Finite Group Databasebeta

← Group #72309515

Character table — Group #72309515

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64
size111122222244448888888888881616161616161616161616161616161616161616323232323232323232323232323232323232
order1222222222222222222222444422244444444444444444444444444444448888
χ11111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111-1-111-1-1-1-11-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111-1-111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111-11-1-1-111-1-1-11-111111111-1-111-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111111111-11-1-1-111-1-1-11-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111
χ711111111111111111111111111-1-11-1-1-1-111-1-1111111111-1-1-1-111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111-1-11-1-1-1-111-1-11-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ91111111111-1-1-1-11111-1-1-1-111-1-1111111111111iiii−i−i−i−i-1-1-1-1-1-1ii−i−iii−i−iii−i−i
χ101111111111-1-1-1-11111-1-1-1-111-1-1111111111111−i−i−i−iiiii-1-1-1-1-1-1−i−iii−i−iii−i−iii
χ111111111111-1-1-1-11111-1-1-1-111-1-11-1-111-1-1-1-11-1-1iiii−i−i−i−i-1-11111ii−i−i−i−iii−i−iii
χ121111111111-1-1-1-11111-1-1-1-111-1-11-1-111-1-1-1-11-1-1−i−i−i−iiiii-1-11111−i−iiiii−i−iii−i−i
χ131111111111-1-1-1-11111-1-1-1-111-1-1-11-1-1-111-1-1-11-1iiii−i−i−i−i11-1-111−i−iiiii−i−i−i−iii
χ141111111111-1-1-1-11111-1-1-1-111-1-1-11-1-1-111-1-1-11-1−i−i−i−iiiii11-1-111ii−i−i−i−iiiii−i−i
χ151111111111-1-1-1-11111-1-1-1-111-1-1-1-11-1-1-1-111-1-11iiii−i−i−i−i1111-1-1−i−iii−i−iiiii−i−i
χ161111111111-1-1-1-11111-1-1-1-111-1-1-1-11-1-1-1-111-1-11−i−i−i−iiiii1111-1-1ii−i−iii−i−i−i−iii
χ172222222222222222-2-22-22-2-2-2-2-202000-2-20002000000000002-200000000000000
χ182222222222222222-2-22-22-2-2-2-2-20-200022000-200000000000-2200000000000000
χ1922222222222222-2-222-22-22-2-2-2-2200-2-20000200000000002-20000000000000000
χ2022222222222222-2-222-22-22-2-2-2-2-200220000-20000000000-220000000000000000
χ2122222222222222-2-2-2-2-2-2-2-222220020000-2-20020000000000002-2000000000000
χ2222222222222222-2-2-2-2-2-2-2-2222200-200002200-2000000000000-22000000000000
χ232222222222-2-2-2-222-2-2-22-22-2-22202000-2-2000200000000000-2200000000000000
χ242222222222-2-2-2-222-2-2-22-22-2-2220-200022000-2000000000002-200000000000000
χ252222222222-2-2-2-2-2-2222-22-2-2-222200-2-2000020000000000-220000000000000000
χ262222222222-2-2-2-2-2-2222-22-2-2-222-200220000-200000000002-20000000000000000
χ272222222222-2-2-2-2-2-2-2-2222222-2-20020000-2-2002000000000000-22000000000000
χ282222222222-2-2-2-2-2-2-2-2222222-2-200-200002200-20000000000002-2000000000000
χ29444444-4-4-4-40000000000004-40000000004-400000000000000000000000000000
χ30444444-4-4-4-40000000000004-4000000000-4400000000000000000000000000000
χ31444444-4-4-4-4000000000000-440000400000000-400000000000000000000000000
χ32444444-4-4-4-4000000000000-440000-400000000400000000000000000000000000
χ334444-4-444-4-40000004-4000000000004-4000000000000000000000000000000000
χ344444-4-444-4-40000004-400000000000-44000000000000000000000000000000000
χ354444-4-444-4-4000000-4400000000400000000-40000000000000000000000000000
χ364444-4-444-4-4000000-4400000000-40000000040000000000000000000000000000
χ374444-4-4-4-44400004-40000000000000004-40000000000000000000000000000000
χ384444-4-4-4-44400004-4000000000000000-440000000000000000000000000000000
χ394444-4-4-4-4440000-4400000000000400000000-4000000000000000000000000000
χ404444-4-4-4-4440000-4400000000000-4000000004000000000000000000000000000
χ414-4-444-44-44-4000000000000004-400000000000000000000000000000000002i−2i2i−2i
χ424-4-444-44-44-4000000000000004-40000000000000000000000000000000000−2i2i−2i2i
χ434-4-444-44-44-400000000000000-4400000000000000000000000000000000002-2-22
χ444-4-444-44-44-400000000000000-440000000000000000000000000000000000-222-2
χ454-4-444-4-44-4444-4-40000000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000000000
χ464-4-444-4-44-4444-4-4000000000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000000000
χ474-4-444-4-44-44-4-44400000000000000000000000022-2-2-2-222000000000000000000
χ484-4-444-4-44-44-4-444000000000000000000000000-2-22222-2-2000000000000000000
χ494-4-44-444-4-440000000040-4000000000000000000000000000000000002i−2i2i−2i0000
χ504-4-44-444-4-440000000040-400000000000000000000000000000000000−2i2i−2i2i0000
χ514-4-44-444-4-4400000000-404000000000000000000000000000000000002-2-220000
χ524-4-44-444-4-4400000000-40400000000000000000000000000000000000-222-20000
χ534-4-44-44-444-400000000040-40000000000000000000000000000002i−2i2i−2i00000000
χ544-4-44-44-444-400000000040-4000000000000000000000000000000−2i2i−2i2i00000000
χ554-4-44-44-444-4000000000-4040000000000000000000000000000002-2-2200000000
χ564-4-44-44-444-4000000000-404000000000000000000000000000000-222-200000000
χ5788-8-80000004-44-40000000000000000000000002i−2i2i−2i2i−2i2i−2i000000000000000000
χ5888-8-80000004-44-4000000000000000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000
χ5988-8-8000000-44-440000000000000000000000002-22-2-22-22000000000000000000
χ6088-8-8000000-44-44000000000000000000000000-22-222-22-2000000000000000000
χ618-88-80000004-4-440000000000000000000000002-2-222-2-22000000000000000000
χ628-88-80000004-4-44000000000000000000000000-222-2-222-2000000000000000000
χ638-88-8000000-444-40000000000000000000000002i−2i−2i2i−2i2i2i−2i000000000000000000
χ648-88-8000000-444-4000000000000000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000

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