Finite Group Databasebeta

← Group #67460

Character table — Group #67460

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36
size1122222444444488888888888888816162424484848
order12236664441212121224888812242424242424242461224448
χ1111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1-1-1-1
χ31111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-11
χ41111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-111-1
χ51111111-1-11-1-1-1-1-11ii−i−i1iiii−i−i−i−i-1111i−i-1
χ61111111-1-11-1-1-1-1-11ii−i−i1iiii−i−i−i−i-11-1-1−ii1
χ71111111-1-11-1-1-1-1-11−i−iii1−i−i−i−iiiii-1111−ii-1
χ81111111-1-11-1-1-1-1-11−i−iii1−i−i−i−iiiii-11-1-1i−i1
χ922222222222222-2-20000200000000-2-200000
χ102222222-2-22-2-2-2-22-200002000000002-200000
χ11222-1-1-1-1222-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-100000
χ12222-1-1-1-1222-1-1-1-122-2-2-2-2-111111111-1-100000
χ13222-1-1-1-1222-1-1-1-1-2-20000-1−i3−i3i3i3−i3−i3i3i31100000
χ14222-1-1-1-1222-1-1-1-1-2-20000-1i3i3−i3−i3i3i3−i3−i31100000
χ15222-1-1-1-1-2-2211112-20000-133−3−3−3−333-1100000
χ16222-1-1-1-1-2-2211112-20000-1−3−33333−3−3-1100000
χ17222-1-1-1-1-2-221111-222i2i−2i−2i-1−i−i−i−iiiii1-100000
χ18222-1-1-1-1-2-221111-22−2i−2i2i2i-1iiii−i−i−i−i1-100000
χ19444444400-40000000000-4000000000000000
χ20444-2-2-2-200-4−2i3−2i32i32i30000002000000000000000
χ21444-2-2-2-200-42i32i3−2i3−2i30000002000000000000000
χ2244-44-4-440000000000000000000000002-2000
χ2344-44-4-44000000000000000000000000-22000
χ244-40400-42i−2i02i−2i2i−2i001+i−1−i1−i−1+i01+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000
χ254-40400-42i−2i02i−2i2i−2i00−1−i1+i−1+i1−i0−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000
χ264-40400-4−2i2i0−2i2i−2i2i001−i−1+i1+i−1−i01−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000
χ274-40400-4−2i2i0−2i2i−2i2i00−1+i1−i−1−i1+i0−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000
χ284-40-2−2i32i322i−2i02ζ7−2ζ72ζ11−2ζ11001+i−1−i1−i−1+i0ζ7−ζ10−ζ7+ζ10−ζ2+ζ11ζ2−ζ11−ζ7−ζ10ζ7+ζ10−ζ2−ζ11ζ2+ζ110000000
χ294-40-2−2i32i322i−2i02ζ7−2ζ72ζ11−2ζ1100−1−i1+i−1+i1−i0−ζ7+ζ10ζ7−ζ10ζ2−ζ11−ζ2+ζ11ζ7+ζ10−ζ7−ζ10ζ2+ζ11−ζ2−ζ110000000
χ304-40-2−2i32i32−2i2i0−2ζ72ζ7−2ζ112ζ11001−i−1+i1+i−1−i0−ζ7−ζ10ζ7+ζ10−ζ2−ζ11ζ2+ζ11ζ7−ζ10−ζ7+ζ10−ζ2+ζ11ζ2−ζ110000000
χ314-40-2−2i32i32−2i2i0−2ζ72ζ7−2ζ112ζ1100−1+i1−i−1−i1+i0ζ7+ζ10−ζ7−ζ10ζ2+ζ11−ζ2−ζ11−ζ7+ζ10ζ7−ζ10ζ2−ζ11−ζ2+ζ110000000
χ324-40-22i3−2i322i−2i02ζ11−2ζ112ζ7−2ζ7001+i−1−i1−i−1+i0−ζ2+ζ11ζ2−ζ11ζ7−ζ10−ζ7+ζ10−ζ2−ζ11ζ2+ζ11−ζ7−ζ10ζ7+ζ100000000
χ334-40-22i3−2i322i−2i02ζ11−2ζ112ζ7−2ζ700−1−i1+i−1+i1−i0ζ2−ζ11−ζ2+ζ11−ζ7+ζ10ζ7−ζ10ζ2+ζ11−ζ2−ζ11ζ7+ζ10−ζ7−ζ100000000
χ344-40-22i3−2i32−2i2i0−2ζ112ζ11−2ζ72ζ7001−i−1+i1+i−1−i0−ζ2−ζ11ζ2+ζ11−ζ7−ζ10ζ7+ζ10−ζ2+ζ11ζ2−ζ11ζ7−ζ10−ζ7+ζ100000000
χ354-40-22i3−2i32−2i2i0−2ζ112ζ11−2ζ72ζ700−1+i1−i−1−i1+i0ζ2+ζ11−ζ2−ζ11ζ7+ζ10−ζ7−ζ10ζ2−ζ11−ζ2+ζ11−ζ7+ζ10ζ7−ζ100000000
χ3688-8-444-400000000000000000000000000000

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