Finite Group Databasebeta

← Group #73073

Character table — Group #73073

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40
size11112222226666888888888888888812122424242424242424
order1244244444224436661212121212121212121212124424448888
χ11111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ4111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ511-1-1-11ii−i−i1-1-1111-1-111-1-1iiii−i−i−i−ii−i1-1i−ii−i1-1
χ611-1-1-11ii−i−i1-1-1111-1-111-1-1iiii−i−i−i−ii−i-11−ii−ii-11
χ711-1-1-11−i−iii1-1-1111-1-111-1-1−i−i−i−iiiii−ii1-1−ii−ii1-1
χ811-1-1-11−i−iii1-1-1111-1-111-1-1−i−i−i−iiiii−ii-11i−ii−i-11
χ922222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12200000000
χ10222222-2-2-2-22222-1-1-1-1-1-1-1-111111111-2-200000000
χ112222-2-20000-22-2222-2-2-2-222000000000000000000
χ122222-2-20000-22-22-1-11111-1-133−3−333−3−30000000000
χ132222-2-20000-22-22-1-11111-1-1−3−333−3−3330000000000
χ1422-2-22-20000-2-2222222-2-2-2-2000000000000000000
χ1522-2-22-20000-2-222-1-1-1-11111−i3−i3i3i3i3i3−i3−i30000000000
χ1622-2-22-20000-2-222-1-1-1-11111i3i3−i3−i3−i3−i3i3i30000000000
χ1722-2-2-222i2i−2i−2i2-2-22-1-111-1-111−i−i−i−iiiii2i−2i00000000
χ1822-2-2-22−2i−2i2i2i2-2-22-1-111-1-111iiii−i−i−i−i−2i2i00000000
χ193333333333-1-1-1-10000000000000000-1-111-1-111-1-1
χ203333333333-1-1-1-10000000000000000-1-1-1-111-1-111
χ21333333-3-3-3-3-1-1-1-10000000000000000111111-1-1-1-1
χ22333333-3-3-3-3-1-1-1-1000000000000000011-1-1-1-11111
χ2333-3-3-333i3i−3i−3i-111-10000000000000000−ii1-1−iii−i-11
χ2433-3-3-333i3i−3i−3i-111-10000000000000000−ii-11i−i−ii1-1
χ2533-3-3-33−3i−3i3i3i-111-10000000000000000i−i1-1i−i−ii-11
χ2633-3-3-33−3i−3i3i3i-111-10000000000000000i−i-11−iii−i1-1
χ274-44i−4i002+2i−2−2i2−2i−2+2i00001-1−i3i33−3i−iζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ10+ζ11−ζ10−ζ11−ζ2−ζ7ζ2+ζ70000000000
χ284-44i−4i002+2i−2−2i2−2i−2+2i00001-1i3−i3−33i−iζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ2+ζ7−ζ2−ζ7−ζ10−ζ11ζ10+ζ110000000000
χ294-44i−4i002+2i−2−2i2−2i−2+2i0000-220000−2i2i−1−i1+i−1−i1+i−1+i1−i1−i−1+i0000000000
χ304-44i−4i00−2−2i2+2i−2+2i2−2i00001-1−i3i33−3i−i−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ10−ζ11ζ10+ζ11ζ2+ζ7−ζ2−ζ70000000000
χ314-44i−4i00−2−2i2+2i−2+2i2−2i00001-1i3−i3−33i−i−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ2−ζ7ζ2+ζ7ζ10+ζ11−ζ10−ζ110000000000
χ324-44i−4i00−2−2i2+2i−2+2i2−2i0000-220000−2i2i1+i−1−i1+i−1−i1−i−1+i−1+i1−i0000000000
χ334-4−4i4i002−2i−2+2i2+2i−2−2i00001-1−i3i3−33−iiζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ10−ζ11−ζ10+ζ11−ζ2+ζ7ζ2−ζ70000000000
χ344-4−4i4i002−2i−2+2i2+2i−2−2i00001-1i3−i33−3−iiζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ2−ζ7−ζ2+ζ7−ζ10+ζ11ζ10−ζ110000000000
χ354-4−4i4i002−2i−2+2i2+2i−2−2i0000-2200002i−2i−1+i1−i−1+i1−i−1−i1+i1+i−1−i0000000000
χ364-4−4i4i00−2+2i2−2i−2−2i2+2i00001-1−i3i3−33−ii−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ10+ζ11ζ10−ζ11ζ2−ζ7−ζ2+ζ70000000000
χ374-4−4i4i00−2+2i2−2i−2−2i2+2i00001-1i3−i33−3−ii−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ2+ζ7ζ2−ζ7ζ10−ζ11−ζ10+ζ110000000000
χ384-4−4i4i00−2+2i2−2i−2−2i2+2i0000-2200002i−2i1−i−1+i1−i−1+i1+i−1−i−1−i1+i0000000000
χ396666-6-600002-22-200000000000000000000000000
χ4066-6-66-6000022-2-200000000000000000000000000

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