Finite Group Databasebeta

← Group #323907

Character table — Group #323907

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444444444444444444448888888888888888161616161616161632323232
order12222222444444448888888822444444448888888888882244444488888888888888882444
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
χ5111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1
χ6111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111
χ7111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-111
χ8111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1111111-1-1
χ91111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11-11-1
χ101111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-11-11
χ111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-11-11
χ121111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111-11-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-111-1-1-1-1111-1-11
χ141111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-111-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1111111-1-1-1-111-111-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-11111-1-11111-1-11-1-11
χ172222222222-2-2-222-20000000022-2-222-2-2-2-20000000000002222-2-2-2-200000000000000000000
χ182222222222-2-2-222-20000000022-2-222-2-2-2-2000000000000-2-2-2-2222200000000000000000000
χ192222222222-2-2-222-200000000-2-2-2-2-2-2222200000000000022-2-222-2-200000000000000000000
χ202222222222-2-2-222-200000000-2-2-2-2-2-22222000000000000-2-222-2-22200000000000000000000
χ2122222222-2-2222-2-222222222222-2-2-2-2-2-222-2-2-2-2-2-2-2-222220000000000000000000000000000
χ2222222222-2-2222-2-2222222222-2-2-2-22222-2-2-2-2-2-22222-2-2-2-20000000000000000000000000000
χ2322222222-2-2222-2-22-2-2-2-2-2-2-2-222-2-2-2-2-2-22222222222-2-2-2-20000000000000000000000000000
χ2422222222-2-2222-2-22-2-2-2-2-2-2-2-2-2-2-2-22222-2-22222-2-2-2-222220000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-2000000002222-2-222-2-2000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ2622222222-2-2-2-2-2-2-2-2000000002222-2-222-2-200000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ2722222222-2-2-2-2-2-2-2-200000000-2-22222-2-222000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ2822222222-2-2-2-2-2-2-2-200000000-2-22222-2-22200000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ29222-2-22-2-22-20002-20i2i2i2i2−i2−i2−i2−i22-2002-20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200002i−2i2i−2i2−22−22−22−2000000000000
χ30222-2-22-2-22-20002-20i2i2i2i2−i2−i2−i2−i22-2002-20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000−2i2i−2i2i−22−22−22−22000000000000
χ31222-2-22-2-22-20002-20i2i2i2i2−i2−i2−i2−i2-2200-220000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200002i−2i−2i2i2−22−2−22−22000000000000
χ32222-2-22-2-22-20002-20i2i2i2i2−i2−i2−i2−i2-2200-220000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000−2i2i2i−2i−22−222−22−2000000000000
χ33222-2-22-2-22-20002-20−i2−i2−i2−i2i2i2i2i22-2002-20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200002i−2i2i−2i−22−22−22−22000000000000
χ34222-2-22-2-22-20002-20−i2−i2−i2−i2i2i2i2i22-2002-20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000−2i2i−2i2i2−22−22−22−2000000000000
χ35222-2-22-2-22-20002-20−i2−i2−i2−i2i2i2i2i2-2200-220000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200002i−2i−2i2i−22−222−22−2000000000000
χ36222-2-22-2-22-20002-20−i2−i2−i2−i2i2i2i2i2-2200-220000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000−2i2i2i−2i2−22−2−22−22000000000000
χ37222-2-22-2-2-22000-220i2i2i2i2−i2−i2−i2−i22-200-220000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i22-22-20000i2−i2−i2i2i2−i2−i2i2000000000000
χ38222-2-22-2-2-22000-220i2i2i2i2−i2−i2−i2−i22-200-220000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2-22-220000−i2i2i2−i2−i2i2i2−i2000000000000
χ39222-2-22-2-2-22000-220i2i2i2i2−i2−i2−i2−i2-22002-20000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i22-2-220000−i2i2i2−i2i2−i2−i2i2000000000000
χ40222-2-22-2-2-22000-220i2i2i2i2−i2−i2−i2−i2-22002-20000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2-222-20000i2−i2−i2i2−i2i2i2−i2000000000000
χ41222-2-22-2-2-22000-220−i2−i2−i2−i2i2i2i2i22-200-220000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i22-22-20000−i2i2i2−i2−i2i2i2−i2000000000000
χ42222-2-22-2-2-22000-220−i2−i2−i2−i2i2i2i2i22-200-220000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2-22-220000i2−i2−i2i2i2−i2−i2i2000000000000
χ43222-2-22-2-2-22000-220−i2−i2−i2−i2i2i2i2i2-22002-20000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i22-2-220000i2−i2−i2i2−i2i2i2−i2000000000000
χ44222-2-22-2-2-22000-220−i2−i2−i2−i2i2i2i2i2-22002-20000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2-222-20000−i2i2i2−i2i2−i2−i2i2000000000000
χ4522-22-2-2-222-222-2-22-22i2i−2i−2i2i2i−2i−2i002-20000002i−2i2i−2i0000000000000000000000002-22i−2i00000000
χ4622-22-2-2-222-222-2-22-22i2i−2i−2i2i2i−2i−2i002-20000002i−2i2i−2i000000000000000000000000-22−2i2i00000000
χ4722-22-2-2-222-222-2-22-2−2i−2i2i2i−2i−2i2i2i002-2000000−2i2i−2i2i0000000000000000000000002-2−2i2i00000000
χ4822-22-2-2-222-222-2-22-2−2i−2i2i2i−2i−2i2i2i002-2000000−2i2i−2i2i000000000000000000000000-222i−2i00000000
χ4922-22-2-2-22-2222-22-2-22i2i−2i−2i2i2i−2i−2i00-22000000−2i2i−2i2i00000000000000000000000000002i−2i2-20000
χ5022-22-2-2-22-2222-22-2-22i2i−2i−2i2i2i−2i−2i00-22000000−2i2i−2i2i0000000000000000000000000000−2i2i-220000
χ5122-22-2-2-22-2222-22-2-2−2i−2i2i2i−2i−2i2i2i00-220000002i−2i2i−2i00000000000000000000000000002i−2i-220000
χ5222-22-2-2-22-2222-22-2-2−2i−2i2i2i−2i−2i2i2i00-220000002i−2i2i−2i0000000000000000000000000000−2i2i2-20000
χ5344-44-4-4-444-4-4-44-4440000000000-440000000000000000000000000000000000000000000000
χ5444-44-4-4-44-44-4-444-4400000000004-40000000000000000000000000000000000000000000000
χ5544-4-44-44-444000-4-402222−22−22−22−222222000000000022−22−2222000000000000000000000000000000000000
χ5644-4-44-44-444000-4-40−22−2222222222−22−220000000000−222222−22000000000000000000000000000000000000
χ5744-4-44-44-4-4-40004402222−22−22−22−2222220000000000−222222−22000000000000000000000000000000000000
χ5844-4-44-44-4-4-4000440−22−2222222222−22−22000000000022−22−2222000000000000000000000000000000000000
χ594-444-4-44-40000000022−2222−2222−2222−22000000004i−4i000000002i2−2i22i2−2i20000000000000000000000000000
χ604-444-4-44-40000000022−2222−2222−2222−2200000000−4i4i00000000−2i22i2−2i22i20000000000000000000000000000
χ614-444-4-44-400000000−2222−2222−2222−2222000000004i−4i00000000−2i22i2−2i22i20000000000000000000000000000
χ624-444-4-44-400000000−2222−2222−2222−222200000000−4i4i000000002i2−2i22i2−2i20000000000000000000000000000
χ634-44-44-4-44004-4400-44i−4i4i−4i−4i4i−4i4i00000000000000000000000000000000000000000000000000
χ644-44-44-4-44004-4400-4−4i4i−4i4i4i−4i4i−4i00000000000000000000000000000000000000000000000000
χ654-44-44-4-4400-44-4004000000000000000000000000004-4-440000000000000000000000000000
χ664-44-44-4-4400-44-400400000000000000000000000000-444-40000000000000000000000000000
χ674-4-4444-4-4000000002i2−2i2−2i22i22i2−2i2−2i22i20000004-40000002i2−2i22i2−2i200000000000000000000000000000000
χ684-4-4444-4-4000000002i2−2i2−2i22i22i2−2i2−2i22i2000000-44000000−2i22i2−2i22i200000000000000000000000000000000
χ694-4-4444-4-400000000−2i22i22i2−2i2−2i22i22i2−2i20000004-4000000−2i22i2−2i22i200000000000000000000000000000000
χ704-4-4444-4-400000000−2i22i22i2−2i2−2i22i22i2−2i2000000-440000002i2−2i22i2−2i200000000000000000000000000000000
χ714-4-4-4-4444004-4-40044-4-44-444-400000000000000000000000000000000000000000000000000
χ724-4-4-4-4444004-4-4004-444-44-4-4400000000000000000000000000000000000000000000000000
χ734-4-4-4-444400-44400-400000000000000000000004-4-4400000000000000000000000000000000
χ744-4-4-4-444400-44400-40000000000000000000000-444-400000000000000000000000000000000

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