Finite Group Databasebeta

← Group #124690

Character table — Group #124690

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11112222222222444444444488888888161616161616161616161616161616161616161616161616
order12442224444444224444444444444444444488888888888888888888
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111-1-1-1-1111111-1-1-1-111-1-111-1-11111-1-1-1-111-1-11111-1-1-1-1
χ611111111111111-1-1-1-1111111-1-1-1-111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-11111
χ711111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-11111
χ811111111111111-1-1-1-1111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1111111-1-1-1-1
χ9111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111111111ii−i−iii−i−i-1-1-1-1ii−i−iii−i−i
χ10111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111111111−i−iii−i−iii-1-1-1-1−i−iii−i−iii
χ11111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1ii−i−iii−i−i1111−i−iii−i−iii
χ12111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1−i−iii−i−iii1111ii−i−iii−i−i
χ13111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1ii−i−i−i−iii-1-111ii−i−i−i−iii
χ14111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1−i−iiiii−i−i-1-111−i−iiiii−i−i
χ15111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111ii−i−i−i−iii11-1-1−i−iiiii−i−i
χ16111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111−i−iiiii−i−i11-1-1ii−i−i−i−iii
χ1722222222222222222222-2-2-2-222-2-2-2-2-2-2000000000000000000000000
χ1822222222222222-2-2-2-222-2-2-2-2-2-222-2-222000000000000000000000000
χ19222222222-2-2-2-222222-2-22222-2-222-2-2-2-2000000000000000000000000
χ20222222222-2-2-2-22-2-2-2-2-2-2222222-2-2-2-222000000000000000000000000
χ2122222-2-22-22222-22-22-2-2-200002-20000000000000000000000i2−i2i2−i2i2−i2i2−i2
χ2222222-2-22-22222-22-22-2-2-200002-20000000000000000000000−i2i2−i2i2−i2i2−i2i2
χ2322222-2-22-22222-2-22-22-2-20000-220000000000000000000000i2−i2i2−i2−i2i2−i2i2
χ2422222-2-22-22222-2-22-22-2-20000-220000000000000000000000−i2i2−i2i2i2−i2i2−i2
χ2522222-2-22-2-2-2-2-2-22-22-2220000-2200000000000000000000002−2−222−2−22
χ2622222-2-22-2-2-2-2-2-22-22-2220000-220000000000000000000000−222−2−222−2
χ2722222-2-22-2-2-2-2-2-2-22-222200002-200000000000000000000002−2−22−222−2
χ2822222-2-22-2-2-2-2-2-2-22-222200002-20000000000000000000000−222−22−2−22
χ2922-2-22-2-2-22000022-2-22002i2i−2i−2i002i−2i000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i000000000000
χ3022-2-22-2-2-22000022-2-22002i2i−2i−2i002i−2i00000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i000000000000
χ3122-2-22-2-2-22000022-2-2200−2i−2i2i2i00−2i2i000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i000000000000
χ3222-2-22-2-2-22000022-2-2200−2i−2i2i2i00−2i2i00000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i000000000000
χ3322-2-22-2-2-2200002-222-2002i2i−2i−2i00−2i2i000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i000000000000
χ3422-2-22-2-2-2200002-222-2002i2i−2i−2i00−2i2i00000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i000000000000
χ3522-2-22-2-2-2200002-222-200−2i−2i2i2i002i−2i000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i000000000000
χ3622-2-22-2-2-2200002-222-200−2i−2i2i2i002i−2i00000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i000000000000
χ3722-2-2-2-22222i2i−2i−2i-200002i−2i2i−2i2i−2i00002-200002-200000000002i−2i00000000
χ3822-2-2-2-22222i2i−2i−2i-200002i−2i2i−2i2i−2i00002-20000-220000000000−2i2i00000000
χ3922-2-2-2-22222i2i−2i−2i-200002i−2i−2i2i−2i2i0000-22002-200000000002i−2i0000000000
χ4022-2-2-2-22222i2i−2i−2i-200002i−2i−2i2i−2i2i0000-2200-220000000000−2i2i0000000000
χ4122-2-2-2-2222−2i−2i2i2i-20000−2i2i2i−2i2i−2i0000-22002-20000000000−2i2i0000000000
χ4222-2-2-2-2222−2i−2i2i2i-20000−2i2i2i−2i2i−2i0000-2200-2200000000002i−2i0000000000
χ4322-2-2-2-2222−2i−2i2i2i-20000−2i2i−2i2i−2i2i00002-200002-20000000000−2i2i00000000
χ4422-2-2-2-2222−2i−2i2i2i-20000−2i2i−2i2i−2i2i00002-20000-2200000000002i−2i00000000
χ454444-44-4-440000-40000004-4-4400000000000000000000000000000000
χ464444-44-4-440000-4000000-444-400000000000000000000000000000000
χ474444-4-44-4-40000400000000000000004-4000000000000000000000000
χ484444-4-44-4-4000040000000000000000-44000000000000000000000000
χ4944-4-4444-4-40000-444-4-400000000000000000000000000000000000000
χ5044-4-4444-4-40000-4-4-44400000000000000000000000000000000000000
χ5144-4-4-44-44-44i4i−4i−4i40000−4i4i000000000000000000000000000000000000
χ5244-4-4-44-44-4−4i−4i4i4i400004i−4i000000000000000000000000000000000000
χ538-88i−8i000004+4i−4−4i4−4i−4+4i0000000000000000000000000000000000000000000
χ548-88i−8i00000−4−4i4+4i−4+4i4−4i0000000000000000000000000000000000000000000
χ558-8−8i8i000004−4i−4+4i4+4i−4−4i0000000000000000000000000000000000000000000
χ568-8−8i8i00000−4+4i4−4i−4−4i4+4i0000000000000000000000000000000000000000000

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