Finite Group Databasebeta

← Group #73243

Character table — Group #73243

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11112222224444333366666612121212444488888816161616444488888816161616
order1222448888444422224488884444366612122424242412121212366612122424242412121212
χ111111111111111111111111111111111111111111111111111111111
χ21111111111-1-1-1-11111111111-1-1-1-11111111111-1-1-1-11111111111-1-1-1-1
χ3111111-1-1-1-111-1-1111111-1-1-1-111-1-1111111-1-1-1-111-1-1111111-1-1-1-111-1-1
χ4111111-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-111
χ511-1-1-1111-1-1i−ii−i11-1-1-1111-1-1i−ii−i11-1-1-1111-1-1i−ii−i11-1-1-1111-1-1i−ii−i
χ611-1-1-1111-1-1−ii−ii11-1-1-1111-1-1−ii−ii11-1-1-1111-1-1−ii−ii11-1-1-1111-1-1−ii−ii
χ711-1-1-11-1-111i−i−ii11-1-1-11-1-111i−i−ii11-1-1-11-1-111i−i−ii11-1-1-11-1-111i−i−ii
χ811-1-1-11-1-111−iii−i11-1-1-11-1-111−iii−i11-1-1-11-1-111−iii−i11-1-1-11-1-111−iii−i
χ92222-2-2000000002222-2-2000000002222-2-2000000002222-2-200000000
χ1022-2-22-20000000022-2-22-20000000022-2-22-20000000022-2-22-200000000
χ112-22-200i2−i2i2−i200002-22-200i2−i2i2−i200002-22-200i2−i2i2−i200002-22-200i2−i2i2−i20000
χ122-22-200−i2i2−i2i200002-22-200−i2i2−i2i200002-22-200−i2i2−i2i200002-22-200−i2i2−i2i20000
χ132-2-2200i2−i2−i2i200002-2-2200i2−i2−i2i200002-2-2200i2−i2−i2i200002-2-2200i2−i2−i2i20000
χ142-2-2200−i2i2i2−i200002-2-2200−i2i2i2−i200002-2-2200−i2i2i2−i200002-2-2200−i2i2i2−i20000
χ151111111111111111111111111111−1+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
χ161111111111-1-1-1-11111111111-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32
χ17111111-1-1-1-111-1-1111111-1-1-1-111-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−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−i321+i321+i32
χ18111111-1-1-1-1-1-111111111-1-1-1-1-1-111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32
χ1911-1-1-1111-1-1i−ii−i11-1-1-1111-1-1i−ii−i−1+i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i32ζ14−ζ14ζ14−ζ14−1−i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i32ζ22−ζ22ζ22−ζ22
χ2011-1-1-1111-1-1−ii−ii11-1-1-1111-1-1−ii−ii−1+i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−ζ14ζ14−ζ14ζ14−1−i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−ζ22ζ22−ζ22ζ22
χ2111-1-1-11-1-111i−i−ii11-1-1-11-1-111i−i−ii−1+i32−1+i321−i321−i321−i32−1+i321−i321−i32−1+i32−1+i32ζ14−ζ14−ζ14ζ14−1−i32−1−i321+i321+i321+i32−1−i321+i321+i32−1−i32−1−i32ζ22−ζ22−ζ22ζ22
χ2211-1-1-11-1-111−iii−i11-1-1-11-1-111−iii−i−1+i32−1+i321−i321−i321−i32−1+i321−i321−i32−1+i32−1+i32−ζ14ζ14ζ14−ζ14−1−i32−1−i321+i321+i321+i32−1−i321+i321+i32−1−i32−1−i32−ζ22ζ22ζ22−ζ22
χ232222-2-2000000002222-2-200000000−1+i3−1+i3−1+i3−1+i31−i31−i300000000−1−i3−1−i3−1−i3−1−i31+i31+i300000000
χ2422-2-22-20000000022-2-22-200000000−1+i3−1+i31−i31−i3−1+i31−i300000000−1−i3−1−i31+i31+i3−1−i31+i300000000
χ252-22-200i2−i2i2−i200002-22-200i2−i2i2−i20000−1+i31−i3−1+i31−i300−ζ5−ζ23ζ5+ζ23−ζ5−ζ23ζ5+ζ230000−1−i31+i3−1−i31+i300−ζ7−ζ13ζ7+ζ13−ζ7−ζ13ζ7+ζ130000
χ262-22-200−i2i2−i2i200002-22-200−i2i2−i2i20000−1+i31−i3−1+i31−i300ζ5+ζ23−ζ5−ζ23ζ5+ζ23−ζ5−ζ230000−1−i31+i3−1−i31+i300ζ7+ζ13−ζ7−ζ13ζ7+ζ13−ζ7−ζ130000
χ272-2-2200i2−i2−i2i200002-2-2200i2−i2−i2i20000−1+i31−i31−i3−1+i300−ζ5−ζ23ζ5+ζ23ζ5+ζ23−ζ5−ζ230000−1−i31+i31+i3−1−i300−ζ7−ζ13ζ7+ζ13ζ7+ζ13−ζ7−ζ130000
χ282-2-2200−i2i2i2−i200002-2-2200−i2i2i2−i20000−1+i31−i31−i3−1+i300ζ5+ζ23−ζ5−ζ23−ζ5−ζ23ζ5+ζ230000−1−i31+i31+i3−1−i300ζ7+ζ13−ζ7−ζ13−ζ7−ζ13ζ7+ζ130000
χ291111111111111111111111111111−1−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
χ301111111111-1-1-1-11111111111-1-1-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32
χ31111111-1-1-1-111-1-1111111-1-1-1-111-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+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+i321−i321−i32
χ32111111-1-1-1-1-1-111111111-1-1-1-1-1-111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32
χ3311-1-1-1111-1-1i−ii−i11-1-1-1111-1-1i−ii−i−1−i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i32ζ22−ζ22ζ22−ζ22−1+i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i32ζ14−ζ14ζ14−ζ14
χ3411-1-1-1111-1-1−ii−ii11-1-1-1111-1-1−ii−ii−1−i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−ζ22ζ22−ζ22ζ22−1+i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−ζ14ζ14−ζ14ζ14
χ3511-1-1-11-1-111i−i−ii11-1-1-11-1-111i−i−ii−1−i32−1−i321+i321+i321+i32−1−i321+i321+i32−1−i32−1−i32ζ22−ζ22−ζ22ζ22−1+i32−1+i321−i321−i321−i32−1+i321−i321−i32−1+i32−1+i32ζ14−ζ14−ζ14ζ14
χ3611-1-1-11-1-111−iii−i11-1-1-11-1-111−iii−i−1−i32−1−i321+i321+i321+i32−1−i321+i321+i32−1−i32−1−i32−ζ22ζ22ζ22−ζ22−1+i32−1+i321−i321−i321−i32−1+i321−i321−i32−1+i32−1+i32−ζ14ζ14ζ14−ζ14
χ372222-2-2000000002222-2-200000000−1−i3−1−i3−1−i3−1−i31+i31+i300000000−1+i3−1+i3−1+i3−1+i31−i31−i300000000
χ3822-2-22-20000000022-2-22-200000000−1−i3−1−i31+i31+i3−1−i31+i300000000−1+i3−1+i31−i31−i3−1+i31−i300000000
χ392-22-200i2−i2i2−i200002-22-200i2−i2i2−i20000−1−i31+i3−1−i31+i300−ζ7−ζ13ζ7+ζ13−ζ7−ζ13ζ7+ζ130000−1+i31−i3−1+i31−i300−ζ5−ζ23ζ5+ζ23−ζ5−ζ23ζ5+ζ230000
χ402-22-200−i2i2−i2i200002-22-200−i2i2−i2i20000−1−i31+i3−1−i31+i300ζ7+ζ13−ζ7−ζ13ζ7+ζ13−ζ7−ζ130000−1+i31−i3−1+i31−i300ζ5+ζ23−ζ5−ζ23ζ5+ζ23−ζ5−ζ230000
χ412-2-2200i2−i2−i2i200002-2-2200i2−i2−i2i20000−1−i31+i31+i3−1−i300−ζ7−ζ13ζ7+ζ13ζ7+ζ13−ζ7−ζ130000−1+i31−i31−i3−1+i300−ζ5−ζ23ζ5+ζ23ζ5+ζ23−ζ5−ζ230000
χ422-2-2200−i2i2i2−i200002-2-2200−i2i2i2−i20000−1−i31+i31+i3−1−i300ζ7+ζ13−ζ7−ζ13−ζ7−ζ13ζ7+ζ130000−1+i31−i31−i3−1+i300ζ5+ζ23−ζ5−ζ23−ζ5−ζ23ζ5+ζ230000
χ4333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000000000
χ443333333333-3-3-3-3-1-1-1-1-1-1-1-1-1-111110000000000000000000000000000
χ45333333-3-3-3-333-3-3-1-1-1-1-1-11111-1-1110000000000000000000000000000
χ46333333-3-3-3-3-3-333-1-1-1-1-1-1111111-1-10000000000000000000000000000
χ4733-3-3-3333-3-33i−3i3i−3i-1-1111-1-1-111−ii−ii0000000000000000000000000000
χ4833-3-3-3333-3-3−3i3i−3i3i-1-1111-1-1-111i−ii−i0000000000000000000000000000
χ4933-3-3-33-3-3333i−3i−3i3i-1-1111-111-1-1−iii−i0000000000000000000000000000
χ5033-3-3-33-3-333−3i3i3i−3i-1-1111-111-1-1i−i−ii0000000000000000000000000000
χ516666-6-600000000-2-2-2-222000000000000000000000000000000000000
χ5266-6-66-600000000-2-222-22000000000000000000000000000000000000
χ536-66-6003i2−3i23i2−3i20000-22-2200−i2i2−i2i200000000000000000000000000000000
χ546-66-600−3i23i2−3i23i20000-22-2200i2−i2i2−i200000000000000000000000000000000
χ556-6-66003i2−3i2−3i23i20000-222-200−i2i2i2−i200000000000000000000000000000000
χ566-6-6600−3i23i23i2−3i20000-222-200i2−i2−i2i200000000000000000000000000000000

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