Finite Group Databasebeta

← Group #73046

Character table — Group #73046

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44
size1111222222333366666688888888888888882424242424242424
order12442444442244244444366612121212121212121212121224448888
χ111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ511-1-1-11ii−i−i11-1-1-11ii−i−i11-1-111-1-1iiii−i−i−i−i1-11-1i−ii−i
χ611-1-1-11ii−i−i11-1-1-11ii−i−i11-1-111-1-1iiii−i−i−i−i-11-11−ii−ii
χ711-1-1-11−i−iii11-1-1-11−i−iii11-1-111-1-1−i−i−i−iiiii1-11-1−ii−ii
χ811-1-1-11−i−iii11-1-1-11−i−iii11-1-111-1-1−i−i−i−iiiii-11-11i−ii−i
χ922222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000
χ10222222-2-2-2-2222222-2-2-2-2-1-1-1-1-1-1-1-11111111100000000
χ112222-2-200002222-2-2000022-2-2-2-2220000000000000000
χ122222-2-200002222-2-20000-1-11111-1-133−3−333−3−300000000
χ132222-2-200002222-2-20000-1-11111-1-1−3−333−3−33300000000
χ1422-2-22-2000022-2-22-200002222-2-2-2-20000000000000000
χ1522-2-22-2000022-2-22-20000-1-1-1-11111−i3−i3i3i3i3i3−i3−i300000000
χ1622-2-22-2000022-2-22-20000-1-1-1-11111i3i3−i3−i3−i3−i3i3i300000000
χ1722-2-2-222i2i−2i−2i22-2-2-222i2i−2i−2i-1-111-1-111−i−i−i−iiiii00000000
χ1822-2-2-22−2i−2i2i2i22-2-2-22−2i−2i2i2i-1-111-1-111iiii−i−i−i−i00000000
χ192-22i−2i001+i−1−i1−i−1+i2-22i−2i001+i−1−i1−i−1+i2-200002i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000
χ202-22i−2i001+i−1−i1−i−1+i2-22i−2i001+i−1−i1−i−1+i-11−i3i33−3−ii−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ700000000
χ212-22i−2i001+i−1−i1−i−1+i2-22i−2i001+i−1−i1−i−1+i-11i3−i3−33−ii−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ1100000000
χ222-22i−2i00−1−i1+i−1+i1−i2-22i−2i00−1−i1+i−1+i1−i2-200002i−2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000
χ232-22i−2i00−1−i1+i−1+i1−i2-22i−2i00−1−i1+i−1+i1−i-11−i3i33−3−iiζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ700000000
χ242-22i−2i00−1−i1+i−1+i1−i2-22i−2i00−1−i1+i−1+i1−i-11i3−i3−33−iiζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ1100000000
χ252-2−2i2i001−i−1+i1+i−1−i2-2−2i2i001−i−1+i1+i−1−i2-20000−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000
χ262-2−2i2i001−i−1+i1+i−1−i2-2−2i2i001−i−1+i1+i−1−i-11−i3i3−33i−i−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ700000000
χ272-2−2i2i001−i−1+i1+i−1−i2-2−2i2i001−i−1+i1+i−1−i-11i3−i33−3i−i−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ1100000000
χ282-2−2i2i00−1+i1−i−1−i1+i2-2−2i2i00−1+i1−i−1−i1+i2-20000−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000
χ292-2−2i2i00−1+i1−i−1−i1+i2-2−2i2i00−1+i1−i−1−i1+i-11−i3i3−33i−iζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ700000000
χ302-2−2i2i00−1+i1−i−1−i1+i2-2−2i2i00−1+i1−i−1−i1+i-11i3−i33−3i−iζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ1100000000
χ313333333333-1-1-1-1-1-1-1-1-1-1000000000000000011-1-111-1-1
χ323333333333-1-1-1-1-1-1-1-1-1-10000000000000000-1-111-1-111
χ33333333-3-3-3-3-1-1-1-1-1-11111000000000000000011-1-1-1-111
χ34333333-3-3-3-3-1-1-1-1-1-111110000000000000000-1-11111-1-1
χ3533-3-3-333i3i−3i−3i-1-1111-1−i−iii00000000000000001-1-11i−i−ii
χ3633-3-3-333i3i−3i−3i-1-1111-1−i−iii0000000000000000-111-1−iii−i
χ3733-3-3-33−3i−3i3i3i-1-1111-1ii−i−i00000000000000001-1-11−iii−i
χ3833-3-3-33−3i−3i3i3i-1-1111-1ii−i−i0000000000000000-111-1i−i−ii
χ396666-6-60000-2-2-2-2220000000000000000000000000000
χ4066-6-66-60000-2-222-220000000000000000000000000000
χ416-66i−6i003+3i−3−3i3−3i−3+3i-22−2i2i00−1−i1+i−1+i1−i000000000000000000000000
χ426-66i−6i00−3−3i3+3i−3+3i3−3i-22−2i2i001+i−1−i1−i−1+i000000000000000000000000
χ436-6−6i6i003−3i−3+3i3+3i−3−3i-222i−2i00−1+i1−i−1−i1+i000000000000000000000000
χ446-6−6i6i00−3+3i3−3i−3−3i3+3i-222i−2i001−i−1+i1+i−1−i000000000000000000000000

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