Finite Group Databasebeta

← Group #254114

Character table — Group #254114

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222244444444444444488888888888888888888161616161616161616161616163232
order12222244444444444444444444444444444444488888888222444444888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1
χ3111111111111111111111-1-1-1-1111111-1-1-1-111-1-1111111111-1-1-1-1-1-1-1-11111-1-1
χ4111111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111
χ511111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-11111-1-111-1-1-1-1-1-1
χ611111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111111111-1-1-1-1-111-1-1-1-1-1-111
χ811111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1
χ91111111111111-1-1-1-11111111111-1-1-1-1111111111111-1-1-1-1-11-11-1-1-1-1-111-1-11-1
χ101111111111111-1-1-1-11111111111-1-1-1-111111111-1-1-1-11111-1-11-11-1-1-1-1-1-111-11
χ111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11-11111111-1-1-11
χ121111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-11-11-11111-1-1111-1
χ131111111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1111111-1-1-1-111-11-111-1-1-1-111-11
χ141111111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-111-1-1-1-111111-11-1111-1-111-1-11-1
χ151111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-11-11-11-1-111-1-1111-1
χ161111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1111111-11-1-1-11111-1-1-11
χ1722222222-2-222-2222222220000-2-2-2-2220000-2-20000000000-200000000000000
χ1822222222-2-222-22222-2-2-2-20000-2-2-2-2-2-20000220000000000200000000000000
χ1922222222-2-222-2-2-2-2-222220000-2-222-2-20000-2-20000000000200000000000000
χ2022222222-2-222-2-2-2-2-2-2-2-2-20000-2-222220000220000000000-200000000000000
χ21222222-2-222-2-2222-2-200002222-2-22-200000000-2-20000000000000002-2000000
χ22222222-2-222-2-2222-2-20000-2-2-2-2-2-22-20000000022000000000000000-22000000
χ23222222-2-222-2-22-2-22200002222-2-2-2200000000-2-2000000000000000-22000000
χ24222222-2-222-2-22-2-2220000-2-2-2-2-2-2-2200000000220000000000000002-2000000
χ25222222-2-2-2-2-2-2-222-2-20000000022-220022-2-2000000000000000002-200000000
χ26222222-2-2-2-2-2-2-222-2-20000000022-2200-2-22200000000000000000-2200000000
χ27222222-2-2-2-2-2-2-2-2-22200000000222-20022-2-200000000000000000-2200000000
χ28222222-2-2-2-2-2-2-2-2-22200000000222-200-2-222000000000000000002-200000000
χ292222-2-22-2-2-22-22000000002i2i−2i−2i2-200000000002i−2i00002i2i−2i−2i0020-20000000000
χ302222-2-22-2-2-22-22000000002i2i−2i−2i2-200000000002i−2i0000−2i−2i2i2i00-2020000000000
χ312222-2-22-2-2-22-2200000000−2i−2i2i2i2-20000000000−2i2i00002i2i−2i−2i00-2020000000000
χ322222-2-22-2-2-22-2200000000−2i−2i2i2i2-20000000000−2i2i0000−2i−2i2i2i0020-20000000000
χ332222-2-2-22-2-2-222000000002i2i−2i−2i-220000000000−2i2i2i2i−2i−2i0000020-200000000000
χ342222-2-2-22-2-2-222000000002i2i−2i−2i-220000000000−2i2i−2i−2i2i2i00000-20200000000000
χ352222-2-2-22-2-2-22200000000−2i−2i2i2i-2200000000002i−2i2i2i−2i−2i00000-20200000000000
χ362222-2-2-22-2-2-22200000000−2i−2i2i2i-2200000000002i−2i−2i−2i2i2i0000020-200000000000
χ372-2-22-222200-2-202-22-22i2i−2i−2i000000002i−2i000000002−22−22−22−2000000000i2−i2i2−i200
χ382-2-22-222200-2-202-22-22i2i−2i−2i000000002i−2i00000000−22−22−22−22000000000−i2i2−i2i200
χ392-2-22-222200-2-202-22-2−2i−2i2i2i00000000−2i2i000000002−22−22−22−2000000000−i2i2−i2i200
χ402-2-22-222200-2-202-22-2−2i−2i2i2i00000000−2i2i00000000−22−22−22−22000000000i2−i2i2−i200
χ412-2-22-222200-2-20-22-222i2i−2i−2i00000000−2i2i000000002−22−2−22−22000000000i2−i2−i2i200
χ422-2-22-222200-2-20-22-222i2i−2i−2i00000000−2i2i00000000−22−222−22−2000000000−i2i2i2−i200
χ432-2-22-222200-2-20-22-22−2i−2i2i2i000000002i−2i000000002−22−2−22−22000000000−i2i2i2−i200
χ442-2-22-222200-2-20-22-22−2i−2i2i2i000000002i−2i00000000−22−222−22−2000000000i2−i2−i2i200
χ454444-4-44-4444-4-4000000000000-4400000000000000000000000000000000000
χ464444-4-4-4444-44-40000000000004-400000000000000000000000000000000000
χ4744-4-400004i−4i00000002-22-22+2i−2−2i2−2i−2+2i0000002-22i−2i2i−2i0000000000000000000000000
χ4844-4-400004i−4i00000002-22-2−2−2i2+2i−2+2i2−2i000000-22−2i2i2i−2i0000000000000000000000000
χ4944-4-400004i−4i0000000-22-222+2i−2−2i2−2i−2+2i000000-22−2i2i−2i2i0000000000000000000000000
χ5044-4-400004i−4i0000000-22-22−2−2i2+2i−2+2i2−2i0000002-22i−2i−2i2i0000000000000000000000000
χ5144-4-40000−4i4i00000002-22-22−2i−2+2i2+2i−2−2i0000002-2−2i2i−2i2i0000000000000000000000000
χ5244-4-40000−4i4i00000002-22-2−2+2i2−2i−2−2i2+2i000000-222i−2i−2i2i0000000000000000000000000
χ5344-4-40000−4i4i0000000-22-222−2i−2+2i2+2i−2−2i000000-222i−2i2i−2i0000000000000000000000000
χ5444-4-40000−4i4i0000000-22-22−2+2i2−2i−2−2i2+2i0000002-2−2i2i2i−2i0000000000000000000000000
χ554-4-444-44-400-4400000000000000000000000000000002i2−2i2−2i22i2000000000000000
χ564-4-444-44-400-440000000000000000000000000000000−2i22i22i2−2i2000000000000000
χ574-4-444-4-44004-40000000000000000000000000002i2−2i2−2i22i20000000000000000000
χ584-4-444-4-44004-4000000000000000000000000000−2i22i22i2−2i20000000000000000000
χ594-4-44-44-4-4004404-4-44000000000000000000000000000000000000000000000
χ604-4-44-44-4-400440-444-4000000000000000000000000000000000000000000000
χ618-88-800000000000004i−4i−4i4i00000000000000000000000000000000000000000
χ628-88-80000000000000−4i4i4i−4i00000000000000000000000000000000000000000

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