Finite Group Databasebeta

← Group #113245

Character table — Group #113245

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222222224444444488888888888888888888888816161616161616161616161616161616
order12222222444444444444224444448888888888888888888888882244444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1
χ51111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-11111-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ91-1-11-1-111-1-111-1-111-111-11-111-11-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-1ii−i−i1-111-1-1ii−i−i
χ101-1-11-1-111-1-111-1-111-111-11-111-11-1-11111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii-11ii−i−i-11-1-111−i−iii
χ111-1-11-1-111-1-111-1-111-111-11-111-11-1-11111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i-11−i−iii-11-1-111ii−i−i
χ121-1-11-1-111-1-111-1-111-111-11-111-11-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-1−i−iii1-111-1-1−i−iii
χ131-1-11-1-111-1-111-1-111-111-11-111-11-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i1-1−i−iii1-1-1-111−i−iii
χ141-1-11-1-111-1-111-1-111-111-11-111-11-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-11−i−iii-1111-1-1ii−i−i
χ151-1-11-1-111-1-111-1-111-111-11-111-11-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-11ii−i−i-1111-1-1−i−iii
χ161-1-11-1-111-1-111-1-111-111-11-111-11-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii1-1ii−i−i1-1-1-111ii−i−i
χ1722222222222222-2-2-222-2-2-2-2-2-22-2222-2-222-2-200000000000000000000000000000000
χ1822222222222222-2-2-222-2-2-2-2-2-22-22-2-222-2-22200000000000000000000000000000000
χ192222222222-2-2-2-2222222-2-2-222-2-2-2000000000000000000000000220000-2-200000000
χ202222222222-2-2-2-2222222-2-2-222-2-2-2000000000000000000000000-2-200002200000000
χ212222222222-2-2-2-2-2-2-222-2222-2-2-22-2000000000000000000000000000000002-22-20000
χ222222222222-2-2-2-2-2-2-222-2222-2-2-22-200000000000000000000000000000000-22-220000
χ2322222222-2-22222222-2-22-2-22-2-2-22-2000000000000000000000000002-22-20000000000
χ2422222222-2-22222222-2-22-2-22-2-2-22-200000000000000000000000000-22-220000000000
χ2522222222-2-22222-2-2-2-2-2-222-222-2-2-2000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ2622222222-2-22222-2-2-2-2-2-222-222-2-2-200000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ2722222222-2-2-2-2-2-2222-2-2222-2-2-22-220000000000000000000000000000000000002-22-2
χ2822222222-2-2-2-2-2-2222-2-2222-2-2-22-22000000000000000000000000000000000000-22-22
χ2922222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222000000000000000022-2-222-2-20000000000000000
χ3022222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222220000000000000000-2-222-2-2220000000000000000
χ312-2-22-2-2222222-2-222-2-2-2-2-222-22-2-22000000000000000000000000002i−2i−2i2i0000000000
χ322-2-22-2-2222222-2-222-2-2-2-2-222-22-2-2200000000000000000000000000−2i2i2i−2i0000000000
χ332-2-22-2-2222222-2-2-2-22-2-222-2-22-2-2220000000022-2-2-2-222000000000000000000000000
χ342-2-22-2-2222222-2-2-2-22-2-222-2-22-2-22200000000-2-22222-2-2000000000000000000000000
χ352-2-22-2-22222-2-22222-2-2-2-22-2-2-2222-20000000000000000000000000000000000002i−2i−2i2i
χ362-2-22-2-22222-2-22222-2-2-2-22-2-2-2222-2000000000000000000000000000000000000−2i2i2i−2i
χ372-2-22-2-22222-2-222-2-22-2-22-2222-22-2-200000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ382-2-22-2-22222-2-222-2-22-2-22-2222-22-2-20000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ392-2-22-2-222-2-222-2-2-2-22222-22-2-2222-222-2-2-2-22200000000000000000000000000000000
χ402-2-22-2-222-2-222-2-2-2-22222-22-2-2222-2-2-22222-2-200000000000000000000000000000000
χ412-2-22-2-222-2-2-2-22222-222-2-22-22-2-2220000000000000000000000002-20000-2200000000
χ422-2-22-2-222-2-2-2-22222-222-2-22-22-2-222000000000000000000000000-2200002-200000000
χ432-2-22-2-222-2-2-2-222-2-222222-22-22-2-22000000000000000000000000000000002-2-220000
χ442-2-22-2-222-2-2-2-222-2-222222-22-22-2-2200000000000000000000000000000000-222-20000
χ454444-4-4-4-44-400000004-400000000000000000000000002-22-22-22-20000000000000000
χ464444-4-4-4-44-400000004-40000000000000000000000000-22-22-22-220000000000000000
χ474444-4-4-4-4-440000000-4400000000000000000000000002-2-222-2-220000000000000000
χ484444-4-4-4-4-440000000-440000000000000000000000000-222-2-222-20000000000000000
χ4944-4-44-44-4004-44-400000000000000002i2−2i2002i2−2i200000000000000000000000000000000
χ5044-4-44-44-4004-44-40000000000000000−2i22i200−2i22i200000000000000000000000000000000
χ5144-4-44-44-400-44-44000000000000002i2−2i2002i2−2i20000000000000000000000000000000000
χ5244-4-44-44-400-44-4400000000000000−2i22i200−2i22i20000000000000000000000000000000000
χ5344-4-4-44-440000004-4400-400000000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ5444-4-4-44-440000004-4400-40000000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ5544-4-4-44-44000000-44-400400000000000000002-2-222-2-22000000000000000000000000
χ5644-4-4-44-44000000-44-40040000000000000000-222-2-222-2000000000000000000000000
χ574-44-44-4-440000004-4-400400000000000000002-22-2-22-22000000000000000000000000
χ584-44-44-4-440000004-4-40040000000000000000-22-222-22-2000000000000000000000000
χ594-44-44-4-44000000-44400-400000000000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ604-44-44-4-44000000-44400-40000000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ614-44-4-444-4004-4-4400000000000000002i2−2i200−2i22i200000000000000000000000000000000
χ624-44-4-444-4004-4-440000000000000000−2i22i2002i2−2i200000000000000000000000000000000
χ634-44-4-444-400-444-4000000000000002i2−2i200−2i22i20000000000000000000000000000000000
χ644-44-4-444-400-444-400000000000000−2i22i2002i2−2i20000000000000000000000000000000000
χ654-4-4444-4-44-40000000-4400000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ664-4-4444-4-44-40000000-440000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ674-4-4444-4-4-4400000004-400000000000000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ684-4-4444-4-4-4400000004-40000000000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000

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