Finite Group Databasebeta

← Group #124692

Character table — Group #124692

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11112222222222444444444488888888161616161616161616161616161616161616161616161616
order1222222222444444444488884488888844444444888888881616161616161616
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
χ51111111111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ61111111111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ71111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ81111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ911111-1-1-1-111111-1-111111111-1-111-1-1-1-111-1-111-1-111-1-111-1-111-1-111-1-1
χ1011111-1-1-1-111111-1-111111111-1-111-1-1-1-111-1-111-1-1-1-111-1-111-1-111-1-111
χ1111111-1-1-1-111111-1-111111111-1-111-1-1-1-1-1-111-1-11111-1-111-1-1-1-111-1-111
χ1211111-1-1-1-111111-1-111111111-1-111-1-1-1-1-1-111-1-111-1-111-1-11111-1-111-1-1
χ1311111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ1411111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ1511111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ1611111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ1722222222222222222222-2-2-2-222-2-2-2-2-2-2000000000000000000000000
χ182222222222222222-2-2-2-22222-2-2-2-2-2-222000000000000000000000000
χ192222222222-2-2-2-2-2-222-2-20000-220000000000000000000000i2−i2i2−i2i2−i2i2−i2
χ202222222222-2-2-2-2-2-222-2-20000-220000000000000000000000−i2i2−i2i2−i2i2−i2i2
χ212222222222-2-2-2-2-2-2-2-22200002-200000000000000000000002−22−2−22−22
χ222222222222-2-2-2-2-2-2-2-22200002-20000000000000000000000−22−222−22−2
χ2322222-2-2-2-222222-2-22222-2-2-2-2-2-2-2-22222000000000000000000000000
χ2422222-2-2-2-222222-2-2-2-2-2-2222222-2-222-2-2000000000000000000000000
χ2522222-2-2-2-22-2-2-2-22222-2-200002-20000000000000000000000i2−i2−i2i2i2−i2−i2i2
χ2622222-2-2-2-22-2-2-2-22222-2-200002-20000000000000000000000−i2i2i2−i2−i2i2i2−i2
χ2722222-2-2-2-22-2-2-2-222-2-2220000-2200000000000000000000002−2−22−222−2
χ2822222-2-2-2-22-2-2-2-222-2-2220000-220000000000000000000000−222−22−2−22
χ292222-222-2-2-222-2-22-200002i2i−2i−2i0000002i−2i000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000
χ302222-222-2-2-222-2-22-200002i2i−2i−2i0000002i−2i00000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000
χ312222-222-2-2-222-2-22-20000−2i−2i2i2i000000−2i2i000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000
χ322222-222-2-2-222-2-22-20000−2i−2i2i2i000000−2i2i00000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000
χ332222-2-2-222-222-2-2-2200002i2i−2i−2i000000−2i2i000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i00000000
χ342222-2-2-222-222-2-2-2200002i2i−2i−2i000000−2i2i00000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i00000000
χ352222-2-2-222-222-2-2-220000−2i−2i2i2i0000002i−2i000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i00000000
χ362222-2-2-222-222-2-2-220000−2i−2i2i2i0000002i−2i00000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i00000000
χ3722-2-2-2000022-22-2002i−2i2i−2i2i−2i2i−2i002-20000002i−2i002-20000000000000000
χ3822-2-2-2000022-22-2002i−2i2i−2i2i−2i2i−2i002-2000000−2i2i00-220000000000000000
χ3922-2-2-2000022-22-2002i−2i2i−2i−2i2i−2i2i00-2200002i−2i002-2000000000000000000
χ4022-2-2-2000022-22-2002i−2i2i−2i−2i2i−2i2i00-220000−2i2i00-22000000000000000000
χ4122-2-2-2000022-22-200−2i2i−2i2i2i−2i2i−2i00-2200002i−2i00-22000000000000000000
χ4222-2-2-2000022-22-200−2i2i−2i2i2i−2i2i−2i00-220000−2i2i002-2000000000000000000
χ4322-2-2-2000022-22-200−2i2i−2i2i−2i2i−2i2i002-20000002i−2i00-220000000000000000
χ4422-2-2-2000022-22-200−2i2i−2i2i−2i2i−2i2i002-2000000−2i2i002-20000000000000000
χ454444-444-4-4-4-4-444-440000000000000000000000000000000000000000
χ464444-4-4-444-4-4-4444-40000000000000000000000000000000000000000
χ4744-4-440000-44-4-440000004-4-4400000000000000000000000000000000
χ4844-4-440000-44-4-44000000-444-400000000000000000000000000000000
χ4944-4-440000-4-444-4000000000000004-400000000000000000000000000
χ5044-4-440000-4-444-400000000000000-4400000000000000000000000000
χ5144-4-4-400004-44-44004i−4i−4i4i000000000000000000000000000000000000
χ5244-4-4-400004-44-4400−4i4i4i−4i000000000000000000000000000000000000
χ538-88-80008-800000000000000000000000000000000000000000000000
χ548-88-8000-8800000000000000000000000000000000000000000000000
χ558-8-8808-80000000000000000000000000000000000000000000000000
χ568-8-880-880000000000000000000000000000000000000000000000000

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