Finite Group Databasebeta

← Group #288595

Character table — Group #288595

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111122222222222244444444444888888888888888888816161616161616161616161616163232
order12222244444488884448888888844448888888888888882244448888888824
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-11111-1-1-1-11-111-111-1-1-1-1-1-11-1-1
χ311111111111111111111111111111111-1-1111111-1-11111-11-1-11-1-111-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111
χ511111111111111111111111-1-1-1-1-1-1-1-11111111-1-1111111-1-1-1-1-1-11-1-111111-1-1
χ611111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-111-1-1-1-1-11-1-11-1111-1-1-1-1111
χ711111111111111111111111-1-1-1-1-1-1-1-11-1-11111-1-1-1-111111-111-11-1-1-1-1-1-1-1-111
χ811111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1111111-1-1-1
χ9111111111111-1-1-1-1111-1-1-1-11111-1-1-1-1-111111111-1-1-1-1-1-1-111-111-1-1-111-1-111-1
χ10111111111111-1-1-1-1111-1-1-1-11111-1-1-1-1-111-1-1-1-111-1-11111-1-11-1-11-111-1-1111-11
χ11111111111111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-111111111-1-1-1-111-111-11-1-1-1-111-1-11
χ12111111111111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1111111111-1-11-1-111111-1-1-11-1
χ13111111111111-1-1-1-1111-1-1-1-1-1-1-1-11111-1111111-1-1-1-1-1-1-1-11-1-11-1-1-11111-1-11-11
χ14111111111111-1-1-1-1111-1-1-1-1-1-1-1-11111-111-1-1-1-1-1-1-1-1111111-111-1-1-1-1-1-11111-1
χ15111111111111-1-1-1-1111-1-1-1-1-1-1-1-11111-1-1-11111-1-111-1-1-1-1-1-11-1-11111-1-111-11-1
χ16111111111111-1-1-1-1111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1111111-111-1111-1-111-1-1-1-11
χ1722222222-2-2222222-2-2-2-2-22200000000-222000000220000000000-2000000-200
χ1822222222-2-2222222-2-2-2-2-22200000000-2-2-2000000-2-200000000002000000200
χ1922222222-2-222-2-2-2-2-2-2-222-2-200000000222000000-2-200000000002000000-200
χ2022222222-2-222-2-2-2-2-2-2-222-2-2000000002-2-2000000220000000000-2000000200
χ21222222-2-2-2-2-2-20000-22200002i2i−2i−2i000000000002i−2i0022-2-200000002i−2i0000000
χ22222222-2-2-2-2-2-20000-22200002i2i−2i−2i000000000002i−2i00-2-2220000000−2i2i0000000
χ23222222-2-2-2-2-2-20000-2220000−2i−2i2i2i00000000000−2i2i0022-2-20000000−2i2i0000000
χ24222222-2-2-2-2-2-20000-2220000−2i−2i2i2i00000000000−2i2i00-2-22200000002i−2i0000000
χ252222-2-22-2222-22222-2-2222-2-200000000-20000000000000020-2-2020000000000
χ262222-2-22-2222-22222-2-2222-2-200000000-200000000000000-20220-20000000000
χ272222-2-22-2222-2-2-2-2-2-2-22-2-22200000000200000000000000202-20-20000000000
χ282222-2-22-2222-2-2-2-2-2-2-22-2-22200000000200000000000000-20-22020000000000
χ292222-2-22-2-2-22-2222222-2-2-2-2-22i2i−2i−2i2i2i−2i−2i2000000−2i2i0000000000000000000000
χ302222-2-22-2-2-22-2222222-2-2-2-2-2−2i−2i2i2i−2i−2i2i2i20000002i−2i0000000000000000000000
χ312222-2-22-2-2-22-2-2-2-2-222-222222i2i−2i−2i−2i−2i2i2i-2000000−2i2i0000000000000000000000
χ322222-2-22-2-2-22-2-2-2-2-222-22222−2i−2i2i2i2i2i−2i−2i-20000002i−2i0000000000000000000000
χ332222-2-2-2222-220000-22-200002222000000022-2-2-2-20000000200-200000000000
χ342222-2-2-2222-220000-22-2000022220000000-2-222-2-20000000-200200000000000
χ352222-2-2-2222-220000-22-20000-2-2-2-2000000022-2-2220000000-200200000000000
χ362222-2-2-2222-220000-22-20000-2-2-2-20000000-2-222220000000200-200000000000
χ372-22-2-222200-2-22i2i−2i−2i000002i−2i0000000002-2i2−i2i2−i2002i−2i2−22−2000000000i2−i22−2000
χ382-22-2-222200-2-22i2i−2i−2i000002i−2i0000000002-2−i2i2−i2i2002i−2i−22−22000000000−i2i2−22000
χ392-22-2-222200-2-22i2i−2i−2i000002i−2i000000000-22i2−i2i2−i200−2i2i2−22−2000000000−i2i2−22000
χ402-22-2-222200-2-22i2i−2i−2i000002i−2i000000000-22−i2i2−i2i200−2i2i−22−22000000000i2−i22−2000
χ412-22-2-222200-2-2−2i−2i2i2i00000−2i2i0000000002-2i2−i2i2−i200−2i2i−22−22000000000i2−i2−22000
χ422-22-2-222200-2-2−2i−2i2i2i00000−2i2i0000000002-2−i2i2−i2i200−2i2i2−22−2000000000−i2i22−2000
χ432-22-2-222200-2-2−2i−2i2i2i00000−2i2i000000000-22i2−i2i2−i2002i−2i−22−22000000000−i2i22−2000
χ442-22-2-222200-2-2−2i−2i2i2i00000−2i2i000000000-22−i2i2−i2i2002i−2i2−22−2000000000i2−i2−22000
χ45444444-4-444-4-400004-4-40000000000000000000000000000000000000000000
χ464444-4-4-44-4-4-4400004-440000000000000000000000000000000000000000000
χ4744-4-400004-4002i2−2i22i2−2i20002i2−2i2002i2−2i22i2−2i22-22-20000000000000000000000000000000
χ4844-4-400004-4002i2−2i22i2−2i20002i2−2i200−2i22i2−2i22i2-22-220000000000000000000000000000000
χ4944-4-400004-400−2i22i2−2i22i2000−2i22i2002i2−2i22i2−2i2-22-220000000000000000000000000000000
χ5044-4-400004-400−2i22i2−2i22i2000−2i22i200−2i22i2−2i22i22-22-20000000000000000000000000000000
χ5144-4-40000-44002i2−2i22i2−2i2000−2i22i20022−22−2222−2i2i2i−2i0000000000000000000000000000000
χ5244-4-40000-44002i2−2i22i2−2i2000−2i22i200−222222−222i−2i−2i2i0000000000000000000000000000000
χ5344-4-40000-4400−2i22i2−2i22i20002i2−2i20022−22−22222i−2i−2i2i0000000000000000000000000000000
χ5444-4-40000-4400−2i22i2−2i22i20002i2−2i200−222222−22−2i2i2i−2i0000000000000000000000000000000
χ554-44-44-44-400-444i4i−4i−4i00000−4i4i000000000000000000000000000000000000000
χ564-44-44-44-400-44−4i−4i4i4i000004i−4i000000000000000000000000000000000000000
χ574-44-44-4-44004-400000000000000000000002i2−2i2−2i22i2000000000000000000000000
χ584-44-44-4-44004-40000000000000000000000−2i22i22i2−2i2000000000000000000000000
χ594-44-4-44-4-4004400000000000000000000000000000022−22−22220000000000000000
χ604-44-4-44-4-40044000000000000000000000000000000−222222−220000000000000000
χ618-8-880000000042−42−42420000000000000000000000000000000000000000000000
χ628-8-8800000000−424242−420000000000000000000000000000000000000000000000

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