Finite Group Databasebeta

← Group #11724242

Character table — Group #11724242

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48
size11222228888888888889999991818181818181818181818181818185454545454545454
order12236663336666666664488884881212121224242424242424241616161616161616
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
χ911-11-1-11111111-1-1-1-1-1-1111111-1-1-1-1-11111-1-111-1-11-11-11-11-1
χ1011-11-1-11111111-1-1-1-1-1-1111111-1-1-1-1-11111-1-111-1-1-11-11-11-11
χ1111-11-1-11111111-1-1-1-1-1-111-1-1-1-1-111-1-111-1-111-1-111i−ii−i−ii−ii
χ1211-11-1-11111111-1-1-1-1-1-111-1-1-1-1-111-1-111-1-111-1-111−ii−iii−ii−i
χ1311-11-1-11111111-1-1-1-1-1-1-1-1ii−i−i1−ii11-1-1ii−i−i−i−iiiζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13
χ1411-11-1-11111111-1-1-1-1-1-1-1-1ii−i−i1−ii11-1-1ii−i−i−i−iii−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13
χ1511-11-1-11111111-1-1-1-1-1-1-1-1−i−iii1i−i11-1-1−i−iiiii−i−i−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23
χ1611-11-1-11111111-1-1-1-1-1-1-1-1−i−iii1i−i11-1-1−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
χ2122-2-111-12-1-12-1-1-2-21111222222-2-2-211-1-1-1-111-1-11100000000
χ2222-2-111-12-1-12-1-1-2-2111122-2-2-2-2-22211-1-111-1-111-1-100000000
χ2322-2-111-12-1-12-1-1-2-21111-2-22i2i−2i−2i2−2i2i-1-111−i−iiiii−i−i00000000
χ2422-2-111-12-1-12-1-1-2-21111-2-2−2i−2i2i2i22i−2i-1-111ii−i−i−i−iii00000000
χ252-20200-2222-2-2-20000002i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000002i−2i2ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ130000000000
χ262-20200-2222-2-2-20000002i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000002i−2i−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ130000000000
χ272-20200-2222-2-2-2000000−2i2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000−2i2i−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ230000000000
χ282-20200-2222-2-2-2000000−2i2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000−2i2i2ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ230000000000
χ292-20-1−i3i312-1-1-21100−i3−i3i3i32i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130003−3−ii−ζ7−ζ23ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ5+ζ13−ζ5−ζ13ζ5−ζ13−ζ5+ζ1300000000
χ302-20-1−i3i312-1-1-21100−i3−i3i3i32i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130003−3−iiζ7+ζ23−ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ5−ζ13ζ5+ζ13−ζ5+ζ13ζ5−ζ1300000000
χ312-20-1−i3i312-1-1-21100−i3−i3i3i3−2i2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000−33i−iζ5+ζ13−ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ7−ζ23−ζ7+ζ2300000000
χ322-20-1−i3i312-1-1-21100−i3−i3i3i3−2i2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000−33i−i−ζ5−ζ13ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ7+ζ23ζ7−ζ2300000000
χ332-20-1i3−i312-1-1-21100i3i3−i3−i32i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000−33−ii−ζ7−ζ23ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ5+ζ13ζ5−ζ1300000000
χ342-20-1i3−i312-1-1-21100i3i3−i3−i32i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000−33−iiζ7+ζ23−ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ5−ζ13−ζ5+ζ1300000000
χ352-20-1i3−i312-1-1-21100i3i3−i3−i3−2i2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230003−3i−iζ5+ζ13−ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ7−ζ23ζ7+ζ23−ζ7+ζ23ζ7−ζ2300000000
χ362-20-1i3−i312-1-1-21100i3i3−i3−i3−2i2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230003−3i−i−ζ5−ζ13ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ7+ζ23−ζ7−ζ23ζ7−ζ23−ζ7+ζ2300000000
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
χ4088-88-8-88-1-1-1-1-1-111111100000000000000000000000000000
χ4188-8-444-4-11−3i321+3i32-11−3i321+3i3211−1+3i32−1−3i32−1+3i32−1−3i3200000000000000000000000000000
χ4288-8-444-4-11+3i321−3i32-11+3i321−3i3211−1−3i32−1+3i32−1−3i32−1+3i3200000000000000000000000000000
χ438-80800-8-1-1-11113-33-3-3300000000000000000000000000000
χ448-80800-8-1-1-1111-33-333-300000000000000000000000000000
χ458-80-4−4i34i34-11−3i321+3i321−1+3i32−1−3i323-3−3+i323+i323−i32−3−i3200000000000000000000000000000
χ468-80-4−4i34i34-11+3i321−3i321−1−3i32−1+3i32-333+i32−3+i32−3−i323−i3200000000000000000000000000000
χ478-80-44i3−4i34-11−3i321+3i321−1+3i32−1−3i32-333−i32−3−i32−3+i323+i3200000000000000000000000000000
χ488-80-44i3−4i34-11+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.