Finite Group Databasebeta

← Group #13136926

Character table — Group #13136926

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111112224448881212121218181818181818181818181824242424242436363636363636363636363648484848727272727272727272
order123366412128242426633662466881212242424241212242424241616161648484848484848486666444121212121212
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-111-1-1-1-1
χ31111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111ii−i−iiiii−i−i−i−i1111-1i−i-1-1ii−i−i
χ41111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111−i−iii−i−i−i−iiiii1111-1−ii-1-1−i−iii
χ5111111111111-1-1-11111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111
χ7111111111111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111ii−i−iiiii−i−i−i−i-1-1-1-11−ii11−i−iii
χ8111111111111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111−i−iii−i−i−i−iiiii-1-1-1-11i−i11ii−i−i
χ9222222222-2-2-200022222222-2-222-2-2-2-222-2-2-2-20000000000000000000000000
χ10222222222-2-2-20002222-2-2-2-222-2-2222222-2-2-2-20000000000000000000000000
χ11222222-2-2-200000022222-22200-2-20000-2-200002−22−222−2−222−2−20000000000000
χ12222222-2-2-200000022222-22200-2-20000-2-20000−22−22−2−222−2−2220000000000000
χ13222222-2-2-20000002222-22-2-200220000-2-20000−i2i2i2−i2−i2−i2i2i2i2i2−i2−i20000000000000
χ14222222-2-2-20000002222-22-2-200220000-2-20000i2−i2−i2i2i2i2−i2−i2−i2−i2i2i20000000000000
χ1533−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i323−3−3i32−3+3i323−3−3i32−3+3i32000011−1−i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32000000ii−i−iζ14ζ22ζ14ζ22−ζ14−ζ22−ζ14−ζ2200001i−i−1−i32−1+i32ζ14ζ22−ζ14−ζ22
χ1633−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i323−3−3i32−3+3i323−3−3i32−3+3i32000011−1−i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32000000−i−iii−ζ14−ζ22−ζ14−ζ22ζ14ζ22ζ14ζ2200001−ii−1−i32−1+i32−ζ14−ζ22ζ14ζ22
χ1733−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i323−3−3i32−3+3i323−3−3i32−3+3i320000-1-11+i321−i32-1-11+i321−i321+i321+i321−i321−i320000001111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i320000-1111+i321−i32−1+i32−1−i32−1+i32−1−i32
χ1833−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i323−3−3i32−3+3i323−3−3i32−3+3i320000-1-11+i321−i32-1-11+i321−i321+i321+i321−i321−i32000000-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i320000-1-1-11+i321−i321−i321+i321−i321+i32
χ1933−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i323−3−3i32−3+3i32-33+3i323−3i32000011−1−i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32000000ii−i−iζ14ζ22ζ14ζ22−ζ14−ζ22−ζ14−ζ220000-1−ii1+i321−i32−ζ14−ζ22ζ14ζ22
χ2033−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i323−3−3i32−3+3i32-33+3i323−3i32000011−1−i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32000000−i−iii−ζ14−ζ22−ζ14−ζ22ζ14ζ22ζ14ζ220000-1i−i1+i321−i32ζ14ζ22−ζ14−ζ22
χ2133−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i323−3−3i32−3+3i32-33+3i323−3i320000-1-11+i321−i32-1-11+i321−i321+i321+i321−i321−i320000001111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3200001-1-1−1−i32−1+i321−i321+i321−i321+i32
χ2233−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i323−3−3i32−3+3i32-33+3i323−3i320000-1-11+i321−i32-1-11+i321−i321+i321+i321−i321−i32000000-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i320000111−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32
χ2333−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i323−3+3i32−3−3i323−3+3i32−3−3i32000011−1+i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32000000ii−i−iζ22ζ14ζ22ζ14−ζ22−ζ14−ζ22−ζ1400001i−i−1+i32−1−i32ζ22ζ14−ζ22−ζ14
χ2433−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i323−3+3i32−3−3i323−3+3i32−3−3i32000011−1+i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32000000−i−iii−ζ22−ζ14−ζ22−ζ14ζ22ζ14ζ22ζ1400001−ii−1+i32−1−i32−ζ22−ζ14ζ22ζ14
χ2533−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i323−3+3i32−3−3i323−3+3i32−3−3i320000-1-11−i321+i32-1-11−i321+i321−i321−i321+i321+i320000001111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i320000-1111−i321+i32−1−i32−1+i32−1−i32−1+i32
χ2633−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i323−3+3i32−3−3i323−3+3i32−3−3i320000-1-11−i321+i32-1-11−i321+i321−i321−i321+i321+i32000000-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i320000-1-1-11−i321+i321+i321−i321+i321−i32
χ2733−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i323−3+3i32−3−3i32-33−3i323+3i32000011−1+i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32000000ii−i−iζ22ζ14ζ22ζ14−ζ22−ζ14−ζ22−ζ140000-1−ii1−i321+i32−ζ22−ζ14ζ22ζ14
χ2833−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i323−3+3i32−3−3i32-33−3i323+3i32000011−1+i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32000000−i−iii−ζ22−ζ14−ζ22−ζ14ζ22ζ14ζ22ζ140000-1i−i1−i321+i32ζ22ζ14−ζ22−ζ14
χ2933−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i323−3+3i32−3−3i32-33−3i323+3i320000-1-11−i321+i32-1-11−i321+i321−i321−i321+i321+i320000001111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3200001-1-1−1+i32−1−i321+i321−i321+i321−i32
χ3033−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i323−3+3i32−3−3i32-33−3i323+3i320000-1-11−i321+i32-1-11−i321+i321−i321−i321+i321+i32000000-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i320000111−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32
χ314444444444444441-21-20000000000001-211-2-200000000000011-2-2000000000
χ32444444444444444-21-21000000000000-21-2-211000000000000-2-211000000000
χ33444444444444-4-4-41-21-20000000000001-211-2-2000000000000-1-122000000000
χ34444444444444-4-4-4-21-21000000000000-21-2-21100000000000022-1-1000000000
χ35444444444-4-4-40001-21-20000000000001-2-1-1220000000000003-300000000000
χ36444444444-4-4-40001-21-20000000000001-2-1-122000000000000-3300000000000
χ37444444444-4-4-4000-21-21000000000000-2122-1-1000000000000003-3000000000
χ38444444444-4-4-4000-21-21000000000000-2122-1-100000000000000-33000000000
χ394-444-4-400000000044-4-40000−2i22i200−2i22i2−2i22i20000000000000000000000000000000
χ404-444-4-400000000044-4-400002i2−2i2002i2−2i22i2−2i20000000000000000000000000000000
χ4166−3−3i3−3+3i3−3−3i3−3+3i36−3−3i3−3+3i3-63+3i33−3i3000000022−1−i3−1+i3-2-2−1−i3−1+i31+i31+i31−i31−i30000000000000000000000000000000
χ4266−3−3i3−3+3i3−3−3i3−3+3i36−3−3i3−3+3i3-63+3i33−3i30000000-2-21+i31−i3221+i31−i3−1−i3−1−i3−1+i3−1+i30000000000000000000000000000000
χ4366−3−3i3−3+3i3−3−3i3−3+3i3-63+3i33−3i300000000002-2−1−i3−1+i3001+i31−i30000000000−i2i2i2−i2ζ5+ζ23ζ7+ζ13−ζ5−ζ23−ζ7−ζ13−ζ5−ζ23−ζ7−ζ13ζ5+ζ23ζ7+ζ130000000000000
χ4466−3−3i3−3+3i3−3−3i3−3+3i3-63+3i33−3i300000000002-2−1−i3−1+i3001+i31−i30000000000i2−i2−i2i2−ζ5−ζ23−ζ7−ζ13ζ5+ζ23ζ7+ζ13ζ5+ζ23ζ7+ζ13−ζ5−ζ23−ζ7−ζ130000000000000
χ4566−3−3i3−3+3i3−3−3i3−3+3i3-63+3i33−3i30000000000-221+i31−i300−1−i3−1+i300000000002−22−2ζ5−ζ23−ζ7+ζ13−ζ5+ζ23ζ7−ζ13ζ5−ζ23−ζ7+ζ13−ζ5+ζ23ζ7−ζ130000000000000
χ4666−3−3i3−3+3i3−3−3i3−3+3i3-63+3i33−3i30000000000-221+i31−i300−1−i3−1+i30000000000−22−22−ζ5+ζ23ζ7−ζ13ζ5−ζ23−ζ7+ζ13−ζ5+ζ23ζ7−ζ13ζ5−ζ23−ζ7+ζ130000000000000
χ4766−3+3i3−3−3i3−3+3i3−3−3i36−3+3i3−3−3i3-63−3i33+3i3000000022−1+i3−1−i3-2-2−1+i3−1−i31−i31−i31+i31+i30000000000000000000000000000000
χ4866−3+3i3−3−3i3−3+3i3−3−3i36−3+3i3−3−3i3-63−3i33+3i30000000-2-21−i31+i3221−i31+i3−1+i3−1+i3−1−i3−1−i30000000000000000000000000000000
χ4966−3+3i3−3−3i3−3+3i3−3−3i3-63−3i33+3i300000000002-2−1+i3−1−i3001−i31+i30000000000−i2i2i2−i2ζ7+ζ13ζ5+ζ23−ζ7−ζ13−ζ5−ζ23−ζ7−ζ13−ζ5−ζ23ζ7+ζ13ζ5+ζ230000000000000
χ5066−3+3i3−3−3i3−3+3i3−3−3i3-63−3i33+3i300000000002-2−1+i3−1−i3001−i31+i30000000000i2−i2−i2i2−ζ7−ζ13−ζ5−ζ23ζ7+ζ13ζ5+ζ23ζ7+ζ13ζ5+ζ23−ζ7−ζ13−ζ5−ζ230000000000000
χ5166−3+3i3−3−3i3−3+3i3−3−3i3-63−3i33+3i30000000000-221−i31+i300−1+i3−1−i300000000002−22−2−ζ7+ζ13ζ5−ζ23ζ7−ζ13−ζ5+ζ23−ζ7+ζ13ζ5−ζ23ζ7−ζ13−ζ5+ζ230000000000000
χ5266−3+3i3−3−3i3−3+3i3−3−3i3-63−3i33+3i30000000000-221−i31+i300−1+i3−1−i30000000000−22−22ζ7−ζ13−ζ5+ζ23−ζ7+ζ13ζ5−ζ23ζ7−ζ13−ζ5+ζ23−ζ7+ζ13ζ5−ζ230000000000000
χ53888888-8-8-80000002-42-4000000000000-2400000000000000000000000000000
χ54888888-8-8-8000000-42-420000000000004-200000000000000000000000000000
χ558-888-8-80000000002-4-240000000000000032−32000000000000000000000000000
χ568-888-8-80000000002-4-2400000000000000−3232000000000000000000000000000
χ578-888-8-8000000000-424-2000000000000000032−320000000000000000000000000
χ588-888-8-8000000000-424-20000000000000000−32320000000000000000000000000
χ5912-12−6−6i3−6+6i36+6i36−6i300000000000000000−2i22i2002ζ7+2ζ13−2ζ7−2ζ132ζ5+2ζ23−2ζ5−2ζ230000000000000000000000000000000
χ6012-12−6−6i3−6+6i36+6i36−6i3000000000000000002i2−2i200−2ζ7−2ζ132ζ7+2ζ13−2ζ5−2ζ232ζ5+2ζ230000000000000000000000000000000
χ6112-12−6+6i3−6−6i36−6i36+6i300000000000000000−2i22i2002ζ5+2ζ23−2ζ5−2ζ232ζ7+2ζ13−2ζ7−2ζ130000000000000000000000000000000
χ6212-12−6+6i3−6−6i36−6i36+6i3000000000000000002i2−2i200−2ζ5−2ζ232ζ5+2ζ23−2ζ7−2ζ132ζ7+2ζ130000000000000000000000000000000

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