Finite Group Databasebeta

← Group #489131

Character table — Group #489131

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111222222222222444444488888888888888888888888881616161616161616161616163232
order122222444444888844488882222444481616161616161616161616161616161644444488888844
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1
χ3111111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111
χ4111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1
χ511111111111111111111111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1
χ611111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ811111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111
χ91111-1-1-1-111111111-11-1-1-11111-1-11-11-1-11111-1-1-1-11111-1-1-1-11-111-1-111-1-11-11-1
χ101111-1-1-1-111111111-11-1-1-11111-1-11-11-1-1-1-1-1-11111-1-1-1-111111-111-1-1-1-1111-1-11
χ111111-1-1-1-111111111-11-1-1-11111-1-1-11-11-11111-1-1-1-1-1-1-1-111111-1-1-111-1-111-111-1
χ121111-1-1-1-111111111-11-1-1-11111-1-1-11-11-1-1-1-1-111111111-1-1-1-11-1-1-11111-1-1-11-11
χ131111-1-1-1-111111111-11-1-1-111-1-1111-11-1-11111-1-1-1-11111-1-1-1-1-11-1-111-1-1111-1-11
χ141111-1-1-1-111111111-11-1-1-111-1-1111-11-1-1-1-1-1-11111-1-1-1-11111-11-1-11111-1-11-11-1
χ151111-1-1-1-111111111-11-1-1-111-1-111-11-11-11111-1-1-1-1-1-1-1-11111-1111-1-111-1-1-11-11
χ161111-1-1-1-111111111-11-1-1-111-1-111-11-11-1-1-1-1-111111111-1-1-1-1-1111-1-1-1-111-111-1
χ17222222222222-2-2-2-2222-2-2-2-200002222-200000000000000000000000000-2-200
χ18222222222222-2-2-2-2222-2-2-2-20000-2-2-2-2-2000000000000000000000000002200
χ19222222222-2-222222-2-2-222-2-222220000-20000000000000000-2-2000000000000
χ20222222222-2-222222-2-2-222-2-2-2-2-2-20000-2000000000000000022000000000000
χ21222222222-2-22-2-2-2-2-2-2-2-2-2220000000020000000000000000002-22-200000000
χ22222222222-2-22-2-2-2-2-2-2-2-2-222000000002000000000000000000-22-2200000000
χ23222222-2-2-222-200002-2-2000000002-2-22022−2−222−2−222−2−222−2−200000000000000
χ24222222-2-2-222-200002-2-2000000002-2-220−2−222−2−222−2−222−2−22200000000000000
χ25222222-2-2-222-200002-2-200000000-222-2022−2−222−2−2−2−222−2−22200000000000000
χ26222222-2-2-222-200002-2-200000000-222-20−2−222−2−22222−2−222−2−200000000000000
χ272222-2-222-222-20000-2-220000000022-2-2022−2−2−2−22222−2−2−2−22200000000000000
χ282222-2-222-222-20000-2-220000000022-2-20−2−22222−2−2−2−22222−2−200000000000000
χ292222-2-222-222-20000-2-2200000000-2-222022−2−2−2−222−2−22222−2−200000000000000
χ302222-2-222-222-20000-2-2200000000-2-2220−2−22222−2−222−2−2−2−22200000000000000
χ312222-2-2-2-22222-2-2-2-2-22-222-2-200002-22-2200000000000000000000000000-2200
χ322222-2-2-2-22222-2-2-2-2-22-222-2-20000-22-222000000000000000000000000002-200
χ332222-2-2-2-22-2-2222222-22-2-2-2-222-2-2000020000000000000000-22000000000000
χ342222-2-2-2-22-2-2222222-22-2-2-2-2-2-2220000200000000000000002-2000000000000
χ352222-2-2-2-22-2-22-2-2-2-22-22222200000000-20000000000000000002-2-2200000000
χ362222-2-2-2-22-2-22-2-2-2-22-22222200000000-2000000000000000000-222-200000000
χ3722-2-22-22-2200-222-2-20002-2002-22-200000000000002−22−22−22−20000002−22−20000
χ3822-2-22-22-2200-222-2-20002-2002-22-20000000000000−22−22−22−22000000−22−220000
χ3922-2-22-22-2200-222-2-20002-200-22-2200000000000002−22−22−22−2000000−22−220000
χ4022-2-22-22-2200-222-2-20002-200-22-220000000000000−22−22−22−220000002−22−20000
χ4122-2-2-22-22200-222-2-2000-22002-2-2200000000000002−22−2−22−220000002−2−220000
χ4222-2-2-22-22200-222-2-2000-22002-2-220000000000000−22−222−22−2000000−222−20000
χ4322-2-2-22-22200-222-2-2000-2200-222-200000000000002−22−2−22−22000000−222−20000
χ4422-2-2-22-22200-222-2-2000-2200-222-20000000000000−22−222−22−20000002−2−220000
χ45444444-4-4-4-4-4-40000-4440000000000000000000000000000000000000000000
χ464444-4-444-4-4-4-4000044-40000000000000000000000000000000000000000000
χ4744-4-44-44-4400-4-4-444000-4400000000000000000000000000000000000000000
χ4844-4-44-4-44-400400000000000000000000000000002-2-222-2-2200000000000000
χ4944-4-44-4-44-40040000000000000000000000000000-222-2-222-200000000000000
χ5044-4-4-444-4-400400000000000000000000000000002-2-22-222-200000000000000
χ5144-4-4-444-4-40040000000000000000000000000000-222-22-2-2200000000000000
χ5244-4-4-44-44400-4-4-4440004-400000000000000000000000000000000000000000
χ534-44-4000004-4022−2222−220000022−2200000000000002ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ50000000000000000000000
χ544-44-4000004-4022−2222−220000022−220000000000000−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ50000000000000000000000
χ554-44-4000004-40−2222−222200000−222200000000000002ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ70000000000000000000000
χ564-44-4000004-40−2222−222200000−22220000000000000−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ70000000000000000000000
χ574-44-400000-44022−2222−2200000−22220000000002ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ500000000000000000000000000
χ584-44-400000-44022−2222−2200000−2222000000000−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ500000000000000000000000000
χ594-44-400000-440−2222−22220000022−220000000002ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ700000000000000000000000000
χ604-44-400000-440−2222−22220000022−22000000000−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ700000000000000000000000000
χ618-8-880000000042−42−42420000000000000000000000000000000000000000000000
χ628-8-8800000000−424242−420000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1).