Finite Group Databasebeta

← Group #67521

Character table — Group #67521

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42
size112222222444444444488888888888888888242424244848
order122344612126888812242424244121216161616242448484848484848481616161644
χ1111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1
χ41111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111
χ51111111111-1-1-1-11-1-1-1-1111ii−i−i-1-1iiii−i−i−i−iii−i−i1-1
χ61111111111-1-1-1-11-1-1-1-1111ii−i−i-1-1iiii−i−i−i−i−i−iii-11
χ71111111111-1-1-1-11-1-1-1-1111−i−iii-1-1−i−i−i−iiiiiii−i−i-11
χ81111111111-1-1-1-11-1-1-1-1111−i−iii-1-1−i−i−i−iiiii−i−iii1-1
χ9222222222222-2-222222-2-2-20000-2-200000000000000
χ102222222222-2-2222-2-2-2-2-2-2-200002200000000000000
χ11222-122-1-1-1-12222-1-1-1-1-12-1-12222-1-1-1-1-1-1-1-1-1-1000000
χ12222-122-1-1-1-12222-1-1-1-1-12-1-1-2-2-2-2-1-111111111000000
χ13222-122-1-1-1-122-2-2-1-1-1-1-1-211000011−i3−i3i3i3−i3−i3i3i3000000
χ14222-122-1-1-1-122-2-2-1-1-1-1-1-211000011i3i3−i3−i3i3i3−i3−i3000000
χ15222-122-1-1-1-1-2-222-11111-2110000-1-133−3−3−3−333000000
χ16222-122-1-1-1-1-2-222-11111-2110000-1-1−3−33333−3−3000000
χ17222-122-1-1-1-1-2-2-2-2-111112-1-12i2i−2i−2i11−i−i−i−iiiii000000
χ18222-122-1-1-1-1-2-2-2-2-111112-1-1−2i−2i2i2i11iiii−i−i−i−i000000
χ1922-222-2222-2002i−2i-200000001+i−1−i1−i−1+i2i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000
χ2022-222-2222-2002i−2i-20000000−1−i1+i−1+i1−i2i−2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000
χ2122-222-2222-200−2i2i-200000001−i−1+i1+i−1−i−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000
χ2222-222-2222-200−2i2i-20000000−1+i1−i−1−i1+i−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000
χ2322-22-222-2-2-22i−2i0022i2i−2i−2i000000000000000001+i−1−i1−i−1+i00
χ2422-22-222-2-2-22i−2i0022i2i−2i−2i00000000000000000−1−i1+i−1+i1−i00
χ2522-22-222-2-2-2−2i2i002−2i−2i2i2i000000000000000001−i−1+i1+i−1−i00
χ2622-22-222-2-2-2−2i2i002−2i−2i2i2i00000000000000000−1+i1−i−1−i1+i00
χ2722-2-12-2-1-1-11002i−2i1−i3i3−i3i303−31+i−1−i1−i−1+i−ii−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11000000
χ2822-2-12-2-1-1-11002i−2i1−i3i3−i3i303−3−1−i1+i−1+i1−i−iiζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11000000
χ2922-2-12-2-1-1-11002i−2i1i3−i3i3−i30−331+i−1−i1−i−1+i−ii−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7000000
χ3022-2-12-2-1-1-11002i−2i1i3−i3i3−i30−33−1−i1+i−1+i1−i−iiζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7000000
χ3122-2-12-2-1-1-1100−2i2i1−i3i3−i3i30−331−i−1+i1+i−1−ii−i−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11000000
χ3222-2-12-2-1-1-1100−2i2i1−i3i3−i3i30−33−1+i1−i−1−i1+ii−iζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11000000
χ3322-2-12-2-1-1-1100−2i2i1i3−i3i3−i303−31−i−1+i1+i−1−ii−i−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7000000
χ3422-2-12-2-1-1-1100−2i2i1i3−i3i3−i303−3−1+i1−i−1−i1+ii−iζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7000000
χ354444-4-44-4-440000-4000000000000000000000000000
χ36444-2-4-4-222-20000223−23−232300000000000000000000000
χ37444-2-4-4-222-200002−232323−2300000000000000000000000
χ3844-4-2-44-22224i−4i00-2−2i−2i2i2i00000000000000000000000
χ3944-4-2-44-2222−4i4i00-22i2i−2i−2i00000000000000000000000
χ408-80800-800000000000000000000000000000000000
χ418-80-400443−43000000000000000000000000000000000
χ428-80-4004−4343000000000000000000000000000000000

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