Finite Group Databasebeta

← Group #72312467

Character table — Group #72312467

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94
size1111222222444444444444444444448888888888888888888888888888161616161616161616161616161616161616161616161616161616163232323232323232
order1222224444222222444444888888884444444444444444888888888888222244444444444444448888888844448888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ91111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-11111-1-1-1-1-1-1-1-111-1-111-1-1
χ101111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-111-1-111
χ111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-11111111111-1-1-1-111
χ121111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111111111-1-11111-1-1
χ131111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111
χ141111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-111-1-111-1-111-1-111-1-1-1-1-1-1-1-1111111-1-111-1-1
χ151111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-11111-1-1
χ161111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11111-1-111111111-1-1-1-111-1-1-1-111
χ1711-1-11-11-11-111-1-11-11-1-1-1111111-1-1-1-1iiii−i−i−i−iii−i−iii−i−i11-1-1iiii−i−i−i−i1-11-1i−ii−i1-11-1i−ii−i11-1-1i−ii−i11-1-1i−ii−i1-11-1
χ1811-1-11-11-11-111-1-11-11-1-1-1111111-1-1-1-1iiii−i−i−i−iii−i−iii−i−i11-1-1iiii−i−i−i−i-11-11−ii−ii-11-11−ii−ii11-1-1i−ii−i11-1-1−ii−ii-11-11
χ1911-1-11-11-11-111-1-11-11-1-1-1111111-1-1-1-1iiii−i−i−i−i−i−iii−i−iii11-1-1iiii−i−i−i−i1-11-1−ii−ii1-11-1−ii−ii-1-111−ii−ii-1-111i−ii−i-11-11
χ2011-1-11-11-11-111-1-11-11-1-1-1111111-1-1-1-1iiii−i−i−i−i−i−iii−i−iii11-1-1iiii−i−i−i−i-11-11i−ii−i-11-11i−ii−i-1-111−ii−ii-1-111−ii−ii1-11-1
χ2111-1-11-11-11-111-1-11-11-1-1-1111111-1-1-1-1−i−i−i−iiiiiii−i−iii−i−i11-1-1−i−i−i−iiiii1-11-1i−ii−i1-11-1i−ii−i-1-111i−ii−i-1-111−ii−ii-11-11
χ2211-1-11-11-11-111-1-11-11-1-1-1111111-1-1-1-1−i−i−i−iiiiiii−i−iii−i−i11-1-1−i−i−i−iiiii-11-11−ii−ii-11-11−ii−ii-1-111i−ii−i-1-111i−ii−i1-11-1
χ2311-1-11-11-11-111-1-11-11-1-1-1111111-1-1-1-1−i−i−i−iiiii−i−iii−i−iii11-1-1−i−i−i−iiiii1-11-1−ii−ii1-11-1−ii−ii11-1-1−ii−ii11-1-1−ii−ii1-11-1
χ2411-1-11-11-11-111-1-11-11-1-1-1111111-1-1-1-1−i−i−i−iiiii−i−iii−i−iii11-1-1−i−i−i−iiiii-11-11i−ii−i-11-11i−ii−i11-1-1−ii−ii11-1-1i−ii−i-11-11
χ2511-1-11-11-11-111-1-11-11-1-1-111-1-1-1-11111iiii−i−i−i−iii−i−iii−i−i-1-111−i−i−i−iiiii1-1-11i−i−ii1-1-11i−i−ii11-1-1−ii−ii-1-111i−i−ii1-1-11
χ2611-1-11-11-11-111-1-11-11-1-1-111-1-1-1-11111iiii−i−i−i−iii−i−iii−i−i-1-111−i−i−i−iiiii-111-1−iii−i-111-1−iii−i11-1-1−ii−ii-1-111−iii−i-111-1
χ2711-1-11-11-11-111-1-11-11-1-1-111-1-1-1-11111iiii−i−i−i−i−i−iii−i−iii-1-111−i−i−i−iiiii1-1-11−iii−i1-1-11−iii−i-1-111i−ii−i11-1-1i−i−ii-111-1
χ2811-1-11-11-11-111-1-11-11-1-1-111-1-1-1-11111iiii−i−i−i−i−i−iii−i−iii-1-111−i−i−i−iiiii-111-1i−i−ii-111-1i−i−ii-1-111i−ii−i11-1-1−iii−i1-1-11
χ2911-1-11-11-11-111-1-11-11-1-1-111-1-1-1-11111−i−i−i−iiiiiii−i−iii−i−i-1-111iiii−i−i−i−i1-1-11i−i−ii1-1-11i−i−ii-1-111−ii−ii11-1-1−iii−i-111-1
χ3011-1-11-11-11-111-1-11-11-1-1-111-1-1-1-11111−i−i−i−iiiiiii−i−iii−i−i-1-111iiii−i−i−i−i-111-1−iii−i-111-1−iii−i-1-111−ii−ii11-1-1i−i−ii1-1-11
χ3111-1-11-11-11-111-1-11-11-1-1-111-1-1-1-11111−i−i−i−iiiii−i−iii−i−iii-1-111iiii−i−i−i−i1-1-11−iii−i1-1-11−iii−i11-1-1i−ii−i-1-111−iii−i1-1-11
χ3211-1-11-11-11-111-1-11-11-1-1-111-1-1-1-11111−i−i−i−iiiii−i−iii−i−iii-1-111iiii−i−i−i−i-111-1i−i−ii-111-1i−i−ii11-1-1i−ii−i-1-111i−i−ii-111-1
χ3322222222222-22-2-2-2-22-2-2-2222-2-222-2-200000000000000002-22-200000000000022220000-2-2-2-200000000000000000000
χ3422222222222-22-2-2-2-22-2-2-2222-2-222-2-200000000000000002-22-2000000000000-2-2-2-20000222200000000000000000000
χ3522222222222-22-2-2-2-22-2-2-22-2-222-2-2220000000000000000-22-2200000000000022-2-20000-2-22200000000000000000000
χ3622222222222-22-2-2-2-22-2-2-22-2-222-2-2220000000000000000-22-22000000000000-2-222000022-2-200000000000000000000
χ372222222222-22-2-2-222-22-2-2-222-2-222-2-20000000000000000-22-220000000022220000-2-2-2-2000000000000000000000000
χ382222222222-22-2-2-222-22-2-2-222-2-222-2-20000000000000000-22-2200000000-2-2-2-200002222000000000000000000000000
χ392222222222-22-2-2-222-22-2-2-2-2-222-2-22200000000000000002-22-20000000022-2-20000-2-222000000000000000000000000
χ402222222222-22-2-2-222-22-2-2-2-2-222-2-22200000000000000002-22-200000000-2-222000022-2-2000000000000000000000000
χ412222222222-2-2-222-2-2-2-222-222222222000000002222-2-2-2-2-2-2-2-20000000000000000000000000000-2-222000000000000
χ422222222222-2-2-222-2-2-2-222-22222222200000000-2-2-2-22222-2-2-2-2000000000000000000000000000022-2-2000000000000
χ432222222222-2-2-222-2-2-2-222-2-2-2-2-2-2-2-2-2000000002222-2-2-2-22222000000000000000000000000000022-2-2000000000000
χ442222222222-2-2-222-2-2-2-222-2-2-2-2-2-2-2-2-200000000-2-2-2-2222222220000000000000000000000000000-2-222000000000000
χ45222222-2-2-2-22-2222-22-22-2-2-200000000000000002-22-22-22-200002i2i−2i−2i2i2i−2i−2i0000000000000000000000002i−2i2i−2i00000000
χ46222222-2-2-2-22-2222-22-22-2-2-200000000000000002-22-22-22-20000−2i−2i2i2i−2i−2i2i2i000000000000000000000000−2i2i−2i2i00000000
χ47222222-2-2-2-22-2222-22-22-2-2-20000000000000000-22-22-22-2200002i2i−2i−2i2i2i−2i−2i000000000000000000000000−2i2i−2i2i00000000
χ48222222-2-2-2-22-2222-22-22-2-2-20000000000000000-22-22-22-220000−2i−2i2i2i−2i−2i2i2i0000000000000000000000002i−2i2i−2i00000000
χ49222222-2-2-2-2-22-2222-22-2-2-220000000022-2-222-2-22-22-2-22-2200000000000000000000000000002-22-20000000000000000
χ50222222-2-2-2-2-22-2222-22-2-2-220000000022-2-222-2-2-22-222-22-20000000000000000000000000000-22-220000000000000000
χ51222222-2-2-2-2-22-2222-22-2-2-2200000000-2-222-2-2222-22-2-22-220000000000000000000000000000-22-220000000000000000
χ52222222-2-2-2-2-22-2222-22-2-2-2200000000-2-222-2-222-22-222-22-200000000000000000000000000002-22-20000000000000000
χ5322-2-22-22-22-22-2-22-22-2-222-2222-2-2-2-22200000000000000002-2-220000000000002i−2i2i−2i0000−2i2i−2i2i00000000000000000000
χ5422-2-22-22-22-22-2-22-22-2-222-2222-2-2-2-22200000000000000002-2-22000000000000−2i2i−2i2i00002i−2i2i−2i00000000000000000000
χ5522-2-22-22-22-22-2-22-22-2-222-22-2-22222-2-20000000000000000-222-20000000000002i−2i−2i2i0000−2i2i2i−2i00000000000000000000
χ5622-2-22-22-22-22-2-22-22-2-222-22-2-22222-2-20000000000000000-222-2000000000000−2i2i2i−2i00002i−2i−2i2i00000000000000000000
χ5722-2-22-22-22-2-2222-2-222-22-2-222-2-2-2-2220000000000000000-222-2000000002-22-20000-22-22000000000000000000000000
χ5822-2-22-22-22-2-2222-2-222-22-2-222-2-2-2-2220000000000000000-222-200000000-22-2200002-22-2000000000000000000000000
χ5922-2-22-22-22-2-2222-2-222-22-2-2-2-22222-2-200000000000000002-2-22000000002-2-220000-222-2000000000000000000000000
χ6022-2-22-22-22-2-2222-2-222-22-2-2-2-22222-2-200000000000000002-2-2200000000-222-200002-2-22000000000000000000000000
χ6122-2-22-22-22-2-2-22-222-222-22-22222-2-2-2-2000000002i2i−2i−2i−2i−2i2i2i-2-2220000000000000000000000000000−2i2i2i−2i000000000000
χ6222-2-22-22-22-2-2-22-222-222-22-22222-2-2-2-200000000−2i−2i2i2i2i2i−2i−2i-2-22200000000000000000000000000002i−2i−2i2i000000000000
χ6322-2-22-22-22-2-2-22-222-222-22-2-2-2-2-22222000000002i2i−2i−2i−2i−2i2i2i22-2-200000000000000000000000000002i−2i−2i2i000000000000
χ6422-2-22-22-22-2-2-22-222-222-22-2-2-2-2-2222200000000−2i−2i2i2i2i2i−2i−2i22-2-20000000000000000000000000000−2i2i2i−2i000000000000
χ6522-2-22-2-22-222-2-2-22222-22-2-200000000000000002i−2i−2i2i2i−2i−2i2i000022-2-2-2-222000000000000000000000000−2i2i2i−2i00000000
χ6622-2-22-2-22-222-2-2-22222-22-2-200000000000000002i−2i−2i2i2i−2i−2i2i0000-2-22222-2-20000000000000000000000002i−2i−2i2i00000000
χ6722-2-22-2-22-222-2-2-22222-22-2-20000000000000000−2i2i2i−2i−2i2i2i−2i000022-2-2-2-2220000000000000000000000002i−2i−2i2i00000000
χ6822-2-22-2-22-222-2-2-22222-22-2-20000000000000000−2i2i2i−2i−2i2i2i−2i0000-2-22222-2-2000000000000000000000000−2i2i2i−2i00000000
χ6922-2-22-2-22-22-222-22-2-2-222-22000000002i2i−2i−2i−2i−2i2i2i2i−2i−2i2i−2i2i2i−2i00000000000000000000000000002-2-220000000000000000
χ7022-2-22-2-22-22-222-22-2-2-222-22000000002i2i−2i−2i−2i−2i2i2i−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000-222-20000000000000000
χ7122-2-22-2-22-22-222-22-2-2-222-2200000000−2i−2i2i2i2i2i−2i−2i2i−2i−2i2i−2i2i2i−2i0000000000000000000000000000-222-20000000000000000
χ7222-2-22-2-22-22-222-22-2-2-222-2200000000−2i−2i2i2i2i2i−2i−2i−2i2i2i−2i2i−2i−2i2i00000000000000000000000000002-2-220000000000000000
χ73444444-4-4-4-4444-4-44-4-4-444-4000000000000000000000000000000000000000000000000000000000000000000000000
χ74444444-4-4-4-4-4-4-4-4-4-4444444000000000000000000000000000000000000000000000000000000000000000000000000
χ754444-4-444-4-4000000000000004i−4i004i−4i2-22-22-22-20000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000
χ764444-4-444-4-4000000000000004i−4i004i−4i-22-22-22-22000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000
χ774444-4-444-4-400000000000000−4i4i00−4i4i2-22-22-22-2000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000
χ784444-4-444-4-400000000000000−4i4i00−4i4i-22-22-22-220000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000
χ794444-4-4-4-4440000000000004-4004-4002-2-222-2-220000000000002-2-222-2-22000000000000000000000000000000000000
χ804444-4-4-4-4440000000000004-4004-400-222-2-222-2000000000000-222-2-222-2000000000000000000000000000000000000
χ814444-4-4-4-444000000000000-4400-44002-2-222-2-22000000000000-222-2-222-2000000000000000000000000000000000000
χ824444-4-4-4-444000000000000-4400-4400-222-2-222-20000000000002-2-222-2-22000000000000000000000000000000000000
χ8344-4-44-4-44-4444-44-4-4-444-44-4000000000000000000000000000000000000000000000000000000000000000000000000
χ8444-4-44-4-44-44-4-444-444-4-4-444000000000000000000000000000000000000000000000000000000000000000000000000
χ8544-4-4-444-4-44000000000000004i−4i00−4i4i2i−2i2i−2i−2i2i−2i2i000000000000-22-222-22-2000000000000000000000000000000000000
χ8644-4-4-444-4-44000000000000004i−4i00−4i4i−2i2i−2i2i2i−2i2i−2i0000000000002-22-2-22-22000000000000000000000000000000000000
χ8744-4-4-444-4-4400000000000000−4i4i004i−4i2i−2i2i−2i−2i2i−2i2i0000000000002-22-2-22-22000000000000000000000000000000000000
χ8844-4-4-444-4-4400000000000000−4i4i004i−4i−2i2i−2i2i2i−2i2i−2i000000000000-22-222-22-2000000000000000000000000000000000000
χ8944-4-4-44-444-40000000000004-400-44002i−2i−2i2i−2i2i2i−2i0000000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000000000000000
χ9044-4-4-44-444-40000000000004-400-4400−2i2i2i−2i2i−2i−2i2i000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000000000
χ9144-4-4-44-444-4000000000000-44004-4002i−2i−2i2i−2i2i2i−2i000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000000000
χ9244-4-4-44-444-4000000000000-44004-400−2i2i2i−2i2i−2i−2i2i0000000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000000000000000
χ9316-1616-16000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9416-16-1616000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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