Finite Group Databasebeta

← Group #11724243

Character table — Group #11724243

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48
size11222228888888888889999991818181818181818181818181818185454545454545454
order12236663336666666662244442446666121212121212121288888888
χ1111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111-1-1-1-11-1-11111-1-1-1-1-1-1-1-1iiii−i−i−i−i
χ4111111111111111111111-1-1-1-11-1-11111-1-1-1-1-1-1-1-1−i−i−i−iiiii
χ51111111111111111111-1-1ii−i−i-1i−i-1-1-1-1iiii−i−i−i−iζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13
χ61111111111111111111-1-1ii−i−i-1i−i-1-1-1-1iiii−i−i−i−i−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13
χ71111111111111111111-1-1−i−iii-1−ii-1-1-1-1−i−i−i−iiiii−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23
χ81111111111111111111-1-1−i−iii-1−ii-1-1-1-1−i−i−i−iiiiiζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23
χ911-111-1-1111111-1-1-1-1-1-1111111-1-1-11-1-1111-1-111-1-11-11-11-11-1
χ1011-111-1-1111111-1-1-1-1-1-1111111-1-1-11-1-1111-1-111-1-1-11-11-11-11
χ1111-111-1-1111111-1-1-1-1-1-111-1-1-1-1-1111-1-11-1-111-1-111i−ii−i−ii−ii
χ1211-111-1-1111111-1-1-1-1-1-111-1-1-1-1-1111-1-11-1-111-1-111−ii−iii−ii−i
χ1311-111-1-1111111-1-1-1-1-1-1-1-1ii−i−i1−ii-111-1ii−i−i−i−iiiζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13
χ1411-111-1-1111111-1-1-1-1-1-1-1-1ii−i−i1−ii-111-1ii−i−i−i−iii−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13
χ1511-111-1-1111111-1-1-1-1-1-1-1-1−i−iii1i−i-111-1−i−iiiii−i−i−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23
χ1611-111-1-1111111-1-1-1-1-1-1-1-1−i−iii1i−i-111-1−i−iiiii−i−iζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23
χ17222-1-1-1-12-1-12-1-122-1-1-1-1222222222-1-1-1-1-1-1-1-1-1-1-1-100000000
χ18222-1-1-1-12-1-12-1-122-1-1-1-122-2-2-2-22-2-2-1-1-1-11111111100000000
χ19222-1-1-1-12-1-12-1-122-1-1-1-1-2-22i2i−2i−2i-22i−2i1111−i−i−i−iiiii00000000
χ20222-1-1-1-12-1-12-1-122-1-1-1-1-2-2−2i−2i2i2i-2−2i2i1111iiii−i−i−i−i00000000
χ2122-2-1-1112-1-12-1-1-2-21111222222-2-2-2-111-1-1-111-1-11100000000
χ2222-2-1-1112-1-12-1-1-2-2111122-2-2-2-2-222-111-111-1-111-1-100000000
χ2322-2-1-1112-1-12-1-1-2-21111-2-22i2i−2i−2i2−2i2i1-1-11−i−iiiii−i−i00000000
χ2422-2-1-1112-1-12-1-1-2-21111-2-2−2i−2i2i2i22i−2i1-1-11ii−i−i−i−iii00000000
χ252-202-200222-2-2-20000002-22i−2i2i−2i000200-22i−2i002i−2i0000000000
χ262-202-200222-2-2-20000002-2−2i2i−2i2i000200-2−2i2i00−2i2i0000000000
χ272-202-200222-2-2-2000000-222-2-22000-20022-200-220000000000
χ282-202-200222-2-2-2000000-22-222-2000-2002-22002-20000000000
χ292-20-11−i3i32-1-1-21100−i3−i3i3i32-22i−2i2i−2i000-1−i3i31−ii3−3−ii3−300000000
χ302-20-11−i3i32-1-1-21100−i3−i3i3i32-2−2i2i−2i2i000-1−i3i31i−i−33i−i−3300000000
χ312-20-11−i3i32-1-1-21100−i3−i3i3i3-222-2-220001i3−i3-1-11−i3i31-1i3−i300000000
χ322-20-11−i3i32-1-1-21100−i3−i3i3i3-22-222-20001i3−i3-11-1i3−i3-11−i3i300000000
χ332-20-11i3−i32-1-1-21100i3i3−i3−i32-22i−2i2i−2i000-1i3−i31−ii−33−ii−3300000000
χ342-20-11i3−i32-1-1-21100i3i3−i3−i32-2−2i2i−2i2i000-1i3−i31i−i3−3i−i3−300000000
χ352-20-11i3−i32-1-1-21100i3i3−i3−i3-222-2-220001−i3i3-1-11i3−i31-1−i3i300000000
χ362-20-11i3−i32-1-1-21100i3i3−i3−i3-22-222-20001−i3i3-11-1−i3i3-11i3−i300000000
χ378888888-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000000
χ38888-4-4-4-4-11−3i321+3i32-11−3i321+3i32-1-11−3i321+3i321−3i321+3i3200000000000000000000000000000
χ39888-4-4-4-4-11+3i321−3i32-11+3i321−3i32-1-11+3i321−3i321+3i321−3i3200000000000000000000000000000
χ4088-888-8-8-1-1-1-1-1-111111100000000000000000000000000000
χ4188-8-4-444-11−3i321+3i32-11−3i321+3i3211−1+3i32−1−3i32−1+3i32−1−3i3200000000000000000000000000000
χ4288-8-4-444-11+3i321−3i32-11+3i321−3i3211−1−3i32−1+3i32−1−3i32−1+3i3200000000000000000000000000000
χ438-808-800-1-1-11113-33-3-3300000000000000000000000000000
χ448-808-800-1-1-1111-33-333-300000000000000000000000000000
χ458-80-44−4i34i3-11−3i321+3i321−1+3i32−1−3i323-3−3+i323+i323−i32−3−i3200000000000000000000000000000
χ468-80-44−4i34i3-11+3i321−3i321−1−3i32−1+3i32-333+i32−3+i32−3−i323−i3200000000000000000000000000000
χ478-80-444i3−4i3-11−3i321+3i321−1+3i32−1−3i32-333−i32−3−i32−3+i323+i3200000000000000000000000000000
χ488-80-444i3−4i3-11+3i321−3i321−1−3i32−1+3i323-3−3−i323−i323+i32−3+i3200000000000000000000000000000

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