Finite Group Databasebeta

← Group #72218521

Character table — Group #72218521

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76
size1111222222444444444444444488888888888888161616161616161616161616161616161616161632323232323232323232323232323232
order1222222222222222222222222222222222224444224444444444444444444444444444444444
χ11111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-11111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111111111111-1-1-1-1-1-1-1-111111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ91-1-111-1-111-1111111-1-1-1-111-1-1-1-111111-1-1-1-1-111-1-11-1ii−i−i1-111-1-111-1-1ii−i−i11-1-1ii−i−iii−i−iii−i−i
χ101-1-111-1-111-1111111-1-1-1-111-1-1-1-111111-1-1-1-1-111-1-11-1−i−iii1-111-1-111-1-1−i−iii11-1-1−i−iii−i−iii−i−iii
χ111-1-111-1-111-1111111-1-1-1-111-1-1-1-111111-1-1-1-1-111-1-1-11ii−i−i-1111-1-1-1-111ii−i−i-1-111ii−i−i−i−iii−i−iii
χ121-1-111-1-111-1111111-1-1-1-111-1-1-1-111111-1-1-1-1-111-1-1-11−i−iii-1111-1-1-1-111−i−iii-1-111−i−iiiii−i−iii−i−i
χ131-1-111-1-111-1111111-1-1-1-111-1-1-1-11-1-1-1-11111-111-1-11-1ii−i−i1-1-1-11111-1-1ii−i−i-1-111−i−iiiii−i−i−i−iii
χ141-1-111-1-111-1111111-1-1-1-111-1-1-1-11-1-1-1-11111-111-1-11-1−i−iii1-1-1-11111-1-1−i−iii-1-111ii−i−i−i−iiiii−i−i
χ151-1-111-1-111-1111111-1-1-1-111-1-1-1-11-1-1-1-11111-111-1-1-11ii−i−i-11-1-111-1-111ii−i−i11-1-1−i−iii−i−iiiii−i−i
χ161-1-111-1-111-1111111-1-1-1-111-1-1-1-11-1-1-1-11111-111-1-1-11−i−iii-11-1-111-1-111−i−iii11-1-1ii−i−iii−i−i−i−iii
χ1722222222222222-2-222222222-2-2-222222222-2-2-2-2-200000000-2-2-2-2000000000000000000000000
χ1822222222222222-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000002222000000000000000000000000
χ19222222222222-2-22222-2-2-2-2-2-2222000000002-2-2-2-200000000000000000000000000002-22-20000
χ20222222222222-2-22222-2-2-2-2-2-2222000000002-2-2-2-20000000000000000000000000000-22-220000
χ21222222222222-2-2-2-222-2-2-2-2-2-2-2-2-200000000-22222000000000000000000000000000000002i−2i2i−2i
χ22222222222222-2-2-2-222-2-2-2-2-2-2-2-2-200000000-2222200000000000000000000000000000000−2i2i−2i2i
χ232222222222-2-22222-2-2-2-2-2-22222-200000000-22-22-20022220000000000-2-2-2-20000000000000000
χ242222222222-2-22222-2-2-2-2-2-22222-200000000-22-22-200-2-2-2-2000000000022220000000000000000
χ252222222222-2-222-2-2-2-2-2-2-2-222-2-22000000002-22-220000000000000000000000002-22-200000000
χ262222222222-2-222-2-2-2-2-2-2-2-222-2-22000000002-22-22000000000000000000000000-22-2200000000
χ272222222222-2-2-2-222-2-22222-2-222-200000000-2-22-22220000220000-2-2-2-200000000000000000000
χ282222222222-2-2-2-222-2-22222-2-222-200000000-2-22-22-2-20000-2-20000222200000000000000000000
χ292222222222-2-2-2-2-2-2-2-22222-2-2-2-220000000022-22-2000000000000000000002-22-2000000000000
χ302222222222-2-2-2-2-2-2-2-22222-2-2-2-220000000022-22-200000000000000000000-22-22000000000000
χ312-2-222-2-222-22222-2-2-2-2-2-222-2-222-22222-2-2-2-22-2-22200000000-2-222000000000000000000000000
χ322-2-222-2-222-22222-2-2-2-2-2-222-2-222-2-2-2-2-222222-2-2220000000022-2-2000000000000000000000000
χ332-2-222-2-222-222-2-222-2-222-2-222-2-2200000000-2-2-22200000000000000000000000000002i−2i−2i2i0000
χ342-2-222-2-222-222-2-222-2-222-2-222-2-2200000000-2-2-2220000000000000000000000000000−2i2i2i−2i0000
χ352-2-222-2-222-222-2-2-2-2-2-222-2-22222-200000000222-2-2000000000000000000000000000000002-2-22
χ362-2-222-2-222-222-2-2-2-2-2-222-2-22222-200000000222-2-200000000000000000000000000000000-222-2
χ372-2-222-2-222-2-2-222222222-2-2-2-2-2-2-20000000022-2-22002i2i−2i−2i0000000000−2i−2i2i2i0000000000000000
χ382-2-222-2-222-2-2-222222222-2-2-2-2-2-2-20000000022-2-2200−2i−2i2i2i00000000002i2i−2i−2i0000000000000000
χ392-2-222-2-222-2-2-222-2-22222-2-2-2-222200000000-2-222-20000000000000000000000002i−2i−2i2i00000000
χ402-2-222-2-222-2-2-222-2-22222-2-2-2-222200000000-2-222-2000000000000000000000000−2i2i2i−2i00000000
χ412-2-222-2-222-2-2-2-2-22222-2-22222-2-2-2000000002-222-22-200002-20000-2-22200000000000000000000
χ422-2-222-2-222-2-2-2-2-22222-2-22222-2-2-2000000002-222-2-220000-22000022-2-200000000000000000000
χ432-2-222-2-222-2-2-2-2-2-2-222-2-2222222200000000-22-2-22000000000000000000002-2-22000000000000
χ442-2-222-2-222-2-2-2-2-2-2-222-2-2222222200000000-22-2-2200000000000000000000-222-2000000000000
χ4544444-4-4-4-44000000004-44-4000000000000000000002-22-200000000002-22-20000000000000000
χ4644444-4-4-4-44000000004-44-400000000000000000000-22-220000000000-22-220000000000000000
χ4744444-4-4-4-4400000000-44-44000000000000000000002-22-20000000000-22-220000000000000000
χ4844444-4-4-4-4400000000-44-4400000000000000000000-22-2200000000002-22-20000000000000000
χ494444-44-44-4-400004-4000000004-4022-2-222-2-200000000000002-22-2000000000000000000000000
χ504444-44-44-4-400004-4000000004-40-2-222-2-2220000000000000-22-22000000000000000000000000
χ514444-44-44-4-40000-4400000000-44022-2-222-2-20000000000000-22-22000000000000000000000000
χ524444-44-44-4-40000-4400000000-440-2-222-2-22200000000000002-22-2000000000000000000000000
χ534444-4-44-44-4004-4000000004-40000000000000000220000-2-200002-22-200000000000000000000
χ544444-4-44-44-4004-4000000004-40000000000000000-2-20000220000-22-2200000000000000000000
χ554444-4-44-44-400-4400000000-440000000000000000220000-2-20000-22-2200000000000000000000
χ564444-4-44-44-400-4400000000-440000000000000000-2-200002200002-22-200000000000000000000
χ574-4-44444-4-4-4000000004-4-44000000000000000000002i−2i−2i2i0000000000−2i2i2i−2i0000000000000000
χ584-4-44444-4-4-4000000004-4-4400000000000000000000−2i2i2i−2i00000000002i−2i−2i2i0000000000000000
χ594-4-44444-4-4-400000000-444-4000000000000000000002i−2i−2i2i00000000002i−2i−2i2i0000000000000000
χ604-4-44444-4-4-400000000-444-400000000000000000000−2i2i2i−2i0000000000−2i2i2i−2i0000000000000000
χ614-4-44-44-4-444004-400000000-4400000000000000002-20000-2200002-2-2200000000000000000000
χ624-4-44-44-4-444004-400000000-440000000000000000-2200002-20000-222-200000000000000000000
χ634-4-44-44-4-44400-44000000004-400000000000000002-20000-220000-222-200000000000000000000
χ644-4-44-44-4-44400-44000000004-40000000000000000-2200002-200002-2-2200000000000000000000
χ654-4-44-4-444-4400004-400000000-44022-2-2-2-22200000000000002-2-22000000000000000000000000
χ664-4-44-4-444-4400004-400000000-440-2-22222-2-20000000000000-222-2000000000000000000000000
χ674-4-44-4-444-440000-44000000004-4022-2-2-2-2220000000000000-222-2000000000000000000000000
χ684-4-44-4-444-440000-44000000004-40-2-22222-2-200000000000002-2-22000000000000000000000000
χ6988-8-80000004-400004-4000000000004-4004-400000000000000000000000000000000000000000
χ7088-8-80000004-400004-400000000000-4400-4400000000000000000000000000000000000000000
χ7188-8-8000000-440000-440000000004-4004-40000000000000000000000000000000000000000000
χ7288-8-8000000-440000-44000000000-4400-440000000000000000000000000000000000000000000
χ738-88-80000004-40000-44000000000004-400-4400000000000000000000000000000000000000000
χ748-88-80000004-40000-4400000000000-44004-400000000000000000000000000000000000000000
χ758-88-8000000-4400004-40000000004-400-440000000000000000000000000000000000000000000
χ768-88-8000000-4400004-4000000000-44004-40000000000000000000000000000000000000000000

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