Finite Group Databasebeta

← Group #138049

Character table — Group #138049

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11111111222244444444444488888888161616161616161616161616161616161616161616161616
order12222222222244444444444444444444444444448888888888888888
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
χ51111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111
χ81111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1
χ9111111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ10111111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ11111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii
χ12111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ1722222222222222-2-2222222-2-2-2-2-2-222-2-2000000000000000000000000
χ1822222222222222-2-2-2-2-2-222-2-2-2-222-2-222000000000000000000000000
χ19222222222222-2-2222222-2-222-2-2-2-2-2-222000000000000000000000000
χ20222222222222-2-222-2-2-2-2-2-222-2-22222-2-2000000000000000000000000
χ21222-2-22-2-2-2-222002i−2i0000002i−2i002-22i−2i00000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i00000000
χ22222-2-22-2-2-2-222002i−2i0000002i−2i002-22i−2i0000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i00000000
χ23222-2-22-2-2-2-222002i−2i0000002i−2i00-22−2i2i00000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i00000000
χ24222-2-22-2-2-2-222002i−2i0000002i−2i00-22−2i2i0000000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i00000000
χ25222-2-22-2-2-2-22200−2i2i000000−2i2i002-2−2i2i00000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i00000000
χ26222-2-22-2-2-2-22200−2i2i000000−2i2i002-2−2i2i0000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i00000000
χ27222-2-22-2-2-2-22200−2i2i000000−2i2i00-222i−2i00000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i00000000
χ28222-2-22-2-2-2-22200−2i2i000000−2i2i00-222i−2i0000000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i00000000
χ292-2-2-2-22222-22-22-22200002-2-2-22-200000000000000000000002i−2i2i−2i0000
χ302-2-2-2-22222-22-22-22200002-2-2-22-20000000000000000000000−2i2i−2i2i0000
χ312-2-2-2-22222-22-22-2-2-200002-222-22000000000000000000000000002-22-2
χ322-2-2-2-22222-22-22-2-2-200002-222-2200000000000000000000000000-22-22
χ332-2-2-2-22222-22-2-22220000-22-2-2-22000000000000000000000000002i−2i−2i2i
χ342-2-2-2-22222-22-2-22220000-22-2-2-2200000000000000000000000000−2i2i2i−2i
χ352-2-2-2-22222-22-2-22-2-20000-22222-200000000000000000000002-2-220000
χ362-2-2-2-22222-22-2-22-2-20000-22222-20000000000000000000000-222-20000
χ3744444444-4-4-4-4000044-4-4000000000000000000000000000000000000
χ3844444444-4-4-4-40000-4-444000000000000000000000000000000000000
χ39444-4-44-4-444-4-44-4000000-440000000000000000000000000000000000
χ40444-4-44-4-444-4-4-440000004-40000000000000000000000000000000000
χ4144-4-44-44-400000000004i−4i0000000000002-22i−2i00000000000000000000
χ4244-4-44-44-400000000004i−4i000000000000-22−2i2i00000000000000000000
χ4344-4-44-44-40000000000−4i4i0000000000002-2−2i2i00000000000000000000
χ4444-4-44-44-40000000000−4i4i000000000000-222i−2i00000000000000000000
χ454-44-44-4-44000000004-40000000000000000002i−2i2i−2i0000000000000000
χ464-44-44-4-44000000004-4000000000000000000−2i2i−2i2i0000000000000000
χ474-44-44-4-4400000000-440000000000000000002i−2i−2i2i0000000000000000
χ484-44-44-4-4400000000-44000000000000000000−2i2i2i−2i0000000000000000
χ494-4-4444-4-44-4-4444000000-4-40000000000000000000000000000000000
χ504-4-4444-4-44-4-44-4-4000000440000000000000000000000000000000000
χ514-4-4444-4-4-444-4004i−4i000000−4i4i00000000000000000000000000000000
χ524-4-4444-4-4-444-400−4i4i0000004i−4i00000000000000000000000000000000
χ534-4-4-4-4444-44-440000000000000000004-4000000000000000000000000
χ544-4-4-4-4444-44-44000000000000000000-44000000000000000000000000
χ5588-88-8-8-88000000000000000000000000000000000000000000000000
χ568-888-8-88-8000000000000000000000000000000000000000000000000

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