Finite Group Databasebeta

← Group #72310322

Character table — Group #72310322

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64
size1111222222444444448888888888161616161616161616161616161616163232323232323232323232323232323232323232
order1222222222222222222222224444224444444444444444444444444444448888
χ11111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ91111111111-1-1-11111-111-1-1-1-111-1-11111-1-1-1-1iiii−i−i−i−i11-1-111-1-1ii−i−iii−i−iii−i−i
χ101111111111-1-1-11111-111-1-1-1-111-1-11111-1-1-1-1iiii−i−i−i−i-1-111-1-111ii−i−i−i−iii−i−iii
χ111111111111-1-1-11111-111-1-1-1-111-1-11111-1-1-1-1−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii−i−iii
χ121111111111-1-1-11111-111-1-1-1-111-1-11111-1-1-1-1−i−i−i−iiiii-1-111-1-111−i−iiiii−i−iii−i−i
χ131111111111-1-1-11111-111-1-1-1-111-1-1-1-1-1-11111iiii−i−i−i−i11-1-1-1-111−i−iiiii−i−i−i−iii
χ141111111111-1-1-11111-111-1-1-1-111-1-1-1-1-1-11111iiii−i−i−i−i-1-11111-1-1−i−iii−i−iiiii−i−i
χ151111111111-1-1-11111-111-1-1-1-111-1-1-1-1-1-11111−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iiiii−i−i
χ161111111111-1-1-11111-111-1-1-1-111-1-1-1-1-1-11111−i−i−i−iiiii-1-11111-1-1ii−i−iii−i−i−i−iii
χ17222222222222222222-2-22-22-2-2-2-2-22-22-222-2-20000000000000000000000000000
χ18222222222222222222-2-22-22-2-2-2-2-2-22-22-2-2220000000000000000000000000000
χ192222222222222-2-2-2-2222-22-22-2-2-2-2000000000000000000002i−2i2i−2i000000000000
χ202222222222222-2-2-2-2222-22-22-2-2-2-200000000000000000000−2i2i−2i2i000000000000
χ212222222222222-2-2-2-22-2-2-2-2-2-2222200000000000000002i−2i2i−2i0000000000000000
χ222222222222222-2-2-2-22-2-2-2-2-2-222220000000000000000−2i2i−2i2i0000000000000000
χ232222222222-2-2-22222-2-2-2-22-22-2-2222-22-2-2-2220000000000000000000000000000
χ242222222222-2-2-22222-2-2-2-22-22-2-222-22-2222-2-20000000000000000000000000000
χ252222222222-2-2-2-2-2-2-2-2222-22-2-2-222000000000000000000002i−2i−2i2i000000000000
χ262222222222-2-2-2-2-2-2-2-2222-22-2-2-22200000000000000000000−2i2i2i−2i000000000000
χ272222222222-2-2-2-2-2-2-2-2-2-2222222-2-200000000000000002i−2i−2i2i0000000000000000
χ282222222222-2-2-2-2-2-2-2-2-2-2222222-2-20000000000000000−2i2i2i−2i0000000000000000
χ292-2-2222-2-2-2222-222-2-2-22-222-2-22-2-220000000000000000000000002i−2i2i−2i00000000
χ302-2-2222-2-2-2222-222-2-2-22-222-2-22-2-22000000000000000000000000−2i2i−2i2i00000000
χ312-2-2222-2-2-2222-222-2-2-2-222-2-22-222-2000000002i2i−2i−2i2i2i−2i−2i00000000000000000000
χ322-2-2222-2-2-2222-222-2-2-2-222-2-22-222-200000000−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ332-2-2222-2-2-2222-2-2-222-22-2-222-2-222-200000000000000000000000000002i−2i2i−2i0000
χ342-2-2222-2-2-2222-2-2-222-22-2-222-2-222-20000000000000000000000000000−2i2i−2i2i0000
χ352-2-2222-2-2-2222-2-2-222-2-22-2-2222-2-22000000000000000000000000000000002-22-2
χ362-2-2222-2-2-2222-2-2-222-2-22-2-2222-2-2200000000000000000000000000000000-22-22
χ372-2-2222-2-2-22-2-2222-2-222-2-2-2222-22-20000000000000000000000002-2-2200000000
χ382-2-2222-2-2-22-2-2222-2-222-2-2-2222-22-2000000000000000000000000-222-200000000
χ392-2-2222-2-2-22-2-2222-2-22-22-222-2-22-220000000022-2-2-2-22200000000000000000000
χ402-2-2222-2-2-22-2-2222-2-22-22-222-2-22-2200000000-2-22222-2-200000000000000000000
χ412-2-2222-2-2-22-2-22-2-22222-22-2-22-22-2200000000000000000000000000002-2-220000
χ422-2-2222-2-2-22-2-22-2-22222-22-2-22-22-220000000000000000000000000000-222-20000
χ432-2-2222-2-2-22-2-22-2-2222-2222-2-22-22-2000000000000000000000000000000002i−2i−2i2i
χ442-2-2222-2-2-22-2-22-2-2222-2222-2-22-22-200000000000000000000000000000000−2i2i2i−2i
χ454444-4-44-4-440004-44-400000000000040-400000000000000000000000000000000
χ464444-4-44-4-440004-44-4000000000000-40400000000000000000000000000000000
χ474444-4-44-4-44000-44-440000000000040-4000000000000000000000000000000000
χ484444-4-44-4-44000-44-4400000000000-404000000000000000000000000000000000
χ494-4-44-4-4-44440004-4-44000000000000000004-40000000000000000000000000000
χ504-4-44-4-4-44440004-4-4400000000000000000-440000000000000000000000000000
χ514-4-44-4-4-4444000-444-40000000000000004-4000000000000000000000000000000
χ524-4-44-4-4-4444000-444-4000000000000000-44000000000000000000000000000000
χ5388888-8-88-8-8000000000000000000000000000000000000000000000000000000
χ548888-88-8-88-8000000000000000000000000000000000000000000000000000000
χ5588-8-80000004-440000-40000000000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ5688-8-80000004-440000-4000000000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ5788-8-8000000-44-4000040000000000000000002-22-2-22-2200000000000000000000
χ5888-8-8000000-44-400004000000000000000000-22-222-22-200000000000000000000
χ598-88-80000004-4-4000040000000000000000002-2-222-2-2200000000000000000000
χ608-88-80000004-4-400004000000000000000000-222-2-222-200000000000000000000
χ618-88-8000000-4440000-40000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000
χ628-88-8000000-4440000-4000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000
χ638-8-888-88-88-8000000000000000000000000000000000000000000000000000000
χ648-8-88-8888-8-8000000000000000000000000000000000000000000000000000000

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