200000000002i2−2i2−2i22i2000000000000000000000000000000000000
χ594-44-444-4-40000000022−2222−2222−2222−2200004-400000000000022−2222−220000000000000000000000000000
χ604-44-444-4-40000000022−2222−2222−2222−220000-44000000000000−2222−22220000000000000000000000000000
χ614-44-444-4-400000000−2222−2222−2222−222200004-4000000000000−2222−22220000000000000000000000000000
χ624-44-444-4-400000000−2222−2222−2222−22220000-4400000000000022−2222−220000000000000000000000000000
χ634-44-4-4-4440000000022−2222−22−2222−22220000004-400000022−2222−2200000000000000000000000000000000
χ644-44-4-4-4440000000022−2222−22−2222−2222000000-44000000−2222−222200000000000000000000000000000000
χ654-44-4-4-44400000000−2222−222222−2222−220000004-4000000−2222−222200000000000000000000000000000000
χ664-44-4-4-44400000000−2222−222222−2222−22000000-4400000022−2222−2200000000000000000000000000000000
χ674-4-444-44-44-440000-400000000000000000000004-4-4400000000000000000000000000000000
χ684-4-444-44-44-440000-40000000000000000000000-444-400000000000000000000000000000000
χ694-4-444-44-4-44-4000044i−4i−4i4i−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ704-4-444-44-4-44-400004−4i4i4i−4i4i−4i−4i4i00000000000000000000000000000000000000000000000000
χ714-4-44-44-444-4-400004000000000000000000000000004-4-440000000000000000000000000000
χ724-4-44-44-444-4-40000400000000000000000000000000-444-40000000000000000000000000000
χ734-4-44-44-44-4440000-44i−4i−4i4i4i−4i−4i4i00000000000000000000000000000000000000000000000000
χ744-4-44-44-44-4440000-4−4i4i4i−4i−4i4i4i−4i00000000000000000000000000000000000000000000000000

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