Finite Group Databasebeta

← Group #135401

Character table — Group #135401

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11112222224444444444444444888888161616161616161616161616161616161616161616161616
order124422244422444444888888884488888888888816161616161616161616161616161616
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i
χ6111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii
χ7111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii
χ8111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i
χ91111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-11111-1-111-1-111-1-111-1-1
χ101111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-111-1-111-1-111-1-111-1-111
χ111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-111-1-111-1-1-1-111-1-111
χ121111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-111-1-11111-1-111-1-1
χ131111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1ii−i−i−i−iiiii−i−i−i−iii
χ141111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1−i−iiiii−i−i−i−iiiii−i−i
χ151111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111ii−i−i−i−iii−i−iiiii−i−i
χ161111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111−i−iiiii−i−iii−i−i−i−iii
χ1722222222222222-2-2-2-22222-2-2-2-2-2-222-2-2000000000000000000000000
χ1822222222222222-2-2-2-2-2-2-2-22222-2-2-2-222000000000000000000000000
χ192222222222-2-2-2-222222222-2-2-2-2-2-2-2-222000000000000000000000000
χ202222222222-2-2-2-22222-2-2-2-22222-2-222-2-2000000000000000000000000
χ2122222-2-22-2-200002i2i−2i−2i00002i2i−2i−2i002-200000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i00000000
χ2222222-2-22-2-200002i2i−2i−2i00002i2i−2i−2i002-20000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i00000000
χ2322222-2-22-2-200002i2i−2i−2i0000−2i−2i2i2i00-2200000000001−i−1+i−1−i1+i1+i−1−i−1+i1−i00000000
χ2422222-2-22-2-200002i2i−2i−2i0000−2i−2i2i2i00-220000000000−1+i1−i1+i−1−i−1−i1+i1−i−1+i00000000
χ2522222-2-22-2-20000−2i−2i2i2i00002i2i−2i−2i00-2200000000001+i−1−i−1+i1−i1−i−1+i−1−i1+i00000000
χ2622222-2-22-2-20000−2i−2i2i2i00002i2i−2i−2i00-220000000000−1−i1+i1−i−1+i−1+i1−i1+i−1−i00000000
χ2722222-2-22-2-20000−2i−2i2i2i0000−2i−2i2i2i002-200000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i00000000
χ2822222-2-22-2-20000−2i−2i2i2i0000−2i−2i2i2i002-20000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i00000000
χ292222-22-2-22-200002i−2i2i−2i2i2i−2i−2i000000002-200000000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i
χ302222-22-2-22-200002i−2i2i−2i2i2i−2i−2i000000002-20000000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i
χ312222-22-2-22-200002i−2i2i−2i−2i−2i2i2i00000000-2200000000000000001−i−1+i−1−i1+i1+i−1−i−1+i1−i
χ322222-22-2-22-200002i−2i2i−2i−2i−2i2i2i00000000-220000000000000000−1+i1−i1+i−1−i−1−i1+i1−i−1+i
χ332222-22-2-22-20000−2i2i−2i2i2i2i−2i−2i00000000-2200000000000000001+i−1−i−1+i1−i1−i−1+i−1−i1+i
χ342222-22-2-22-20000−2i2i−2i2i2i2i−2i−2i00000000-220000000000000000−1−i1+i1−i−1+i−1+i1−i1+i−1−i
χ352222-22-2-22-20000−2i2i−2i2i−2i−2i2i2i000000002-200000000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i
χ362222-22-2-22-20000−2i2i−2i2i−2i−2i2i2i000000002-20000000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i
χ3722-2-2-2-2222-2000000002-22-22-22-22-20000002i−2i2i−2i000000000000000000
χ3822-2-2-2-2222-2000000002-22-22-22-22-2000000−2i2i−2i2i000000000000000000
χ3922-2-2-2-2222-2000000002-22-2-22-22-2200002i−2i00002i−2i0000000000000000
χ4022-2-2-2-2222-2000000002-22-2-22-22-220000−2i2i0000−2i2i0000000000000000
χ4122-2-2-2-2222-200000000-22-222-22-2-2200002i−2i0000−2i2i0000000000000000
χ4222-2-2-2-2222-200000000-22-222-22-2-220000−2i2i00002i−2i0000000000000000
χ4322-2-2-2-2222-200000000-22-22-22-222-20000002i−2i−2i2i000000000000000000
χ4422-2-2-2-2222-200000000-22-22-22-222-2000000−2i2i2i−2i000000000000000000
χ454444-4-44-4-4400004-4-4400000000000000000000000000000000000000
χ464444-4-44-4-440000-444-400000000000000000000000000000000000000
χ4744-4-4444-4-4-444-4-4000000000000000000000000000000000000000000
χ4844-4-4444-4-4-4-4-444000000000000000000000000000000000000000000
χ4944-4-44-4-4-444000000004i−4i−4i4i0000000000000000000000000000000000
χ5044-4-44-4-4-44400000000−4i4i4i−4i0000000000000000000000000000000000
χ5144-4-4-44-44-440000000000004i−4i−4i4i000000000000000000000000000000
χ5244-4-4-44-44-44000000000000−4i4i4i−4i000000000000000000000000000000
χ538-88i−8i0000004-44i−4i000000000000000000000000000000000000000000
χ548-88i−8i000000-44−4i4i000000000000000000000000000000000000000000
χ558-8−8i8i0000004-4−4i4i000000000000000000000000000000000000000000
χ568-8−8i8i000000-444i−4i000000000000000000000000000000000000000000

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