Finite Group Databasebeta

← Group #63751

Character table — Group #63751

Order 288.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48
size111166666688881212111166666688881212111166666688881212
order1222448888366644366612122424242436661212366612122424242436661212
χ1111111111111111111111111111111111111111111111111
χ2111111-1-1-1-11111-1-1111111-1-1-1-11111-1-1111111-1-1-1-11111-1-1
χ31-11-11-1ii−i−i11-1-1i−i1-11-11-1ii−i−i11-1-1i−i1-11-11-1ii−i−i11-1-1i−i
χ41-11-11-1−i−iii11-1-1−ii1-11-11-1−i−iii11-1-1−ii1-11-11-1−i−iii11-1-1−ii
χ52222220000-1-1-1-1002222220000-1-1-1-1002222220000-1-1-1-100
χ622-2-2002−22−2-111-10022-2-2002−22−2-111-10022-2-2002−22−2-111-100
χ722-2-200−22−22-111-10022-2-200−22−22-111-10022-2-200−22−22-111-100
χ82-22-22-20000-1-111002-22-22-20000-1-111002-22-22-20000-1-11100
χ92-2-2200i2−i2−i2i2-11-11002-2-2200i2−i2−i2i2-11-11002-2-2200i2−i2−i2i2-11-1100
χ102-2-2200−i2i2i2−i2-11-11002-2-2200−i2i2i2−i2-11-11002-2-2200−i2i2i2−i2-11-1100
χ113333-1-111110000-1-13333-1-111110000-1-13333-1-111110000-1-1
χ123333-1-1-1-1-1-10000113333-1-1-1-1-1-10000113333-1-1-1-1-1-1000011
χ133-33-3-11ii−i−i0000−ii3-33-3-11ii−i−i0000−ii3-33-3-11ii−i−i0000−ii
χ143-33-3-11−i−iii0000i−i3-33-3-11−i−iii0000i−i3-33-3-11−i−iii0000i−i
χ1544-4-40000001-1-110044-4-40000001-1-110044-4-40000001-1-1100
χ164-4-440000001-11-1004-4-440000001-11-1004-4-440000001-11-100
χ171111111111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ18111111-1-1-1-11111-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32
χ191-11-11-1ii−i−i11-1-1i−i−1+i321−i32−1+i321−i32−1+i321−i32ζ14ζ14−ζ14−ζ14−1+i32−1+i321−i321−i32ζ14−ζ14−1−i321+i32−1−i321+i32−1−i321+i32ζ22ζ22−ζ22−ζ22−1−i32−1−i321+i321+i32ζ22−ζ22
χ201-11-11-1−i−iii11-1-1−ii−1+i321−i32−1+i321−i32−1+i321−i32−ζ14−ζ14ζ14ζ14−1+i32−1+i321−i321−i32−ζ14ζ14−1−i321+i32−1−i321+i32−1−i321+i32−ζ22−ζ22ζ22ζ22−1−i32−1−i321+i321+i32−ζ22ζ22
χ212222220000-1-1-1-100−1+i3−1+i3−1+i3−1+i3−1+i3−1+i300001−i321−i321−i321−i3200−1−i3−1−i3−1−i3−1−i3−1−i3−1−i300001+i321+i321+i321+i3200
χ2222-2-2002−22−2-111-100−1+i3−1+i31−i31−i300ζ5−ζ23−ζ5+ζ23ζ5−ζ23−ζ5+ζ231−i32−1+i32−1+i321−i3200−1−i3−1−i31+i31+i300−ζ7+ζ13ζ7−ζ13−ζ7+ζ13ζ7−ζ131+i32−1−i32−1−i321+i3200
χ2322-2-200−22−22-111-100−1+i3−1+i31−i31−i300−ζ5+ζ23ζ5−ζ23−ζ5+ζ23ζ5−ζ231−i32−1+i32−1+i321−i3200−1−i3−1−i31+i31+i300ζ7−ζ13−ζ7+ζ13ζ7−ζ13−ζ7+ζ131+i32−1−i32−1−i321+i3200
χ242-22-22-20000-1-11100−1+i31−i3−1+i31−i3−1+i31−i300001−i321−i32−1+i32−1+i3200−1−i31+i3−1−i31+i3−1−i31+i300001+i321+i32−1−i32−1−i3200
χ252-2-2200i2−i2−i2i2-11-1100−1+i31−i31−i3−1+i300−ζ5−ζ23ζ5+ζ23ζ5+ζ23−ζ5−ζ231−i32−1+i321−i32−1+i3200−1−i31+i31+i3−1−i300−ζ7−ζ13ζ7+ζ13ζ7+ζ13−ζ7−ζ131+i32−1−i321+i32−1−i3200
χ262-2-2200−i2i2i2−i2-11-1100−1+i31−i31−i3−1+i300ζ5+ζ23−ζ5−ζ23−ζ5−ζ23ζ5+ζ231−i32−1+i321−i32−1+i3200−1−i31+i31+i3−1−i300ζ7+ζ13−ζ7−ζ13−ζ7−ζ13ζ7+ζ131+i32−1−i321+i32−1−i3200
χ273333-1-111110000-1-1−3+3i32−3+3i32−3+3i32−3+3i321−i321−i32−1+i32−1+i32−1+i32−1+i3200001−i321−i32−3−3i32−3−3i32−3−3i32−3−3i321+i321+i32−1−i32−1−i32−1−i32−1−i3200001+i321+i32
χ283333-1-1-1-1-1-1000011−3+3i32−3+3i32−3+3i32−3+3i321−i321−i321−i321−i321−i321−i320000−1+i32−1+i32−3−3i32−3−3i32−3−3i32−3−3i321+i321+i321+i321+i321+i321+i320000−1−i32−1−i32
χ293-33-3-11ii−i−i0000−ii−3+3i323−3i32−3+3i323−3i321−i32−1+i32ζ14ζ14−ζ14−ζ140000−ζ14ζ14−3−3i323+3i32−3−3i323+3i321+i32−1−i32ζ22ζ22−ζ22−ζ220000−ζ22ζ22
χ303-33-3-11−i−iii0000i−i−3+3i323−3i32−3+3i323−3i321−i32−1+i32−ζ14−ζ14ζ14ζ140000ζ14−ζ14−3−3i323+3i32−3−3i323+3i321+i32−1−i32−ζ22−ζ22ζ22ζ220000ζ22−ζ22
χ3144-4-40000001-1-1100−2+2i3−2+2i32−2i32−2i3000000−1+i321−i321−i32−1+i3200−2−2i3−2−2i32+2i32+2i3000000−1−i321+i321+i32−1−i3200
χ324-4-440000001-11-100−2+2i32−2i32−2i3−2+2i3000000−1+i321−i32−1+i321−i3200−2−2i32+2i32+2i3−2−2i3000000−1−i321+i32−1−i321+i3200
χ331111111111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32
χ34111111-1-1-1-11111-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32
χ351-11-11-1ii−i−i11-1-1i−i−1−i321+i32−1−i321+i32−1−i321+i32ζ22ζ22−ζ22−ζ22−1−i32−1−i321+i321+i32ζ22−ζ22−1+i321−i32−1+i321−i32−1+i321−i32ζ14ζ14−ζ14−ζ14−1+i32−1+i321−i321−i32ζ14−ζ14
χ361-11-11-1−i−iii11-1-1−ii−1−i321+i32−1−i321+i32−1−i321+i32−ζ22−ζ22ζ22ζ22−1−i32−1−i321+i321+i32−ζ22ζ22−1+i321−i32−1+i321−i32−1+i321−i32−ζ14−ζ14ζ14ζ14−1+i32−1+i321−i321−i32−ζ14ζ14
χ372222220000-1-1-1-100−1−i3−1−i3−1−i3−1−i3−1−i3−1−i300001+i321+i321+i321+i3200−1+i3−1+i3−1+i3−1+i3−1+i3−1+i300001−i321−i321−i321−i3200
χ3822-2-2002−22−2-111-100−1−i3−1−i31+i31+i300−ζ7+ζ13ζ7−ζ13−ζ7+ζ13ζ7−ζ131+i32−1−i32−1−i321+i3200−1+i3−1+i31−i31−i300ζ5−ζ23−ζ5+ζ23ζ5−ζ23−ζ5+ζ231−i32−1+i32−1+i321−i3200
χ3922-2-200−22−22-111-100−1−i3−1−i31+i31+i300ζ7−ζ13−ζ7+ζ13ζ7−ζ13−ζ7+ζ131+i32−1−i32−1−i321+i3200−1+i3−1+i31−i31−i300−ζ5+ζ23ζ5−ζ23−ζ5+ζ23ζ5−ζ231−i32−1+i32−1+i321−i3200
χ402-22-22-20000-1-11100−1−i31+i3−1−i31+i3−1−i31+i300001+i321+i32−1−i32−1−i3200−1+i31−i3−1+i31−i3−1+i31−i300001−i321−i32−1+i32−1+i3200
χ412-2-2200i2−i2−i2i2-11-1100−1−i31+i31+i3−1−i300−ζ7−ζ13ζ7+ζ13ζ7+ζ13−ζ7−ζ131+i32−1−i321+i32−1−i3200−1+i31−i31−i3−1+i300−ζ5−ζ23ζ5+ζ23ζ5+ζ23−ζ5−ζ231−i32−1+i321−i32−1+i3200
χ422-2-2200−i2i2i2−i2-11-1100−1−i31+i31+i3−1−i300ζ7+ζ13−ζ7−ζ13−ζ7−ζ13ζ7+ζ131+i32−1−i321+i32−1−i3200−1+i31−i31−i3−1+i300ζ5+ζ23−ζ5−ζ23−ζ5−ζ23ζ5+ζ231−i32−1+i321−i32−1+i3200
χ433333-1-111110000-1-1−3−3i32−3−3i32−3−3i32−3−3i321+i321+i32−1−i32−1−i32−1−i32−1−i3200001+i321+i32−3+3i32−3+3i32−3+3i32−3+3i321−i321−i32−1+i32−1+i32−1+i32−1+i3200001−i321−i32
χ443333-1-1-1-1-1-1000011−3−3i32−3−3i32−3−3i32−3−3i321+i321+i321+i321+i321+i321+i320000−1−i32−1−i32−3+3i32−3+3i32−3+3i32−3+3i321−i321−i321−i321−i321−i321−i320000−1+i32−1+i32
χ453-33-3-11ii−i−i0000−ii−3−3i323+3i32−3−3i323+3i321+i32−1−i32ζ22ζ22−ζ22−ζ220000−ζ22ζ22−3+3i323−3i32−3+3i323−3i321−i32−1+i32ζ14ζ14−ζ14−ζ140000−ζ14ζ14
χ463-33-3-11−i−iii0000i−i−3−3i323+3i32−3−3i323+3i321+i32−1−i32−ζ22−ζ22ζ22ζ220000ζ22−ζ22−3+3i323−3i32−3+3i323−3i321−i32−1+i32−ζ14−ζ14ζ14ζ140000ζ14−ζ14
χ4744-4-40000001-1-1100−2−2i3−2−2i32+2i32+2i3000000−1−i321+i321+i32−1−i3200−2+2i3−2+2i32−2i32−2i3000000−1+i321−i321−i32−1+i3200
χ484-4-440000001-11-100−2−2i32+2i32+2i3−2−2i3000000−1−i321+i32−1−i321+i3200−2+2i32−2i32−2i3−2+2i3000000−1+i321−i32−1+i321−i3200

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.