Finite Group Databasebeta

← Group #11923339

Character table — Group #11923339

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1122222334444444446666688888888888812121212121212121212121616161616161616161618182424242424242424243232323236363648484848
order1234688442233661224242248833666612122424242444446812121212126666121224242424246612122424242424666622812121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111−1−i32−1+i32−1−i32−1+i3211111111−1−i32−1+i3211−1−i32−1+i32−1−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+i3211−1−i32−1+i32111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32111−1−i32−1−i32−1+i32−1+i32
χ311111111111−1+i32−1−i32−1+i32−1−i3211111111−1+i32−1−i3211−1+i32−1−i32−1+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−i3211−1+i32−1−i32111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32111−1+i32−1+i32−1−i32−1−i32
χ4111111111-1-111111111111111-1-111111111-1-1-1-11111111-1-1-1-11111111111-1-111111-1-1-1-1-1-11-1-1-1-1
χ5111111111-1-1−1−i32−1+i32−1−i32−1+i3211111111−1−i32−1+i32-1-1−1−i32−1+i32−1−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−i32−1+i32-1-11−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32-1-111+i321+i321−i321−i32
χ6111111111-1-1−1+i32−1−i32−1+i32−1−i3211111111−1+i32−1−i32-1-1−1+i32−1−i32−1+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+i32−1−i32-1-11−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32-1-111−i321−i321+i321+i32
χ71111111-1-11111111111-11-1-111111111111111-1-1111-1-1-1-11111111111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1
χ81111111-1-111−1−i32−1+i32−1−i32−1+i321111-11-1-1−1−i32−1+i3211−1−i32−1+i32−1−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+i32-1-11+i321−i321111+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32-1-1-11+i321+i321−i321−i32
χ91111111-1-111−1+i32−1−i32−1+i32−1−i321111-11-1-1−1+i32−1−i3211−1+i32−1−i32−1+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−i32-1-11−i321+i321111−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32-1-1-11−i321−i321+i321+i32
χ101111111-1-1-1-111111111-11-1-111-1-111111111-1-111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11-1-1-1-1-1-1-1-111-11111
χ111111111-1-1-1-1−1−i32−1+i32−1−i32−1+i321111-11-1-1−1−i32−1+i32-1-1−1−i32−1+i32−1−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+i32-1-11+i321−i32-1-111+i321+i321−i321−i321+i321+i321−i321−i3211-1−1−i32−1−i32−1+i32−1+i32
χ121111111-1-1-1-1−1+i32−1−i32−1+i32−1−i321111-11-1-1−1+i32−1−i32-1-1−1+i32−1−i32−1+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−i32-1-11−i321+i32-1-111−i321−i321+i321+i321−i321−i321+i321+i3211-1−1+i32−1+i32−1−i32−1−i32
χ1311111-1-1111-111111-1-1111-1-1111-11111-1-1-1-11-11-11-1111111-11-111-1-1-1-111111-1-1-1-1-1-11-11-11-1-11-11-1
χ1411111-1-1111-1−1−i32−1+i32−1−i32−1+i321-1-1111-1-1−1−i32−1+i321-1−1−i32−1+i32−1−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−i3211−1−i32−1+i321-1-11+i321+i321−i321−i32−1−i321+i32−1+i321−i321-1-1−1−i321+i32−1+i321−i32
χ1511111-1-1111-1−1+i32−1−i32−1+i32−1−i321-1-1111-1-1−1+i32−1−i321-1−1+i32−1−i32−1+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+i3211−1+i32−1−i321-1-11−i321−i321+i321+i32−1+i321−i32−1−i321+i321-1-1−1+i321−i32−1−i321+i32
χ1611111-1-111-1111111-1-1111-1-111-111111-1-1-1-1-11-111-111111-11-1111-1-1-1-11111-11-1-1-1-1-1-11-11-11-1-11-11
χ1711111-1-111-11−1−i32−1+i32−1−i32−1+i321-1-1111-1-1−1−i32−1+i32-11−1−i32−1+i32−1−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−i3211−1−i32−1+i32-11-11+i321+i321−i321−i321+i32−1−i321−i32−1+i32-11-11+i32−1−i321−i32−1+i32
χ1811111-1-111-11−1+i32−1−i32−1+i32−1−i321-1-1111-1-1−1+i32−1−i32-11−1+i32−1−i32−1+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+i3211−1+i32−1−i32-11-11−i321−i321+i321+i321−i32−1+i321+i32−1−i32-11-11−i32−1+i321+i32−1−i32
χ1911111-1-1-1-11-111111-1-11-1111111-11111-1-1-1-11-1-111-11-1-1-1-11-11-111-1-1-1-1-1-1-1-11-1-111111-11-1-111-11-11
χ2011111-1-1-1-11-1−1−i32−1+i32−1−i32−1+i321-1-11-1111−1−i32−1+i321-1−1−i32−1+i32−1−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+i321−i321-1-1−1−i32−1−i32−1+i32−1+i32−1−i321+i32−1+i321−i32-1111+i32−1−i321−i32−1+i32
χ2111111-1-1-1-11-1−1+i32−1−i32−1+i32−1−i321-1-11-1111−1+i32−1−i321-1−1+i32−1−i32−1+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−i321+i321-1-1−1+i32−1+i32−1−i32−1−i32−1+i321−i32−1−i321+i32-1111−i32−1+i321+i32−1−i32
χ2211111-1-1-1-1-1111111-1-11-111111-111111-1-1-1-1-111-11-11-1-1-1-1-11-1111-1-1-1-1-1-1-1-1-11-11111-11-111-111-11-1
χ2311111-1-1-1-1-11−1−i32−1+i32−1−i32−1+i321-1-11-1111−1−i32−1+i32-11−1−i32−1+i32−1−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−i32-1-11+i321−i32-11-1−1−i32−1−i32−1+i32−1+i321+i32−1−i321−i32−1+i321-11−1−i321+i32−1+i321−i32
χ2411111-1-1-1-1-11−1+i32−1−i32−1+i32−1−i321-1-11-1111−1+i32−1−i32-11−1+i32−1−i32−1+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+i32-1-11−i321+i32-11-1−1+i32−1+i32−1−i32−1−i321−i32−1+i321+i32−1−i321-11−1+i321−i32−1−i321+i32
χ25222-220022002222-200-2-2200220022-2-200000000-20222220000-2-200002-2-2-2000000000000000000
χ26222-22002200−1−i3−1+i3−1−i3−1+i3-200-2-2200−1−i3−1+i300−1−i3−1+i31+i31−i300000000-202−1−i3−1−i3−1+i3−1+i300001+i31−i300002-21+i31−i3000000000000000000
χ27222-22002200−1+i3−1−i3−1+i3−1−i3-200-2-2200−1+i3−1−i300−1+i3−1−i31−i31+i300000000-202−1+i3−1+i3−1−i3−1−i300001−i31+i300002-21−i31+i3000000000000000000
χ28222-2200-2-2002222-200-22200220022-2-200000000-202-2-2-2-20000-2-20000-2222000000000000000000
χ29222-2200-2-200−1−i3−1+i3−1−i3−1+i3-200-22200−1−i3−1+i300−1−i3−1+i31+i31−i300000000-2021+i31+i31−i31−i300001+i31−i30000-22−1−i3−1+i3000000000000000000
χ30222-2200-2-200−1+i3−1−i3−1+i3−1−i3-200-22200−1+i3−1−i300−1+i3−1−i31−i31+i300000000-2021−i31−i31+i31+i300001−i31+i30000-22−1+i3−1−i3000000000000000000
χ3122-12-12200222222-1-1-120200-1-1-1-1-1-12222222200-12-100002222-1-1-1-1-1-10000-1-1-10000-1-1-1-10000000
χ3222-12-1220022−1−i3−1+i3−1−i3−1+i3-1-1-1202001+i321−i32-1-11+i321−i32−1−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−i320000-1-1-100001+i321+i321−i321−i320000000
χ3322-12-1220022−1+i3−1−i3−1+i3−1−i3-1-1-1202001−i321+i32-1-11−i321+i32−1+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+i320000-1-1-100001−i321−i321+i321+i320000000
χ3422-12-12200-2-22222-1-1-120200-1-111-1-1222222-2-200-12-10000-2-2-2-2-1-1-1-1-1-1000011-1000011110000000
χ3522-12-12200-2-2−1−i3−1+i3−1−i3−1+i3-1-1-1202001+i321−i32111+i321−i32−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3-2-200-12-100001+i31+i31−i31−i31+i321−i321+i321+i321−i321−i32000011-10000−1−i32−1−i32−1+i32−1+i320000000
χ3622-12-12200-2-2−1+i3−1−i3−1+i3−1−i3-1-1-1202001−i321+i32111−i321+i32−1+i3−1−i3−1+i3−1+i3−1−i3−1−i3-2-200-12-100001−i31−i31+i31+i31−i321+i321−i321−i321+i321+i32000011-10000−1+i32−1+i32−1−i32−1−i320000000
χ3722-12-1-2-2002-22222-11120200-1-1-11-1-122-2-2-2-22-200-1-2-100002-22-2-1-111110000-1110000-11-110000000
χ3822-12-1-2-2002-2−1−i3−1+i3−1−i3−1+i3-111202001+i321−i32-111+i321−i32−1−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+i320000-11100001+i32−1−i321−i32−1+i320000000
χ3922-12-1-2-2002-2−1+i3−1−i3−1+i3−1−i3-111202001−i321+i32-111−i321+i32−1+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−i320000-11100001−i32−1+i321+i32−1−i320000000
χ4022-12-1-2-200-222222-11120200-1-11-1-1-122-2-2-2-2-2200-1-2-10000-22-22-1-1111100001-1100001-11-10000000
χ4122-12-1-2-200-22−1−i3−1+i3−1−i3−1+i3-111202001+i321−i321-11+i321−i32−1−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+i3200001-110000−1−i321+i32−1+i321−i320000000
χ4222-12-1-2-200-22−1+i3−1−i3−1+i3−1−i3-111202001−i321+i321-11−i321+i32−1+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−i3200001-110000−1+i321−i32−1−i321+i320000000
χ43333333333330000333-13-133003300000000-1-133-1-1-100000000000000-1-100-1-1-100000000-1-1-10000
χ44333333333-3-30000333-13-13300-3-30000000011-3-3-1-1-100000000000000-1-10011-10000000011-10000
χ453333333-3-3330000333-1-3-1-3-3003300000000-1-1-3-3-1-1-1000000000000001100-1-1-1000000001110000
χ463333333-3-3-3-30000333-1-3-1-3-300-3-3000000001133-1-1-100000000000000110011-100000000-1-110000
χ4733333-3-3333-300003-3-3-13-1-3-3003-300000000-113-3-11-100000000000000-1-100-11100000000-1110000
χ4833333-3-333-3300003-3-3-13-1-3-300-33000000001-1-33-11-100000000000000-1-1001-11000000001-110000
χ4933333-3-3-3-33-300003-3-3-1-3-133003-300000000-11-33-11-1000000000000001100-111000000001-1-10000
χ5033333-3-3-3-3-3300003-3-3-1-3-13300-33000000001-13-3-11-10000000000000011001-1100000000-11-10000
χ5144-2-4-20000004444200-40400-2-200-2-2-4-40000000020-2000000002200000000000000000000000000
χ5244-2-4-2000000−2−2i3−2+2i3−2−2i3−2+2i3200-404001+i31−i3001+i31−i32+2i32−2i30000000020-200000000−1−i3−1+i300000000000000000000000000
χ5344-2-4-2000000−2+2i3−2−2i3−2+2i3−2−2i3200-404001−i31+i3001−i31+i32−2i32+2i30000000020-200000000−1+i3−1−i300000000000000000000000000
χ544-440-422−224i−4i00-2-222022−22000−2i22i2-2-20022002−22−200000002i−2i2i−2i0000002−22−20000000−i2i2−i2i200000000000
χ554-440-422−224i−4i001+i31−i3−1−i3−1+i3022−22000−2i22i21+i31−i300−1−i3−1+i300−ζ7+ζ13ζ7−ζ13ζ5−ζ23−ζ5+ζ2300000002ζ22−2ζ222ζ14−2ζ14000000−ζ7+ζ13ζ7−ζ13ζ5−ζ23−ζ5+ζ230000000ζ7+ζ13−ζ7−ζ13ζ5+ζ23−ζ5−ζ2300000000000
χ564-440-422−224i−4i001−i31+i3−1+i3−1−i3022−22000−2i22i21−i31+i300−1+i3−1−i300ζ5−ζ23−ζ5+ζ23−ζ7+ζ13ζ7−ζ1300000002ζ14−2ζ142ζ22−2ζ22000000ζ5−ζ23−ζ5+ζ23−ζ7+ζ13ζ7−ζ130000000ζ5+ζ23−ζ5−ζ23ζ7+ζ13−ζ7−ζ1300000000000
χ574-440-422−22−4i4i00-2-222022−220002i2−2i2-2-20022002−22−20000000−2i2i−2i2i0000002−22−20000000i2−i2i2−i200000000000
χ584-440-422−22−4i4i001+i31−i3−1−i3−1+i3022−220002i2−2i21+i31−i300−1−i3−1+i300−ζ7+ζ13ζ7−ζ13ζ5−ζ23−ζ5+ζ230000000−2ζ222ζ22−2ζ142ζ14000000−ζ7+ζ13ζ7−ζ13ζ5−ζ23−ζ5+ζ230000000−ζ7−ζ13ζ7+ζ13−ζ5−ζ23ζ5+ζ2300000000000
χ594-440-422−22−4i4i001−i31+i3−1+i3−1−i3022−220002i2−2i21−i31+i300−1+i3−1−i300ζ5−ζ23−ζ5+ζ23−ζ7+ζ13ζ7−ζ130000000−2ζ142ζ14−2ζ222ζ22000000ζ5−ζ23−ζ5+ζ23−ζ7+ζ13ζ7−ζ130000000−ζ5−ζ23ζ5+ζ23−ζ7−ζ13ζ7+ζ1300000000000
χ604-440-4−22224i−4i00-2-2220−22220002i2−2i2-2-2002200−22−2200000002i−2i2i−2i000000−22−220000000i2−i2i2−i200000000000
χ614-440-4−22224i−4i001+i31−i3−1−i3−1+i30−22220002i2−2i21+i31−i300−1−i3−1+i300ζ7−ζ13−ζ7+ζ13−ζ5+ζ23ζ5−ζ2300000002ζ22−2ζ222ζ14−2ζ14000000ζ7−ζ13−ζ7+ζ13−ζ5+ζ23ζ5−ζ230000000−ζ7−ζ13ζ7+ζ13−ζ5−ζ23ζ5+ζ2300000000000
χ624-440-4−22224i−4i001−i31+i3−1+i3−1−i30−22220002i2−2i21−i31+i300−1+i3−1−i300−ζ5+ζ23ζ5−ζ23ζ7−ζ13−ζ7+ζ1300000002ζ14−2ζ142ζ22−2ζ22000000−ζ5+ζ23ζ5−ζ23ζ7−ζ13−ζ7+ζ130000000−ζ5−ζ23ζ5+ζ23−ζ7−ζ13ζ7+ζ1300000000000
χ634-440-4−2222−4i4i00-2-2220−2222000−2i22i2-2-2002200−22−220000000−2i2i−2i2i000000−22−220000000−i2i2−i2i200000000000
χ644-440-4−2222−4i4i001+i31−i3−1−i3−1+i30−2222000−2i22i21+i31−i300−1−i3−1+i300ζ7−ζ13−ζ7+ζ13−ζ5+ζ23ζ5−ζ230000000−2ζ222ζ22−2ζ142ζ14000000ζ7−ζ13−ζ7+ζ13−ζ5+ζ23ζ5−ζ230000000ζ7+ζ13−ζ7−ζ13ζ5+ζ23−ζ5−ζ2300000000000
χ654-440-4−2222−4i4i001−i31+i3−1+i3−1−i30−2222000−2i22i21−i31+i300−1+i3−1−i300−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
χ6866-36-36600660000-3-3-3-20-20000-3-300000000-2-2001-21000000000000000000111000000000000000
χ6966-36-36600-6-60000-3-3-3-20-20000330000000022001-21000000000000000000-1-11000000000000000
χ7066-36-3-6-6006-60000-333-20-20000-3300000000-22001210000000000000000001-1-1000000000000000
χ7166-36-3-6-600-660000-333-20-200003-3000000002-200121000000000000000000-11-1000000000000000
χ728-8-40442−420000-4-4440−2222000002200-2-20022−2222−2200000000000000000−22−220000000000000000000000
χ738-8-40442−4200002+2i32−2i3−2−2i3−2+2i30−222200000−1−i3−1+i3001+i31−i300−2ζ7+2ζ132ζ7−2ζ132ζ5−2ζ23−2ζ5+2ζ2300000000000000000ζ7−ζ13−ζ7+ζ13−ζ5+ζ23ζ5−ζ230000000000000000000000
χ748-8-40442−4200002−2i32+2i3−2+2i3−2−2i30−222200000−1+i3−1−i3001−i31+i3002ζ5−2ζ23−2ζ5+2ζ23−2ζ7+2ζ132ζ7−2ζ1300000000000000000−ζ5+ζ23ζ5−ζ23ζ7−ζ13−ζ7+ζ130000000000000000000000
χ758-8-404−42420000-4-444022−22000002200-2-200−2222−2222000000000000000002−22−20000000000000000000000
χ768-8-404−424200002+2i32−2i3−2−2i3−2+2i3022−2200000−1−i3−1+i3001+i31−i3002ζ7−2ζ13−2ζ7+2ζ13−2ζ5+2ζ232ζ5−2ζ2300000000000000000−ζ7+ζ13ζ7−ζ13ζ5−ζ23−ζ5+ζ230000000000000000000000
χ778-8-404−424200002−2i32+2i3−2+2i3−2−2i3022−2200000−1+i3−1−i3001−i31+i300−2ζ5+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.