Finite Group Databasebeta

← Group #130554

Character table — Group #130554

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size1111222244444444444444488888888888881616161616161616161616161632323232
order12222244444444444444444224444444444422444444444448888
χ111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111-1-1-1-1-1-1111-1-1111111-1-1-1-1-1iiii−i−i−i−iii−i−i
χ41111111111111111111-1-1-1-1-1-1111-1-1111111-1-1-1-1-1−i−i−i−iiiii−i−iii
χ5111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-111-1-111-1-11-11-1
χ6111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-111-1-111-11-11
χ7111111111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-111-1-11ii−i−i−i−iiii−i−ii
χ8111111111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-111-1-11−i−iiiii−i−i−iii−i
χ9111111111-1-1-1-11111111111111-1-11111-1-1-1-1-1-1-1-1111111111-1-1-1-1
χ10111111111-1-1-1-11111111111111-1-11111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111
χ11111111111-1-1-1-1111111-1-1-1-1-1-11-1-1-1-111-1-1-1-11111-1iiii−i−i−i−i−i−iii
χ12111111111-1-1-1-1111111-1-1-1-1-1-11-1-1-1-111-1-1-1-11111-1−i−i−i−iiiiiii−i−i
χ13111111111-1-1-1-111-1-1-1-11111111-1-1-1-1-1-1111111-1-1-111-1-111-1-1-11-11
χ14111111111-1-1-1-111-1-1-1-11111111-1-1-1-1-1-1111111-1-1-1-1-111-1-1111-11-1
χ15111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1-111-1-11111-1-1111ii−i−i−i−iii−iii−i
χ16111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1-111-1-11111-1-1111−i−iiiii−i−ii−i−ii
χ172222222222222-2-2000022-2-22-2-2-2-200000000002-20000000000000
χ182222222222222-2-20000-2-222-22-2-2-20000000000-220000000000000
χ19222222222-2-2-2-2-2-2000022-2-22-2-2220000000000-220000000000000
χ20222222222-2-2-2-2-2-20000-2-222-22-22200000000002-20000000000000
χ21222222-2-2-200002222222222-2-2-20022-2-200000000-2000000000000
χ22222222-2-2-20000222222-2-2-2-222-200-2-2-2-2000000002000000000000
χ23222222-2-2-2000022-2-2-2-22222-2-2-200-2-222000000002000000000000
χ24222222-2-2-2000022-2-2-2-2-2-2-2-222-200222200000000-2000000000000
χ25222222-2-2-20000-2-2000022-2-2-22200000022-2-22-2000000000000000
χ26222222-2-2-20000-2-2000022-2-2-222000000-2-222-22000000000000000
χ27222222-2-2-20000-2-20000-2-2222-2200000022-2-2-22000000000000000
χ28222222-2-2-20000-2-20000-2-2222-22000000-2-2222-2000000000000000
χ292-2-222-200000002-222-2-22i−2i2i−2i000002i−2i000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000
χ302-2-222-200000002-222-2-22i−2i2i−2i000002i−2i00000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000
χ312-2-222-200000002-222-2-2−2i2i−2i2i00000−2i2i000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000
χ322-2-222-200000002-222-2-2−2i2i−2i2i00000−2i2i00000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000
χ332-2-222-200000002-2-2-2222i−2i2i−2i00000−2i2i000000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i0000
χ342-2-222-200000002-2-2-2222i−2i2i−2i00000−2i2i00000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000
χ352-2-222-200000002-2-2-222−2i2i−2i2i000002i−2i000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i0000
χ362-2-222-200000002-2-2-222−2i2i−2i2i000002i−2i00000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000
χ374444-4-444-444-4-40000000000000000000000000000000000000000
χ384444-4-444-4-4-4440000000000000000000000000000000000000000
χ394444-4-4-4-44000000000000000004-40000000000000000000000000
χ404444-4-4-4-4400000000000000000-440000000000000000000000000
χ4144-4-4004-40004i−4i002i−2i2i−2i000000000002i−2i2-22-200000000000000000
χ4244-4-4004-40004i−4i00−2i2i−2i2i00000000000−2i2i-22-2200000000000000000
χ4344-4-4004-4000−4i4i002i−2i2i−2i000000000002i−2i-22-2200000000000000000
χ4444-4-4004-4000−4i4i00−2i2i−2i2i00000000000−2i2i2-22-200000000000000000
χ4544-4-400-4404i−4i00002i−2i2i−2i00000000000−2i2i2-2-2200000000000000000
χ4644-4-400-4404i−4i0000−2i2i−2i2i000000000002i−2i-222-200000000000000000
χ4744-4-400-440−4i4i00002i−2i2i−2i00000000000−2i2i-222-200000000000000000
χ4844-4-400-440−4i4i0000−2i2i−2i2i000000000002i−2i2-2-2200000000000000000
χ494-4-444-40000000-4400004i−4i−4i4i000000000000000000000000000000
χ504-4-444-40000000-440000−4i4i4i−4i000000000000000000000000000000
χ518-88-8000000000004i−4i−4i4i0000000000000000000000000000000000
χ528-88-800000000000−4i4i4i−4i0000000000000000000000000000000000
χ538-8-88-8800000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).