Finite Group Databasebeta

← Group #72318093

Character table — Group #72318093

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70
size111122222244444444444488888888888888881616161616161616161616163232323232323232323232323232323232323232
order1222222222222244444444222244444444444422224444444444444444888888888888
χ11111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111iiii−i−i−i−i-1-1-1-1iiii−i−i−i−i
χ6111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111−i−i−i−iiiii-1-1-1-1−i−i−i−iiiii
χ7111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1iiii−i−i−i−i1111−i−i−i−iiiii
χ8111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1−i−i−i−iiiii1111iiii−i−i−i−i
χ91111111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-111-1-111-1-1-1-111-1-111-1-111-1-111-1-111-1-1
χ101111111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-111-1-111-1-1-1-1-1-111-1-11111-1-1-1-111-1-111
χ111111111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111-1-111-1-111
χ121111111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-11111-1-111-1-1
χ131111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-111-1-1-1-1ii−i−i−i−iii-1-111ii−i−i−i−iii
χ141111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-111-1-1-1-1−i−iiiii−i−i-1-111−i−iiiii−i−i
χ151111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-11111ii−i−i−i−iii11-1-1−i−iiiii−i−i
χ161111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-11111−i−iiiii−i−i11-1-1ii−i−i−i−iii
χ172222222222222222222222-2-2-2-2-2-2-2-222222222-2-200-2-200000000000000000000000000
χ18222222222222222222-2-2-2-22222-2-2-2-222-2-2-2-2-2-22200-2-200000000000000000000000000
χ192222222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-222-2-2-2-222002200000000000000000000000000
χ202222222222-2-2-2-22222-2-2-2-22222-2-2-2-2-2-2-2-22222-2-2002200000000000000000000000000
χ2122222-2-2-22-200002-22-222222-22-222-2-200-2-200000000000000000000000000002-2002-200
χ2222222-2-2-22-200002-22-222222-22-222-2-200-2-20000000000000000000000000000-2200-2200
χ2322222-2-2-22-200002-22-22222-22-22-2-22200-2-20000000000000000000000000000002-2002-2
χ2422222-2-2-22-200002-22-22222-22-22-2-22200-2-2000000000000000000000000000000-2200-22
χ2522222-2-2-22-200002-22-2-2-2-2-22-22-2-2-22200220000000000000000000000000000002i−2i00−2i2i
χ2622222-2-2-22-200002-22-2-2-2-2-22-22-2-2-2220022000000000000000000000000000000−2i2i002i−2i
χ2722222-2-2-22-200002-22-2-2-2-2-2-22-2222-2-2002200000000000000000000000000002i−2i00−2i2i00
χ2822222-2-2-22-200002-22-2-2-2-2-2-22-2222-2-200220000000000000000000000000000−2i2i002i−2i00
χ292-2-22-222-22-20000-222-222-2-222-2-22-22-2002-20000000000000000002i−2i002i−2i000000000000
χ302-2-22-222-22-20000-222-222-2-222-2-22-22-2002-2000000000000000000−2i2i00−2i2i000000000000
χ312-2-22-222-22-20000-222-222-2-2-2-222-22-22002-200000000000000002-2002-200000000000000
χ322-2-22-222-22-20000-222-222-2-2-2-222-22-22002-20000000000000000-2200-2200000000000000
χ332-2-22-222-22-20000-222-2-2-22222-2-2-22-2200-2200000000000000002i−2i00−2i2i00000000000000
χ342-2-22-222-22-20000-222-2-2-22222-2-2-22-2200-220000000000000000−2i2i002i−2i00000000000000
χ352-2-22-222-22-20000-222-2-2-222-2-2222-22-200-220000000000000000002-200-22000000000000
χ362-2-22-222-22-20000-222-2-2-222-2-2222-22-200-22000000000000000000-22002-2000000000000
χ372-2-22-2-2-22220000-2-22222-2-22-2-222-2-2200-2200000000000022-2-200000000002-200000000
χ382-2-22-2-2-22220000-2-22222-2-22-2-222-2-2200-22000000000000-2-2220000000000-2200000000
χ392-2-22-2-2-22220000-2-22222-2-2-222-2-222-200-220000002-2002-20000000000002-20000000000
χ402-2-22-2-2-22220000-2-22222-2-2-222-2-222-200-22000000-2200-22000000000000-220000000000
χ412-2-22-2-2-22220000-2-222-2-2222-2-22-222-2002-20000002-2002-2000000000000-220000000000
χ422-2-22-2-2-22220000-2-222-2-2222-2-22-222-2002-2000000-2200-220000000000002-20000000000
χ432-2-22-2-2-22220000-2-222-2-222-222-22-2-22002-200000000000022-2-20000000000-2200000000
χ442-2-22-2-2-22220000-2-222-2-222-222-22-2-22002-2000000000000-2-22200000000002-200000000
χ4544444444444444-4-4-4-4000000000000-4-400000000000000000000000000000000000000
χ464444444444-4-4-4-4-4-4-4-40000000000004400000000000000000000000000000000000000
χ4744444-4-4-44-40000-44-44000000000000000044-4-400000000000000000000000000000000
χ4844444-4-4-44-40000-44-440000000000000000-4-44400000000000000000000000000000000
χ494444-44-4-4-44000000000000000000004-4000000002200-2-22-22-200000000000000000000
χ504444-44-4-4-44000000000000000000004-400000000-2-20022-22-2200000000000000000000
χ514444-44-4-4-4400000000000000000000-44000000002200-2-2-22-2200000000000000000000
χ524444-44-4-4-4400000000000000000000-4400000000-2-200222-22-200000000000000000000
χ534-4-444-44-4-4444-4-4000000000000000000000000002-200-222-2-2200000000000000000000
χ544-4-444-44-4-4444-4-400000000000000000000000000-22002-2-222-200000000000000000000
χ554-4-444-44-4-44-4-444000000000000000000000000002-200-22-222-200000000000000000000
χ564-4-444-44-4-44-4-44400000000000000000000000000-22002-22-2-2200000000000000000000
χ574-4-44-444-44-400004-4-44000000000000000000004-4000000000000000000000000000000
χ584-4-44-444-44-400004-4-4400000000000000000000-44000000000000000000000000000000
χ594-4-44-4-4-4444000044-4-40000000000000000000000004-400000000000000000000000000
χ604-4-44-4-4-4444000044-4-4000000000000000000000000-4400000000000000000000000000
χ618888-8-888-8-8000000000000000000000000000000000000000000000000000000000000
χ6288-8-80000004-44-400004i−4i4i−4i000000000000004i−4i00000000000000000000000000000000
χ6388-8-80000004-44-40000−4i4i−4i4i00000000000000−4i4i00000000000000000000000000000000
χ6488-8-8000000-44-4400004i−4i4i−4i00000000000000−4i4i00000000000000000000000000000000
χ6588-8-8000000-44-440000−4i4i−4i4i000000000000004i−4i00000000000000000000000000000000
χ668-88-80000004-4-4400004i−4i−4i4i0000000000004i−4i0000000000000000000000000000000000
χ678-88-80000004-4-440000−4i4i4i−4i000000000000−4i4i0000000000000000000000000000000000
χ688-88-8000000-444-400004i−4i−4i4i000000000000−4i4i0000000000000000000000000000000000
χ698-88-8000000-444-40000−4i4i4i−4i0000000000004i−4i0000000000000000000000000000000000
χ708-8-8888-88-8-8000000000000000000000000000000000000000000000000000000000000

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