Finite Group Databasebeta

← Group #72253837

Character table — Group #72253837

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11222224444444444444448888888888888888888881616161616161616161616161616161616161616162424242424242424242424242424242432323232323296969696
order1223446222224446661212121222222444444666666661212246666688121212121212121224242424222244444444444448121224244488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ31111111111111111111111111111111111111111111-1-1111-1-1-1-111-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111-1-1111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-11-1-1-1-1-1111111-1-111111-1-111111-111-1-1-1-11111111-11-1-1-11111-1-1-1-1-1-1-1-1-1-11-11-1
χ6111111111111111111111111-1-1-11-1-1-1-1-1111111-1-111111-1-111111-111-1-1-1-11111-1-1-11-1111-1-1-1-11111-1-1-1-1-1-1-11-11
χ7111111111111111111111111-1-1-11-1-1-1-1-1111111-1-111-1-11-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1111-11-1-1-11111-1-1-1-1111111-11-11
χ8111111111111111111111111-1-1-11-1-1-1-1-1111111-1-111-1-11-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-1-1-111111111111-11-1
χ91111111-1-11111111111111-1-111-1-1-111-1-111-1-1-1-1-1-11111-11111-1-1-1-11111-1-1-1-1-1-111-11-11-1-111-1-111-1-1-11-1-111-1-111
χ101111111-1-11111111111111-1-111-1-1-111-1-111-1-1-1-1-1-11111-11111-1-1-1-11111-1-1-1-1-1-1-1-11-11-111-1-111-1-111-11-1-11111-1-1
χ111111111-1-11111111111111-1-111-1-1-111-1-111-1-1-1-1-1-111-1-1-111-1-111-1-1-1-111-1-1111111-11-11-1-111-1-111-1-11-111-1-111-1-1
χ121111111-1-11111111111111-1-111-1-1-111-1-111-1-1-1-1-1-111-1-1-111-1-111-1-1-1-111-1-11111-1-11-11-111-1-111-1-1111-111-1-1-1-111
χ131111111-1-11111111111111-1-1-1-11-11-1-11111-1-1-1-1111111-1-1-111-1-1-1111-1-111-1-1-1-111-1-1-1-11111-1-1-1-1111-111-1-1-111-1
χ141111111-1-11111111111111-1-1-1-11-11-1-11111-1-1-1-1111111-1-1-111-1-1-1111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-11-111-1-11-1-11
χ151111111-1-11111111111111-1-1-1-11-11-1-11111-1-1-1-11111-1-1-1-1-1-1-111-11-1-1-1-111111111-1-1-1-11111-1-1-1-111-11-1-1111-1-11
χ161111111-1-11111111111111-1-1-1-11-11-1-11111-1-1-1-11111-1-1-1-1-1-1-111-11-1-1-1-1111111-1-11111-1-1-1-11111-1-1-11-1-111-111-1
χ172222222222-2-22-2-222222222-2222-22-2-2-2-2-2-2222222-2-200-2220000-2200-2-2-2-2000000000000000000000000000000
χ182222222222-2-22-2-222222222-2-2-2-2-2-22222-2-22222-2-2-2-200-2-2-20000-2-2002222000000000000000000000000000000
χ19222222222-22-2-22-2-2-222-2-22-22000-2000002-222-2-2002-2002000000-20000000000022202000-2-2-2-200000000000000
χ20222222222-22-2-22-2-2-222-2-22-22000-2000002-222-2-2002-2002000000-200000000000-2-2-20-2000222200000000000000
χ21222222222-2-22-2-22-2-222-2-22-2-2000200000-2222-2-200-2200-2000000200000000000000202220000-2-2-2-20000000000
χ22222222222-2-22-2-22-2-222-2-22-2-2000200000-2222-2-200-2200-2000000200000000000000-20-2-2-2000022220000000000
χ232222222-2-22-2-22-2-22222222-2222-22-2-2-222-2-2-2-2-2-2-2-2-2-20022200002-200-2-222000000000000000000000000000000
χ242222222-2-22-2-22-2-22222222-22-2-222222-2-2-2-2-2-2-2-222-2-2002-2-20000220022-2-2000000000000000000000000000000
χ252222222-2-2-22-2-22-2-2-222-2-222-20002000002-2-2-222002-200-200000020000000000022-20-2000-2-22200000000000000
χ262222222-2-2-22-2-22-2-2-222-2-222-20002000002-2-2-222002-200-2000000200000000000-2-220200022-2-200000000000000
χ272222222-2-2-2-22-2-22-2-222-2-2222000-200000-22-2-22200-22002000000-200000000000000202-2-20000-2-2220000000000
χ282222222-2-2-2-22-2-22-2-222-2-2222000-200000-22-2-22200-22002000000-200000000000000-20-222000022-2-20000000000
χ292222-2-220022-2-2-22222-2-2-2-2000020-2002-22-2000022-220000000000-200002-20000002-2-2200002-22-2000000000000
χ302222-2-220022-2-2-22222-2-2-2-2000020-2002-22-2000022-220000000000-200002-2000000-222-20000-22-22000000000000
χ312222-2-220022-2-2-22222-2-2-2-20000-20200-222-20000-2-2-22000000000020000-2200000022-2-200002-2-22000000000000
χ322222-2-220022-2-2-22222-2-2-2-20000-20200-222-20000-2-2-22000000000020000-22000000-2-2220000-222-2000000000000
χ332222-2-22002-22-22-2222-2-2-2-2000020-200-22-220000222-20000000000-20000-2200002-200002-22-200002-20000000000
χ342222-2-22002-22-22-2222-2-2-2-2000020-200-22-220000222-20000000000-20000-220000-220000-22-220000-220000000000
χ352222-2-22002-22-22-2222-2-2-2-20000-202002-2-220000-2-22-20000000000200002-200002-20000-222-20000-220000000000
χ362222-2-22002-22-22-2222-2-2-2-20000-202002-2-220000-2-22-20000000000200002-20000-2200002-2-2200002-20000000000
χ372222-2-2200-2222-2-2-2-22-222-2002-20002-20022000000-2-20002-2000000002-20000000020-202-200-2200-220000000000
χ382222-2-2200-2222-2-2-2-22-222-2002-20002-20022000000-2-20002-2000000002-200000000-2020-22002-2002-20000000000
χ392222-2-2200-2222-2-2-2-22-222-200-22000-220022000000-2-2000-2200000000-220000000020-20-2200-22002-20000000000
χ402222-2-2200-2222-2-2-2-22-222-200-22000-220022000000-2-2000-2200000000-2200000000-20202-2002-200-220000000000
χ412222-2-2200-2-2-2222-2-22-222-2002-2000-2200-2-2000000220002-200000000-220000002-20-20200-2200-22000000000000
χ422222-2-2200-2-2-2222-2-22-222-2002-2000-2200-2-2000000220002-200000000-22000000-22020-2002-2002-2000000000000
χ432222-2-2200-2-2-2222-2-22-222-200-220002-200-2-200000022000-22000000002-20000002-2020-200-22002-2000000000000
χ442222-2-2200-2-2-2222-2-22-222-200-220002-200-2-200000022000-22000000002-2000000-220-202002-200-22000000000000
χ45222-122-122222222-1-1-1-1-1-1-122222222222-1-1-1-1-1-1-1-1-1-122-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1000000000000000022-1-1-1-10000
χ46222-122-122222222-1-1-1-1-1-1-122222222222-1-1-1-1-1-1-1-1-1-1-2-2-1-1-111-2-2-1-111-1-1-1-111110000000000000000-2-211110000
χ47222-122-122222222-1-1-1-1-1-1-122-2-2-22-2-2-2-2-2-1-1-1-1-1-111-1-122-111-1-122-11-1-11111-1-1-1-10000000000000000-2-211110000
χ48222-122-122222222-1-1-1-1-1-1-122-2-2-22-2-2-2-2-2-1-1-1-1-1-111-1-1-2-2-11111-2-2-111111111111000000000000000022-1-1-1-10000
χ49222-122-1222-2-22-2-2-1-1-1-1-1-1-12-2222-22-2-2-2-211-1-1-1-1-1-111001-1-1i3−i3001-1i3−i31111i3i3−i3−i3000000000000000000i3−i3i3−i30000
χ50222-122-1222-2-22-2-2-1-1-1-1-1-1-12-2222-22-2-2-2-211-1-1-1-1-1-111001-1-1−i3i3001-1−i3i31111−i3−i3i3i3000000000000000000−i3i3−i3i30000
χ51222-122-1222-2-22-2-2-1-1-1-1-1-1-12-2-2-2-2-2-2222211-1-1-1-1111100111i3−i30011i3−i3-1-1-1-1i3i3−i3−i3000000000000000000−i3i3−i3i30000
χ52222-122-1222-2-22-2-2-1-1-1-1-1-1-12-2-2-2-2-2-2222211-1-1-1-1111100111−i3i30011−i3i3-1-1-1-1−i3−i3i3i3000000000000000000i3−i3i3−i30000
χ53222-122-1-2-2222222-1-1-1-1-1-1-1-2-222-2-2-222-2-2-1-1111111-1-1221-1-1-1-1-2-211-1-1-1-11111110000000000000000-2211-1-10000
χ54222-122-1-2-2222222-1-1-1-1-1-1-1-2-222-2-2-222-2-2-1-1111111-1-1-2-21-1-111221111-1-111-1-1-1-100000000000000002-2-1-1110000
χ55222-122-1-2-2222222-1-1-1-1-1-1-1-2-2-2-22-22-2-222-1-11111-1-1-1-122111-1-1-2-21-1-1-111-1-1111100000000000000002-2-1-1110000
χ56222-122-1-2-2222222-1-1-1-1-1-1-1-2-2-2-22-22-2-222-1-11111-1-1-1-1-2-211111221-11111-1-1-1-1-1-10000000000000000-2211-1-10000
χ57222-122-1-2-22-2-22-2-2-1-1-1-1-1-1-1-2222-22-2-2-222111111111100-1-1-1i3−i300-11i3−i311-1-1−i3−i3i3i3000000000000000000−i3i3i3−i30000
χ58222-122-1-2-22-2-22-2-2-1-1-1-1-1-1-1-2222-22-2-2-222111111111100-1-1-1−i3i300-11−i3i311-1-1i3i3−i3−i3000000000000000000i3−i3−i3i30000
χ59222-122-1-2-22-2-22-2-2-1-1-1-1-1-1-1-22-2-222222-2-2111111-1-11100-111i3−i300-1-1i3−i3-1-111−i3−i3i3i3000000000000000000i3−i3−i3i30000
χ60222-122-1-2-22-2-22-2-2-1-1-1-1-1-1-1-22-2-222222-2-2111111-1-11100-111−i3i300-1-1−i3i3-1-111i3i3−i3−i3000000000000000000−i3i3i3−i30000
χ61444-244-244-44-4-44-422-2-222-2-44000-400000-22-2-22200-2200-200000020000000000000000000000000000000000000
χ62444-244-244-4-44-4-4422-2-222-2-4-40004000002-2-2-222002-2002000000-20000000000000000000000000000000000000
χ63444-244-2-4-4-44-4-44-422-2-222-24-4000400000-2222-2-200-22002000000-20000000000000000000000000000000000000
χ64444-244-2-4-4-4-44-4-4422-2-222-244000-4000002-222-2-2002-200-200000020000000000000000000000000000000000000
χ65444-2-4-4-20044-4-4-44-2-2-22222000040-4004-4-220000-2-22-2000000000020000-22000000000000000000000000000000
χ66444-2-4-4-20044-4-4-44-2-2-222220000-40400-44-220000222-20000000000-200002-2000000000000000000000000000000
χ67444-2-4-4-2004-44-44-4-2-2-22222000040-400-442-20000-2-2-220000000000200002-2000000000000000000000000000000
χ68444-2-4-4-2004-44-44-4-2-2-222220000-404004-42-2000022-220000000000-20000-22000000000000000000000000000000
χ69444-2-4-4-200-4444-4-422-22-2-22004-40004-400-2-200000022000-2200000000-2200000000000000000000000000000000
χ70444-2-4-4-200-4444-4-422-22-2-2200-44000-4400-2-2000000220002-2000000002-200000000000000000000000000000000
χ71444-2-4-4-200-4-4-444422-22-2-22004-4000-440022000000-2-2000-22000000002-200000000000000000000000000000000
χ72444-2-4-4-200-4-4-444422-22-2-2200-440004-40022000000-2-20002-200000000-2200000000000000000000000000000000
χ7344-44-4444-400000000-4-400400000000000004-40000002-2000222-200-2-200002-22-200000000000000000000000000
χ7444-44-4444-400000000-4-400400000000000004-4000000-22000-2-2-2200220000-22-2200000000000000000000000000
χ7544-44-444-4400000000-4-40040000000000000-440000002-200022-2200-2-20000-22-2200000000000000000000000000
χ7644-44-444-4400000000-4-40040000000000000-44000000-22000-2-22-2002200002-22-200000000000000000000000000
χ7744-4-2-44-24-40000002i3−2i3222i3−2i3-20000000000000-222i3−2i300002-2000−1+i3−1−i32-2001−i31+i30000−1+i31−i3−1−i31+i300000000000000000000000000
χ7844-4-2-44-24-40000002i3−2i3222i3−2i3-20000000000000-222i3−2i30000-220001−i31+i3-2200−1+i3−1−i300001−i3−1+i31+i3−1−i300000000000000000000000000
χ7944-4-2-44-24-4000000−2i32i322−2i32i3-20000000000000-22−2i32i300002-2000−1−i3−1+i32-2001+i31−i30000−1−i31+i3−1+i31−i300000000000000000000000000
χ8044-4-2-44-24-4000000−2i32i322−2i32i3-20000000000000-22−2i32i30000-220001+i31−i3-2200−1−i3−1+i300001+i3−1−i31−i3−1+i300000000000000000000000000
χ8144-4-2-44-2-440000002i3−2i3222i3−2i3-200000000000002-2−2i32i300002-2000−1+i3−1−i3-22001−i31+i300001−i3−1+i31+i3−1−i300000000000000000000000000
χ8244-4-2-44-2-440000002i3−2i3222i3−2i3-200000000000002-2−2i32i30000-220001−i31+i32-200−1+i3−1−i30000−1+i31−i3−1−i31+i300000000000000000000000000
χ8344-4-2-44-2-44000000−2i32i322−2i32i3-200000000000002-22i3−2i300002-2000−1−i3−1+i3-22001+i31−i300001+i3−1−i31−i3−1+i300000000000000000000000000
χ8444-4-2-44-2-44000000−2i32i322−2i32i3-200000000000002-22i3−2i30000-220001+i31−i32-200−1−i3−1+i30000−1−i31+i3−1+i31−i300000000000000000000000000
χ8588-888-880000000000-8800-800000000000000000000000000000000000000000000000000000000000000000000
χ8688-8-48-8-4000000004i3−4i34-4−4i34i3400000000000000000000000000000000000000000000000000000000000000000000
χ8788-8-48-8-400000000−4i34i34-44i3−4i3400000000000000000000000000000000000000000000000000000000000000000000
χ8816-1601600-1600000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ8916-160-8008000000000000000000000000000000004i3−4i30000000000000000000000000000000000000000000000000
χ9016-160-800800000000000000000000000000000000−4i34i30000000000000000000000000000000000000000000000000

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