Finite Group Databasebeta

← Group #64255

Character table — Group #64255

Order 288.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48
size111166666688881212111166666688881212111166666688881212
order1244248888361212243612126122424242436121261236121261224242424361212612
χ1111111111111111111111111111111111111111111111111
χ2111111-1-1-1-11111-1-1111111-1-1-1-11111-1-1111111-1-1-1-11111-1-1
χ311-1-1-1111-1-111-1-11-111-1-1-1111-1-111-1-11-111-1-1-1111-1-111-1-11-1
χ411-1-1-11-1-11111-1-1-1111-1-1-11-1-11111-1-1-1111-1-1-11-1-11111-1-1-11
χ52222220000-1-1-1-1002222220000-1-1-1-1002222220000-1-1-1-100
χ622-2-2-220000-1-1110022-2-2-220000-1-1110022-2-2-220000-1-11100
χ72-22i−2i00i2−i22−2-11i−i002-22i−2i00i2−i22−2-11i−i002-22i−2i00i2−i22−2-11i−i00
χ82-22i−2i00−i2i2−22-11i−i002-22i−2i00−i2i2−22-11i−i002-22i−2i00−i2i2−22-11i−i00
χ92-2−2i2i00i2−i2−22-11−ii002-2−2i2i00i2−i2−22-11−ii002-2−2i2i00i2−i2−22-11−ii00
χ102-2−2i2i00−i2i22−2-11−ii002-2−2i2i00−i2i22−2-11−ii002-2−2i2i00−i2i22−2-11−ii00
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
χ1333-3-31-111-1-10000-1133-3-31-111-1-10000-1133-3-31-111-1-10000-11
χ1433-3-31-1-1-11100001-133-3-31-1-1-11100001-133-3-31-1-1-11100001-1
χ154-44i−4i0000001-1−ii004-44i−4i0000001-1−ii004-44i−4i0000001-1−ii00
χ164-4−4i4i0000001-1i−i004-4−4i4i0000001-1i−i004-4−4i4i0000001-1i−i00
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
χ1911-1-1-1111-1-111-1-11-1−1+i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i321−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i321+i32
χ2011-1-1-11-1-11111-1-1-11−1+i32−1+i321−i321−i321−i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−1−i32−1−i321+i321+i321+i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i32
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
χ2222-2-2-220000-1-11100−1+i3−1+i31−i31−i31−i3−1+i300001−i321−i32−1+i32−1+i3200−1−i3−1−i31+i31+i31+i3−1−i300001+i321+i32−1−i32−1−i3200
χ232-22i−2i00i2−i22−2-11i−i00−1+i31−i32ζ14−2ζ1400−ζ5−ζ23ζ5+ζ23ζ5−ζ23−ζ5+ζ231−i32−1+i32ζ14−ζ1400−1−i31+i32ζ22−2ζ2200−ζ7−ζ13ζ7+ζ13−ζ7+ζ13ζ7−ζ131+i32−1−i32ζ22−ζ2200
χ242-22i−2i00−i2i2−22-11i−i00−1+i31−i32ζ14−2ζ1400ζ5+ζ23−ζ5−ζ23−ζ5+ζ23ζ5−ζ231−i32−1+i32ζ14−ζ1400−1−i31+i32ζ22−2ζ2200ζ7+ζ13−ζ7−ζ13ζ7−ζ13−ζ7+ζ131+i32−1−i32ζ22−ζ2200
χ252-2−2i2i00i2−i2−22-11−ii00−1+i31−i3−2ζ142ζ1400−ζ5−ζ23ζ5+ζ23−ζ5+ζ23ζ5−ζ231−i32−1+i32−ζ14ζ1400−1−i31+i3−2ζ222ζ2200−ζ7−ζ13ζ7+ζ13ζ7−ζ13−ζ7+ζ131+i32−1−i32−ζ22ζ2200
χ262-2−2i2i00−i2i22−2-11−ii00−1+i31−i3−2ζ142ζ1400ζ5+ζ23−ζ5−ζ23ζ5−ζ23−ζ5+ζ231−i32−1+i32−ζ14ζ1400−1−i31+i3−2ζ222ζ2200ζ7+ζ13−ζ7−ζ13−ζ7+ζ13ζ7−ζ131+i32−1−i32−ζ22ζ2200
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
χ2933-3-31-111-1-10000-11−3+3i32−3+3i323−3i323−3i32−1+i321−i32−1+i32−1+i321−i321−i3200001−i32−1+i32−3−3i32−3−3i323+3i323+3i32−1−i321+i32−1−i32−1−i321+i321+i3200001+i32−1−i32
χ3033-3-31-1-1-11100001-1−3+3i32−3+3i323−3i323−3i32−1+i321−i321−i321−i32−1+i32−1+i320000−1+i321−i32−3−3i32−3−3i323+3i323+3i32−1−i321+i321+i321+i32−1−i32−1−i320000−1−i321+i32
χ314-44i−4i0000001-1−ii00−2+2i32−2i34ζ14−4ζ14000000−1+i321−i32−ζ14ζ1400−2−2i32+2i34ζ22−4ζ22000000−1−i321+i32−ζ22ζ2200
χ324-4−4i4i0000001-1i−i00−2+2i32−2i3−4ζ144ζ14000000−1+i321−i32ζ14−ζ1400−2−2i32+2i3−4ζ224ζ22000000−1−i321+i32ζ22−ζ2200
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
χ3511-1-1-1111-1-111-1-11-1−1−i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i321+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i321−i32
χ3611-1-1-11-1-11111-1-1-11−1−i32−1−i321+i321+i321+i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1+i32−1+i321−i321−i321−i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i32
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
χ3822-2-2-220000-1-11100−1−i3−1−i31+i31+i31+i3−1−i300001+i321+i32−1−i32−1−i3200−1+i3−1+i31−i31−i31−i3−1+i300001−i321−i32−1+i32−1+i3200
χ392-22i−2i00i2−i22−2-11i−i00−1−i31+i32ζ22−2ζ2200−ζ7−ζ13ζ7+ζ13−ζ7+ζ13ζ7−ζ131+i32−1−i32ζ22−ζ2200−1+i31−i32ζ14−2ζ1400−ζ5−ζ23ζ5+ζ23ζ5−ζ23−ζ5+ζ231−i32−1+i32ζ14−ζ1400
χ402-22i−2i00−i2i2−22-11i−i00−1−i31+i32ζ22−2ζ2200ζ7+ζ13−ζ7−ζ13ζ7−ζ13−ζ7+ζ131+i32−1−i32ζ22−ζ2200−1+i31−i32ζ14−2ζ1400ζ5+ζ23−ζ5−ζ23−ζ5+ζ23ζ5−ζ231−i32−1+i32ζ14−ζ1400
χ412-2−2i2i00i2−i2−22-11−ii00−1−i31+i3−2ζ222ζ2200−ζ7−ζ13ζ7+ζ13ζ7−ζ13−ζ7+ζ131+i32−1−i32−ζ22ζ2200−1+i31−i3−2ζ142ζ1400−ζ5−ζ23ζ5+ζ23−ζ5+ζ23ζ5−ζ231−i32−1+i32−ζ14ζ1400
χ422-2−2i2i00−i2i22−2-11−ii00−1−i31+i3−2ζ222ζ2200ζ7+ζ13−ζ7−ζ13−ζ7+ζ13ζ7−ζ131+i32−1−i32−ζ22ζ2200−1+i31−i3−2ζ142ζ1400ζ5+ζ23−ζ5−ζ23ζ5−ζ23−ζ5+ζ231−i32−1+i32−ζ14ζ1400
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
χ4533-3-31-111-1-10000-11−3−3i32−3−3i323+3i323+3i32−1−i321+i32−1−i32−1−i321+i321+i3200001+i32−1−i32−3+3i32−3+3i323−3i323−3i32−1+i321−i32−1+i32−1+i321−i321−i3200001−i32−1+i32
χ4633-3-31-1-1-11100001-1−3−3i32−3−3i323+3i323+3i32−1−i321+i321+i321+i32−1−i32−1−i320000−1−i321+i32−3+3i32−3+3i323−3i323−3i32−1+i321−i321−i321−i32−1+i32−1+i320000−1+i321−i32
χ474-44i−4i0000001-1−ii00−2−2i32+2i34ζ22−4ζ22000000−1−i321+i32−ζ22ζ2200−2+2i32−2i34ζ14−4ζ14000000−1+i321−i32−ζ14ζ1400
χ484-4−4i4i0000001-1i−i00−2−2i32+2i3−4ζ224ζ22000000−1−i321+i32ζ22−ζ2200−2+2i32−2i3−4ζ144ζ14000000−1+i321−i32ζ14−ζ1400

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