Finite Group Databasebeta

← Group #153302

Character table — Group #153302

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41
size1111224444448888888888881616161616161616161632323232323232
order12442424444422448888888824888888884444888
χ111111111111111111111111111111111111111111
χ2111111111111111111111111-1-111-1-111111-1-1-1-1-1-1
χ311111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111-1-1
χ411111111111111111111-1-1-1-1-1-11111-1-1-1-1-11-1-1-111
χ51111111111111111-1-1-1-1111111-1-111-1-1-1-111-1-11-1-1
χ61111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-111-111
χ71111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111
χ81111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1111-1-1-1
χ9222222222222-2-2-2-2000022220000000000-2000000
χ10222222222222-2-2-2-20000-2-2-2-200000000002000000
χ112222222-2-2-2-222-2-220000000000002200000-200000
χ122222222-2-2-2-222-2-22000000000000-2-200000200000
χ132222222-2-2-2-22-222-20000000022000000000000-200
χ142222222-2-2-2-22-222-200000000-2-2000000000000200
χ1522-2-22-2-222-2-2222-2-2000000000000002i2i−2i−2i0000000
χ1622-2-22-2-222-2-2222-2-200000000000000−2i−2i2i2i0000000
χ1722-2-22-2-222-2-22-2-2222i2i−2i−2i0000002i−2i0000000000000
χ1822-2-22-2-222-2-22-2-222−2i−2i2i2i000000−2i2i0000000000000
χ1922-2-22-2-2-2-22222-22-2000000000000000000002i−2i000
χ2022-2-22-2-2-2-22222-22-200000000000000000000−2i2i000
χ2122-2-22-2-2-2-2222-22-22000000000000000000000002-2
χ2222-2-22-2-2-2-2222-22-2200000000000000000000000-22
χ23444444-40000-400002222000000-2-20000000000000
χ24444444-40000-40000-2-2-2-2000000220000000000000
χ2544-4-44-440000-400002i2i−2i−2i000000−2i2i0000000000000
χ2644-4-44-440000-40000−2i−2i2i2i0000002i−2i0000000000000
χ2744-4-4-44000000000000002i2i−2i−2i2-2002i−2i00000000000
χ2844-4-4-44000000000000002i2i−2i−2i-2200−2i2i00000000000
χ2944-4-4-4400000000000000−2i−2i2i2i2-200−2i2i00000000000
χ3044-4-4-4400000000000000−2i−2i2i2i-22002i−2i00000000000
χ314-44i−4i0002-22i−2i000002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ30000001+i−1−i1−i−1+i0000000
χ324-44i−4i0002-22i−2i000002ζ−2ζ2ζ3−2ζ3−2ζ2ζ−2ζ32ζ3000000−1−i1+i−1+i1−i0000000
χ334-44i−4i0002-22i−2i00000−2ζ2ζ−2ζ32ζ32ζ−2ζ2ζ3−2ζ3000000−1−i1+i−1+i1−i0000000
χ344-44i−4i0002-22i−2i00000−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ30000001+i−1−i1−i−1+i0000000
χ354-4−4i4i0002-2−2i2i000002ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ0000001−i−1+i1+i−1−i0000000
χ364-4−4i4i0002-2−2i2i000002ζ3−2ζ32ζ−2ζ−2ζ32ζ3−2ζ2ζ000000−1+i1−i−1−i1+i0000000
χ374-4−4i4i0002-2−2i2i00000−2ζ32ζ3−2ζ2ζ2ζ3−2ζ32ζ−2ζ000000−1+i1−i−1−i1+i0000000
χ384-4−4i4i0002-2−2i2i00000−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ0000001−i−1+i1+i−1−i0000000
χ398888-8-800000000000000000000000000000000000
χ408-88i−8i000-44−4i4i000000000000000000000000000000
χ418-8−8i8i000-444i−4i000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.