Finite Group Databasebeta

← Group #72312218

Character table — Group #72312218

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70
size11112222224444444444448888888816161616161616161616161616161616161616161616161632323232323232323232323232323232
order1222222222222222224444222222442244444444444444444444444444444488888888
χ11111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ5111111111111111111111111111111-1-11111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ6111111111111111111111111111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111
χ91111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111-1-1-1-111-1-1iiii−i−i−i−iii−i−iii−i−i11-1-1ii−i−i
χ101111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111-1-1-1-111-1-1−i−i−i−iiiii−i−iii−i−iii11-1-1−i−iii
χ111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-1-1-111iiii−i−i−i−iii−i−i−i−iii-1-111−i−iii
χ121111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-1-1-111−i−i−i−iiiii−i−iiiii−i−i-1-111ii−i−i
χ131111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1111111-1-1iiii−i−i−i−i−i−iii−i−iii-1-111ii−i−i
χ141111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1111111-1-1−i−i−i−iiiiiii−i−iii−i−i-1-111−i−iii
χ151111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-111iiii−i−i−i−i−i−iiiii−i−i11-1-1−i−iii
χ161111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-111−i−i−i−iiiiiii−i−i−i−iii11-1-1ii−i−i
χ17222222222222222222-2-2-2-222-2-2-2-2-2-20000000000000000000000002-22-2000000000000
χ18222222222222222222-2-2-2-222-2-2-2-2-2-2000000000000000000000000-22-22000000000000
χ192222222222222-2-22-2-22222-2-2-2-2-2-2220022-2-2000000-2-222000000000000000000000000
χ202222222222222-2-22-2-22222-2-2-2-2-2-22200-2-22200000022-2-2000000000000000000000000
χ212222222222222-2-22-2-2-2-2-2-2-2-22222-2-200000000000000000000000000002i−2i2i−2i00000000
χ222222222222222-2-22-2-2-2-2-2-2-2-22222-2-20000000000000000000000000000−2i2i−2i2i00000000
χ232222222222-2-2-222-2222222-2-2-2-222-2-2002222000000-2-2-2-2000000000000000000000000
χ242222222222-2-2-222-2222222-2-2-2-222-2-200-2-2-2-20000002222000000000000000000000000
χ252222222222-2-2-222-222-2-2-2-2-2-222-2-22200000000000000000000000000002-2-2200000000
χ262222222222-2-2-222-222-2-2-2-2-2-222-2-2220000000000000000000000000000-222-200000000
χ272222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-222220000000000000000000000002i−2i−2i2i000000000000
χ282222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-22222000000000000000000000000−2i2i2i−2i000000000000
χ292-2-2222-2-22-222-222-2-2-222-2-22-22-22-22-22-200002-222-2-20000000000000000000000000000
χ302-2-2222-2-22-222-222-2-2-222-2-22-22-22-22-2-220000-22-2-2220000000000000000000000000000
χ312-2-2222-2-22-222-222-2-2-2-2-2222-2-22-22-2200000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ322-2-2222-2-22-222-222-2-2-2-2-2222-2-22-22-220000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ332-2-2222-2-22-222-2-2-2-22222-2-2-22-22-222-2000000000000000000000000000000002i−2i2i−2i0000
χ342-2-2222-2-22-222-2-2-2-22222-2-2-22-22-222-200000000000000000000000000000000−2i2i−2i2i0000
χ352-2-2222-2-22-222-2-2-2-222-2-222-222-22-2-220000000000000000000000000000000000002-22-2
χ362-2-2222-2-22-222-2-2-2-222-2-222-222-22-2-22000000000000000000000000000000000000-22-22
χ372-2-2222-2-22-2-2-22222-2-222-2-2-22-222-2-22000000000000000000000000000000002i−2i−2i2i0000
χ382-2-2222-2-22-2-2-22222-2-222-2-2-22-222-2-2200000000000000000000000000000000−2i2i2i−2i0000
χ392-2-2222-2-22-2-2-22222-2-2-2-222-222-2-222-20000000000000000000000000000000000002i−2i−2i2i
χ402-2-2222-2-22-2-2-22222-2-2-2-222-222-2-222-2000000000000000000000000000000000000−2i2i2i−2i
χ412-2-2222-2-22-2-2-22-2-222222-2-22-22-2-22-222-200002-2-2-2220000000000000000000000000000
χ422-2-2222-2-22-2-2-22-2-222222-2-22-22-2-22-22-220000-2222-2-20000000000000000000000000000
χ432-2-2222-2-22-2-2-22-2-2222-2-2222-2-222-22-2000000000000000022-2-2-2-2220000000000000000
χ442-2-2222-2-22-2-2-22-2-2222-2-2222-2-222-22-20000000000000000-2-22222-2-20000000000000000
χ4544444-4-4-4-44000000004-44-40000000000004-40000000000000000000000000000000000
χ4644444-4-4-4-44000000004-44-4000000000000-440000000000000000000000000000000000
χ4744444-4-4-4-4400000000-44-4400000000004-4000000000000000000000000000000000000
χ4844444-4-4-4-4400000000-44-440000000000-44000000000000000000000000000000000000
χ494444-4-44-44-40004-404-4000000000000220000-2-22-22-20000000000000000000000000000
χ504444-4-44-44-40004-404-4000000000000-2-2000022-22-220000000000000000000000000000
χ514444-4-44-44-4000-440-44000000000000220000-2-2-22-220000000000000000000000000000
χ524444-4-44-44-4000-440-44000000000000-2-20000222-22-20000000000000000000000000000
χ534-4-444-444-4-4000000004-4-4400000000000000000000004i−4i000000000000000000000000
χ544-4-444-444-4-4000000004-4-440000000000000000000000−4i4i000000000000000000000000
χ554-4-444-444-4-400000000-444-4000000000000000000004i−4i00000000000000000000000000
χ564-4-444-444-4-400000000-444-400000000000000000000−4i4i00000000000000000000000000
χ574-4-44-4-4-44440004-40-440000000000002-20000-222-2-220000000000000000000000000000
χ584-4-44-4-4-44440004-40-44000000000000-2200002-2-222-20000000000000000000000000000
χ594-4-44-4-4-4444000-4404-40000000000002-20000-22-222-20000000000000000000000000000
χ604-4-44-4-4-4444000-4404-4000000000000-2200002-22-2-220000000000000000000000000000
χ618888-88-88-8-8000000000000000000000000000000000000000000000000000000000000
χ6288-8-80000004-4400-40000000000000000000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ6388-8-80000004-4400-4000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ6488-8-8000000-44-40040000000000000000000000000000002-22-2-22-220000000000000000
χ6588-8-8000000-44-4004000000000000000000000000000000-22-222-22-20000000000000000
χ668-88-80000004-4-40040000000000000000000000000000002-2-222-2-220000000000000000
χ678-88-80000004-4-4004000000000000000000000000000000-222-2-222-20000000000000000
χ688-88-8000000-44400-40000000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ698-88-8000000-44400-4000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ708-8-88-888-8-88000000000000000000000000000000000000000000000000000000000000

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