Finite Group Databasebeta

← Group #119405

Character table — Group #119405

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111111111111144444444444488888888888888888888888816161616161616161616161616161616
order12222222222222224444444444448888888888888888888888882244444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
χ51111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ91111-1-1-1-111-1-1-1-1111111-1-11-1-1-1-11iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11-1ii−i−iii−i−i1-111-1-1
χ101111-1-1-1-111-1-1-1-1111111-1-11-1-1-1-11iiii−i−i−i−iiiii−i−i−i−i-1-1-1-111111-1−i−iii−i−iii1-1-1-111
χ111111-1-1-1-111-1-1-1-1111111-1-11-1-1-1-11iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-11ii−i−i−i−iii-11-1-111
χ121111-1-1-1-111-1-1-1-1111111-1-11-1-1-1-11iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111-11−i−iiiii−i−i-1111-1-1
χ131111-1-1-1-111-1-1-1-1111111-1-11-1-1-1-11−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-11−i−iiiii−i−i-11-1-111
χ141111-1-1-1-111-1-1-1-1111111-1-11-1-1-1-11−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111-11ii−i−i−i−iii-1111-1-1
χ151111-1-1-1-111-1-1-1-1111111-1-11-1-1-1-11−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11-1−i−iii−i−iii1-111-1-1
χ161111-1-1-1-111-1-1-1-1111111-1-11-1-1-1-11−i−i−i−iiiii−i−i−i−iiiii-1-1-1-111111-1ii−i−iii−i−i1-1-1-111
χ17222222222222222222-2-22-2-2-2-22-2-20000000000000000000000000000002-22-2000000
χ18222222222222222222-2-22-2-2-2-22-2-2000000000000000000000000000000-22-22000000
χ192222222222222222-2-222-22-2-2-2-22-2000000000000000000000000002-22-20000000000
χ202222222222222222-2-222-22-2-2-2-22-200000000000000000000000000-22-220000000000
χ212222222222222222-2-2-2-2-2-2222-2-220000000000000000000000002200000000-2-20000
χ222222222222222222-2-2-2-2-2-2222-2-22000000000000000000000000-2-200000000220000
χ232222-2-2-2-222-2-2-2-22222-2-2-22-222-22-20000000000000000000000000000002i−2i−2i2i000000
χ242222-2-2-2-222-2-2-2-22222-2-2-22-222-22-2000000000000000000000000000000−2i2i2i−2i000000
χ252222-2-2-2-222-2-2-2-222-2-2222-2-2222-2-2000000000000000000000000002i−2i−2i2i0000000000
χ262222-2-2-2-222-2-2-2-222-2-2222-2-2222-2-200000000000000000000000000−2i2i2i−2i0000000000
χ272222-2-2-2-222-2-2-2-222-2-2-2-2222-2-22220000000000000000000000002-200000000-220000
χ282222-2-2-2-222-2-2-2-222-2-2-2-2222-2-2222000000000000000000000000-22000000002-20000
χ292-2-2-222-2-22222-2-22-22-22-222-22-2-2-22000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ302-2-2-222-2-22222-2-22-22-22-222-22-2-2-2200000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ312-2-2-222-2-22222-2-22-22-2-222-22-22-22-200000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ322-2-2-222-2-22222-2-22-22-2-222-22-22-22-20000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ332-2-2-222-2-22222-2-22-2-222-2-222-222-2-20000000000000000000000000000000000002i−2i2i−2i
χ342-2-2-222-2-22222-2-22-2-222-2-222-222-2-2000000000000000000000000000000000000−2i2i−2i2i
χ352-2-2-222-2-22222-2-22-2-22-22-2-2-22-222222-2-222-2-200000000000000000000000000000000
χ362-2-2-222-2-22222-2-22-2-22-22-2-2-22-2222-2-222-2-22200000000000000000000000000000000
χ372-2-2-2-2-22222-2-2222-22-22-2-2-2-2-222220000000022-2-2-2-222000000000000000000000000
χ382-2-2-2-2-22222-2-2222-22-22-2-2-2-2-2222200000000-2-22222-2-2000000000000000000000000
χ392-2-2-2-2-22222-2-2222-22-2-22-2222-22-2-200000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ402-2-2-2-2-22222-2-2222-22-2-22-2222-22-2-20000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ412-2-2-2-2-22222-2-2222-2-222-22-222-2-22-20000000000000000000000000000000000002i−2i−2i2i
χ422-2-2-2-2-22222-2-2222-2-222-22-222-2-22-2000000000000000000000000000000000000−2i2i2i−2i
χ432-2-2-2-2-22222-2-2222-2-22-2222-2-22-2-222i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ442-2-2-2-2-22222-2-2222-2-22-2222-2-22-2-22−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ45444-4444-44-4-4-44-4-4-4000000000000000000002-22-22-22-2000000000000000000000000
χ46444-4444-44-4-4-44-4-4-400000000000000000000-22-22-22-22000000000000000000000000
χ47444-4-4-4-444-444-44-4-4000000000000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ48444-4-4-4-444-444-44-4-400000000000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ4944-444-444-444-4-4-4-4-40000000000002-22-22-22-200000000000000000000000000000000
χ5044-444-444-444-4-4-4-4-4000000000000-22-22-22-2200000000000000000000000000000000
χ5144-44-44-4-4-44-4444-4-40000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000
χ5244-44-44-4-4-44-4444-4-4000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000
χ5344-4-44-44-4-4-4-44-444400000000000000000000000000002-22-22-22-20000000000000000
χ5444-4-44-44-4-4-4-44-44440000000000000000000000000000-22-22-22-220000000000000000
χ5544-4-4-44-44-4-44-44-44400000000000000000000000000002-22-2-22-220000000000000000
χ5644-4-4-44-44-4-44-44-4440000000000000000000000000000-22-222-22-20000000000000000
χ574-4444-4-44-4-4-444-44-400000000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ584-4444-4-44-4-4-444-44-40000000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ594-444-444-4-4-44-4-444-400000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ604-444-444-4-4-44-4-444-40000000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ614-44-44-4-4-4-444-444-440000000000002-2-222-2-2200000000000000000000000000000000
χ624-44-44-4-4-4-444-444-44000000000000-222-2-222-200000000000000000000000000000000
χ634-44-4-4444-44-44-4-4-440000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000
χ644-44-4-4444-44-44-4-4-44000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000
χ654-4-4444-444-4-4-4-44-44000000000000000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ664-4-4444-444-4-4-4-44-4400000000000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ674-4-44-4-44-44-4444-4-44000000000000000000002-2-22-222-2000000000000000000000000
χ684-4-44-4-44-44-4444-4-4400000000000000000000-222-22-2-22000000000000000000000000

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