Finite Group Databasebeta

← Group #4464

Character table — Group #4464

Order 192.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39
size111122222222222244444444444444444121212122424
order1222344446661212121248888121212122424242424242424888824
χ1111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1
χ311111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1
χ411111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111
χ511111-1-1-1-1111-1-1-1-11ii−i−i11-1-1iiii−i−i−i−iii−i−i1-1
χ611111-1-1-1-1111-1-1-1-11ii−i−i11-1-1iiii−i−i−i−i−i−iii-11
χ711111-1-1-1-1111-1-1-1-11−i−iii11-1-1−i−i−i−iiiiiii−i−i-11
χ811111-1-1-1-1111-1-1-1-11−i−iii11-1-1−i−i−i−iiiii−i−iii1-1
χ92222222-2-22222222-20000-2-2-2-200000000000000
χ1022222-2-222222-2-2-2-2-20000-2-22200000000000000
χ112222-12222-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-1-1000000
χ122222-12222-1-1-1-1-1-1-12-2-2-2-2-1-1-1-111111111000000
χ132222-122-2-2-1-1-1-1-1-1-1-200001111−i3−i3i3i3−i3−i3i3i3000000
χ142222-122-2-2-1-1-1-1-1-1-1-200001111i3i3−i3−i3i3i3−i3−i3000000
χ152222-1-2-222-1-1-11111-2000011-1-133−3−3−3−333000000
χ162222-1-2-222-1-1-11111-2000011-1-1−3−33333−3−3000000
χ172222-1-2-2-2-2-1-1-1111122i2i−2i−2i-1-111−i−i−i−iiiii000000
χ182222-1-2-2-2-2-1-1-111112−2i−2i2i2i-1-111iiii−i−i−i−i000000
χ1922-2-22002i−2i2-2-2000001+i−1−i1−i−1+i002i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000
χ2022-2-22002i−2i2-2-200000−1−i1+i−1+i1−i002i−2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000
χ2122-2-2200−2i2i2-2-2000001−i−1+i1+i−1−i00−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000
χ2222-2-2200−2i2i2-2-200000−1+i1−i−1−i1+i00−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000
χ2322-2-2-1002i−2i-111−i3−i3i3i301+i−1−i1−i−1+i3−3−ii−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11000000
χ2422-2-2-1002i−2i-111−i3−i3i3i30−1−i1+i−1+i1−i3−3−iiζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11000000
χ2522-2-2-1002i−2i-111i3i3−i3−i301+i−1−i1−i−1+i−33−ii−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7000000
χ2622-2-2-1002i−2i-111i3i3−i3−i30−1−i1+i−1+i1−i−33−iiζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7000000
χ2722-2-2-100−2i2i-111−i3−i3i3i301−i−1+i1+i−1−i−33i−i−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11000000
χ2822-2-2-100−2i2i-111−i3−i3i3i30−1+i1−i−1−i1+i−33i−iζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11000000
χ2922-2-2-100−2i2i-111i3i3−i3−i301−i−1+i1+i−1−i3−3i−i−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7000000
χ3022-2-2-100−2i2i-111i3i3−i3−i30−1+i1−i−1−i1+i3−3i−iζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7000000
χ312-22-222i−2i00-22-22i−2i2i−2i000000000000000001+i−1−i1−i−1+i00
χ322-22-222i−2i00-22-22i−2i2i−2i00000000000000000−1−i1+i−1+i1−i00
χ332-22-22−2i2i00-22-2−2i2i−2i2i000000000000000001−i−1+i1+i−1−i00
χ342-22-22−2i2i00-22-2−2i2i−2i2i00000000000000000−1+i1−i−1−i1+i00
χ354-44-4-24i−4i002-22−2i2i−2i2i00000000000000000000000
χ364-44-4-2−4i4i002-222i−2i2i−2i00000000000000000000000
χ374-4-4440000-4-44000000000000000000000000000
χ384-4-44-2000022-223−23−232300000000000000000000000
χ394-4-44-2000022-2−232323−2300000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.