Finite Group Databasebeta

← Group #11923332

Character table — Group #11923332

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1122222334444444446666688888888888812121212121212121212121616161616161616161618182424242424242424243232323236363648484848
order12346884433446612242422488336612121212242424242222681212121212121212121212242424242466662424242424121212124486666
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111-1-111111111111111-1-1111111-1-1-1-11111111-1-1-1-111111111-1-11111111-1-1-1-1-1-11-1-1-1-1
χ3111111111−1−i32−1+i3211−1−i32−1+i3211111111−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321111111−1−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+i321111−1−i32−1+i321−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32111−1−i32−1−i32−1+i32−1+i32
χ4111111111−1−i32−1+i32-1-1−1−i32−1+i3211111111−1−i32−1+i32−1−i32−1+i32-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-1111−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211-1-1−1−i32−1+i321−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32-1-111+i321+i321−i321−i32
χ5111111111−1+i32−1−i3211−1+i32−1−i3211111111−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321111111−1+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−i321111−1+i32−1−i321−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32111−1+i32−1+i32−1−i32−1−i32
χ6111111111−1+i32−1−i32-1-1−1+i32−1−i3211111111−1+i32−1−i32−1+i32−1−i32-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-1111−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211-1-1−1+i32−1−i321−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32-1-111−i321−i321+i321+i32
χ71111111-1-11111111111-11-1-111111111111111-1-1111-1-1-1-11111111111-1-111-1-11-1-1-1-11111-1-1-1-1-1-1-1
χ81111111-1-111-1-1111111-11-1-11111-1-1111111-1-111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11-1-1-1-1-1-1-1-111-11111
χ91111111-1-1−1−i32−1+i3211−1−i32−1+i321111-11-1-1−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211-1-11111+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1111+i321−i3211+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32-1-1-11+i321+i321−i321−i32
χ101111111-1-1−1−i32−1+i32-1-1−1−i32−1+i321111-11-1-1−1−i32−1+i32−1−i32−1+i32-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1111111+i321+i321−i321−i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-11+i321−i3211+i321+i321−i321−i321+i321+i321−i321−i3211-1−1−i32−1−i32−1+i32−1+i32
χ111111111-1-1−1+i32−1−i3211−1+i32−1−i321111-11-1-1−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211-1-11111−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1111−i321+i3211−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32-1-1-11−i321−i321+i321+i32
χ121111111-1-1−1+i32−1−i32-1-1−1+i32−1−i321111-11-1-1−1+i32−1−i32−1+i32−1−i32-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1111111−i321−i321+i321+i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-11−i321+i3211−i321−i321+i321+i321−i321−i321+i321+i3211-1−1+i32−1+i32−1−i32−1−i32
χ1311111-1-111111-1111-1-1111-1-111111-111-1-1-1-11-11-11-1111111-11-111-1-1-1-1111-111-1-1-1-1-11-11-11-1-11-11-1
χ1411111-1-11111-11111-1-1111-1-11111-1111-1-1-1-1-11-111-111111-11-1111-1-1-1-111-1111-1-1-1-1-1-11-11-11-1-11-11
χ1511111-1-111−1−i32−1+i321-1−1−i32−1+i321-1-1111-1-1−1−i32−1+i32−1−i32−1+i321-1−1−i32−1+i321+i321+i321−i321−i321-11-11-11−1−i32−1−i32−1+i32−1+i32−1−i321+i32−1+i321−i32−1−i32−1+i321+i321+i321−i321−i32111-1−1−i32−1+i32-11+i321+i321−i321−i32−1−i321+i32−1+i321−i321-1-1−1−i321+i32−1+i321−i32
χ1611111-1-111−1−i32−1+i32-11−1−i32−1+i321-1-1111-1-1−1−i32−1+i32−1−i32−1+i32-11−1−i32−1+i321+i321+i321−i321−i32-11-111-11−1−i32−1−i32−1+i32−1+i321+i32−1−i321−i32−1+i32−1−i32−1+i321+i321+i321−i321−i3211-11−1−i32−1+i32-11+i321+i321−i321−i321+i32−1−i321−i32−1+i32-11-11+i32−1−i321−i32−1+i32
χ1711111-1-111−1+i32−1−i321-1−1+i32−1−i321-1-1111-1-1−1+i32−1−i32−1+i32−1−i321-1−1+i32−1−i321−i321−i321+i321+i321-11-11-11−1+i32−1+i32−1−i32−1−i32−1+i321−i32−1−i321+i32−1+i32−1−i321−i321−i321+i321+i32111-1−1+i32−1−i32-11−i321−i321+i321+i32−1+i321−i32−1−i321+i321-1-1−1+i321−i32−1−i321+i32
χ1811111-1-111−1+i32−1−i32-11−1+i32−1−i321-1-1111-1-1−1+i32−1−i32−1+i32−1−i32-11−1+i32−1−i321−i321−i321+i321+i32-11-111-11−1+i32−1+i32−1−i32−1−i321−i32−1+i321+i32−1−i32−1+i32−1−i321−i321−i321+i321+i3211-11−1+i32−1−i32-11−i321−i321+i321+i321−i32−1+i321+i32−1−i32-11-11−i32−1+i321+i32−1−i32
χ1911111-1-1-1-1111-1111-1-11-111111111-111-1-1-1-11-1-111-11-1-1-1-11-11-111-1-1-1-1-1-11-1-1-1-111111-11-1-111-11-11
χ2011111-1-1-1-111-11111-1-11-11111111-1111-1-1-1-1-111-11-11-1-1-1-1-11-1111-1-1-1-1-1-1-11-1-1-11111-11-111-111-11-1
χ2111111-1-1-1-1−1−i32−1+i321-1−1−i32−1+i321-1-11-1111−1−i32−1+i32−1−i32−1+i321-1−1−i32−1+i321+i321+i321−i321−i321-1-111-111+i321+i321−i321−i32−1−i321+i32−1+i321−i32−1−i32−1+i321+i321+i321−i321−i32-1-11-11+i321−i32-1−1−i32−1−i32−1+i32−1+i32−1−i321+i32−1+i321−i32-1111+i32−1−i321−i32−1+i32
χ2211111-1-1-1-1−1−i32−1+i32-11−1−i32−1+i321-1-11-1111−1−i32−1+i32−1−i32−1+i32-11−1−i32−1+i321+i321+i321−i321−i32-111-11-111+i321+i321−i321−i321+i32−1−i321−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-1-1-111+i321−i32-1−1−i32−1−i32−1+i32−1+i321+i32−1−i321−i32−1+i321-11−1−i321+i32−1+i321−i32
χ2311111-1-1-1-1−1+i32−1−i321-1−1+i32−1−i321-1-11-1111−1+i32−1−i32−1+i32−1−i321-1−1+i32−1−i321−i321−i321+i321+i321-1-111-111−i321−i321+i321+i32−1+i321−i32−1−i321+i32−1+i32−1−i321−i321−i321+i321+i32-1-11-11−i321+i32-1−1+i32−1+i32−1−i32−1−i32−1+i321−i32−1−i321+i32-1111−i32−1+i321+i32−1−i32
χ2411111-1-1-1-1−1+i32−1−i32-11−1+i32−1−i321-1-11-1111−1+i32−1−i32−1+i32−1−i32-11−1+i32−1−i321−i321−i321+i321+i32-111-11-111−i321−i321+i321+i321−i32−1+i321+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-1-1-111−i321+i32-1−1+i32−1+i32−1−i32−1−i321−i32−1+i321+i32−1−i321-11−1+i321−i32−1−i321+i32
χ25222-220022220022-200-2-2200222200-2-200000000-20222220000-2-200002-200-2-20000000000000000
χ26222-220022−1−i3−1+i300−1−i3−1+i3-200-2-2200−1−i3−1+i3−1−i3−1+i3001+i31−i300000000-202−1−i3−1−i3−1+i3−1+i300001+i31−i300002-2001+i31−i30000000000000000
χ27222-220022−1+i3−1−i300−1+i3−1−i3-200-2-2200−1+i3−1−i3−1+i3−1−i3001−i31+i300000000-202−1+i3−1+i3−1−i3−1−i300001−i31+i300002-2001−i31+i30000000000000000
χ28222-2200-2-2220022-200-22200222200-2-200000000-202-2-2-2-20000-2-20000-2200220000000000000000
χ29222-2200-2-2−1−i3−1+i300−1−i3−1+i3-200-22200−1−i3−1+i3−1−i3−1+i3001+i31−i300000000-2021+i31+i31−i31−i300001+i31−i30000-2200−1−i3−1+i30000000000000000
χ30222-2200-2-2−1+i3−1−i300−1+i3−1−i3-200-22200−1+i3−1−i3−1+i3−1−i3001−i31+i300000000-2021−i31−i31+i31+i300001−i31+i30000-2200−1+i3−1−i30000000000000000
χ3122-12-12200222222-1-1-120200-1-1-1-1-1-12222222200-12-100002222-1-1-1-1-1-100-1-100-10000-1-1-1-10000000
χ3222-12-1220022-2-222-1-1-120200-1-1-1-111222222-2-200-12-10000-2-2-2-2-1-1-1-1-1-1001100-1000011110000000
χ3322-12-12200−1−i3−1+i322−1−i3−1+i3-1-1-1202001+i321−i321+i321−i32-1-1−1−i3−1+i3−1−i3−1−i3−1+i3−1+i32200-12-10000−1−i3−1−i3−1+i3−1+i31+i321−i321+i321+i321−i321−i3200-1-100-100001+i321+i321−i321−i320000000
χ3422-12-12200−1−i3−1+i3-2-2−1−i3−1+i3-1-1-1202001+i321−i321+i321−i3211−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3-2-200-12-100001+i31+i31−i31−i31+i321−i321+i321+i321−i321−i32001100-10000−1−i32−1−i32−1+i32−1+i320000000
χ3522-12-12200−1+i3−1−i322−1+i3−1−i3-1-1-1202001−i321+i321−i321+i32-1-1−1+i3−1−i3−1+i3−1+i3−1−i3−1−i32200-12-10000−1+i3−1+i3−1−i3−1−i31−i321+i321−i321−i321+i321+i3200-1-100-100001−i321−i321+i321+i320000000
χ3622-12-12200−1+i3−1−i3-2-2−1+i3−1−i3-1-1-1202001−i321+i321−i321+i3211−1+i3−1−i3−1+i3−1+i3−1−i3−1−i3-2-200-12-100001−i31−i31+i31+i31−i321+i321−i321−i321+i321+i32001100-10000−1+i32−1+i32−1−i32−1−i320000000
χ3722-12-1-2-200222-222-11120200-1-1-1-1-1122-2-2-2-22-200-1-2-100002-22-2-1-1111100-110010000-11-110000000
χ3822-12-1-2-20022-2222-11120200-1-1-1-11-122-2-2-2-2-2200-1-2-10000-22-22-1-11111001-100100001-11-10000000
χ3922-12-1-2-200−1−i3−1+i32-2−1−i3−1+i3-111202001+i321−i321+i321−i32-11−1−i3−1+i31+i31+i31−i31−i32-200-1-2-10000−1−i31+i3−1+i31−i31+i321−i32−1−i32−1−i32−1+i32−1+i3200-1100100001+i32−1−i321−i32−1+i320000000
χ4022-12-1-2-200−1−i3−1+i3-22−1−i3−1+i3-111202001+i321−i321+i321−i321-1−1−i3−1+i31+i31+i31−i31−i3-2200-1-2-100001+i3−1−i31−i3−1+i31+i321−i32−1−i32−1−i32−1+i32−1+i32001-10010000−1−i321+i32−1+i321−i320000000
χ4122-12-1-2-200−1+i3−1−i32-2−1+i3−1−i3-111202001−i321+i321−i321+i32-11−1+i3−1−i31−i31−i31+i31+i32-200-1-2-10000−1+i31−i3−1−i31+i31−i321+i32−1+i32−1+i32−1−i32−1−i3200-1100100001−i32−1+i321+i32−1−i320000000
χ4222-12-1-2-200−1+i3−1−i3-22−1+i3−1−i3-111202001−i321+i321−i321+i321-1−1+i3−1−i31−i31−i31+i31+i3-2200-1-2-100001−i3−1+i31+i3−1−i31−i321+i32−1+i32−1+i32−1−i32−1−i32001-10010000−1+i321−i32−1−i321+i320000000
χ43333333333003300333-13-133000033000000-1-133-1-1-100000000000000-1-1-1-100-100000000-1-1-10000
χ4433333333300-3-300333-13-1330000-3-300000011-3-3-1-1-100000000000000-1-11100-10000000011-10000
χ453333333-3-3003300333-1-3-1-3-3000033000000-1-1-3-3-1-1-10000000000000011-1-100-1000000001110000
χ463333333-3-300-3-300333-1-3-1-3-30000-3-30000001133-1-1-100000000000000111100-100000000-1-110000
χ4733333-3-333003-3003-3-3-13-1-3-300003-3000000-113-3-11-100000000000000-1-1-1100100000000-1110000
χ4833333-3-33300-33003-3-3-13-1-3-30000-330000001-1-33-11-100000000000000-1-11-1001000000001-110000
χ4933333-3-3-3-3003-3003-3-3-1-3-13300003-3000000-11-33-11-10000000000000011-11001000000001-1-10000
χ5033333-3-3-3-300-33003-3-3-1-3-1330000-330000001-13-3-11-100000000000000111-100100000000-11-10000
χ5144-2-4-20000440044200-40400-2-2-2-200-4-40000000020-2000000002200000000000000000000000000
χ5244-2-4-20000−2−2i3−2+2i300−2−2i3−2+2i3200-404001+i31−i31+i31−i3002+2i32−2i30000000020-200000000−1−i3−1+i300000000000000000000000000
χ5344-2-4-20000−2+2i3−2−2i300−2+2i3−2−2i3200-404001−i31+i31−i31+i3002−2i32+2i30000000020-200000000−1+i3−1−i300000000000000000000000000
χ544-440-422−224i−4i-2-20022022−22000−2i22i2-2-22200002−22−200000002i−2i2i−2i0000002−22−20000000−i2i2−i2i200000000000
χ554-440-422−224i−4i1+i31−i300−1−i3−1+i3022−22000−2i22i21+i31−i3−1−i3−1+i30000−ζ7+ζ13ζ7−ζ13ζ5−ζ23−ζ5+ζ2300000002ζ22−2ζ222ζ14−2ζ14000000−ζ7+ζ13ζ7−ζ13ζ5−ζ23−ζ5+ζ230000000ζ7+ζ13−ζ7−ζ13ζ5+ζ23−ζ5−ζ2300000000000
χ564-440-422−224i−4i1−i31+i300−1+i3−1−i3022−22000−2i22i21−i31+i3−1+i3−1−i30000ζ5−ζ23−ζ5+ζ23−ζ7+ζ13ζ7−ζ1300000002ζ14−2ζ142ζ22−2ζ22000000ζ5−ζ23−ζ5+ζ23−ζ7+ζ13ζ7−ζ130000000ζ5+ζ23−ζ5−ζ23ζ7+ζ13−ζ7−ζ1300000000000
χ574-440-422−22−4i4i-2-20022022−220002i2−2i2-2-22200002−22−20000000−2i2i−2i2i0000002−22−20000000i2−i2i2−i200000000000
χ584-440-422−22−4i4i1+i31−i300−1−i3−1+i3022−220002i2−2i21+i31−i3−1−i3−1+i30000−ζ7+ζ13ζ7−ζ13ζ5−ζ23−ζ5+ζ230000000−2ζ222ζ22−2ζ142ζ14000000−ζ7+ζ13ζ7−ζ13ζ5−ζ23−ζ5+ζ230000000−ζ7−ζ13ζ7+ζ13−ζ5−ζ23ζ5+ζ2300000000000
χ594-440-422−22−4i4i1−i31+i300−1+i3−1−i3022−220002i2−2i21−i31+i3−1+i3−1−i30000ζ5−ζ23−ζ5+ζ23−ζ7+ζ13ζ7−ζ130000000−2ζ142ζ14−2ζ222ζ22000000ζ5−ζ23−ζ5+ζ23−ζ7+ζ13ζ7−ζ130000000−ζ5−ζ23ζ5+ζ23−ζ7−ζ13ζ7+ζ1300000000000
χ604-440-4−22224i−4i-2-200220−22220002i2−2i2-2-2220000−22−2200000002i−2i2i−2i000000−22−220000000i2−i2i2−i200000000000
χ614-440-4−22224i−4i1+i31−i300−1−i3−1+i30−22220002i2−2i21+i31−i3−1−i3−1+i30000ζ7−ζ13−ζ7+ζ13−ζ5+ζ23ζ5−ζ2300000002ζ22−2ζ222ζ14−2ζ14000000ζ7−ζ13−ζ7+ζ13−ζ5+ζ23ζ5−ζ230000000−ζ7−ζ13ζ7+ζ13−ζ5−ζ23ζ5+ζ2300000000000
χ624-440-4−22224i−4i1−i31+i300−1+i3−1−i30−22220002i2−2i21−i31+i3−1+i3−1−i30000−ζ5+ζ23ζ5−ζ23ζ7−ζ13−ζ7+ζ1300000002ζ14−2ζ142ζ22−2ζ22000000−ζ5+ζ23ζ5−ζ23ζ7−ζ13−ζ7+ζ130000000−ζ5−ζ23ζ5+ζ23−ζ7−ζ13ζ7+ζ1300000000000
χ634-440-4−2222−4i4i-2-200220−2222000−2i22i2-2-2220000−22−220000000−2i2i−2i2i000000−22−220000000−i2i2−i2i200000000000
χ644-440-4−2222−4i4i1+i31−i300−1−i3−1+i30−2222000−2i22i21+i31−i3−1−i3−1+i30000ζ7−ζ13−ζ7+ζ13−ζ5+ζ23ζ5−ζ230000000−2ζ222ζ22−2ζ142ζ14000000ζ7−ζ13−ζ7+ζ13−ζ5+ζ23ζ5−ζ230000000ζ7+ζ13−ζ7−ζ13ζ5+ζ23−ζ5−ζ2300000000000
χ654-440-4−2222−4i4i1−i31+i300−1+i3−1−i30−2222000−2i22i21−i31+i3−1+i3−1−i30000−ζ5+ζ23ζ5−ζ23ζ7−ζ13−ζ7+ζ130000000−2ζ142ζ14−2ζ222ζ22000000−ζ5+ζ23ζ5−ζ23ζ7−ζ13−ζ7+ζ130000000ζ5+ζ23−ζ5−ζ23ζ7+ζ13−ζ7−ζ1300000000000
χ66666-660066000000-6002-6-200000000000000000020-200000000000000-2200000000000000000000
χ67666-6600-6-6000000-60026-200000000000000000020-2000000000000002-200000000000000000000
χ6866-36-36600006600-3-3-3-20-2000000-3-3000000-2-2001-21000000000000000011001000000000000000
χ6966-36-3660000-6-600-3-3-3-20-20000003300000022001-210000000000000000-1-1001000000000000000
χ7066-36-3-6-600006-600-333-20-2000000-33000000-220012100000000000000001-100-1000000000000000
χ7166-36-3-6-60000-6600-333-20-20000003-30000002-2001210000000000000000-1100-1000000000000000
χ728-8-40442−4200-4-400440−22220000022-2-2000022−2222−2200000000000000000−22−220000000000000000000000
χ738-8-40442−42002+2i32−2i300−2−2i3−2+2i30−222200000−1−i3−1+i31+i31−i30000−2ζ7+2ζ132ζ7−2ζ132ζ5−2ζ23−2ζ5+2ζ2300000000000000000ζ7−ζ13−ζ7+ζ13−ζ5+ζ23ζ5−ζ230000000000000000000000
χ748-8-40442−42002−2i32+2i300−2+2i3−2−2i30−222200000−1+i3−1−i31−i31+i300002ζ5−2ζ23−2ζ5+2ζ23−2ζ7+2ζ132ζ7−2ζ1300000000000000000−ζ5+ζ23ζ5−ζ23ζ7−ζ13−ζ7+ζ130000000000000000000000
χ758-8-404−424200-4-40044022−220000022-2-20000−2222−2222000000000000000002−22−20000000000000000000000
χ768-8-404−4242002+2i32−2i300−2−2i3−2+2i3022−2200000−1−i3−1+i31+i31−i300002ζ7−2ζ13−2ζ7+2ζ13−2ζ5+2ζ232ζ5−2ζ2300000000000000000−ζ7+ζ13ζ7−ζ13ζ5−ζ23−ζ5+ζ230000000000000000000000
χ778-8-404−4242002−2i32+2i300−2+2i3−2−2i3022−2200000−1+i3−1−i31−i31+i30000−2ζ5+2ζ232ζ5−2ζ232ζ7−2ζ13−2ζ7+2ζ1300000000000000000ζ5−ζ23−ζ5+ζ23−ζ7+ζ13ζ7−ζ130000000000000000000000
χ781212-6-12-6000000000060040-4000000000000000000-202000000000000000000000000000000000000

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