Finite Group Databasebeta

← Group #173844

Character table — Group #173844

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size1111111144444444444488888888888881616161616161616161616161616161616163232
order12222222444444444444224444444444444444488888888888844
χ111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-1-1-1-1-1-11-1-11-111111111-1-1-1-1-1-1
χ41111111111111111111111111-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111-1-11-1-11111-1-1-1-11-1-11-1-11111-1-1-1-11111-1-1
χ611111111111111111111-1-11-1-11111-1-1-1-11-1-11-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111-1-11-1-1-1-1-1-11111-1-11-1-111111-1-1-1-1-1-1-1-111
χ811111111111111111111-1-11-1-1-1-1-1-11111-1-11-1-11-1-1-1-111111111-1-1
χ9111111111-1-1-1-1-1-11111111-1-1-111-1-111-1-11-11-11-111-1-111-1-111-1-11-1
χ10111111111-1-1-1-1-1-11111111-1-1-111-1-111-1-11-11-11-1-1-111-1-111-1-111-11
χ11111111111-1-1-1-1-1-11111111-1-1-1-1-111-1-111-1-1-111111-1-111-1-1-1-111-11
χ12111111111-1-1-1-1-1-11111111-1-1-1-1-111-1-111-1-1-1111-1-111-1-11111-1-11-1
χ13111111111-1-1-1-1-1-111111-1-1-11111-1-1-1-11111-1-1-1111-1-1-1-11111-1-1-11
χ14111111111-1-1-1-1-1-111111-1-1-11111-1-1-1-11111-1-1-11-1-11111-1-1-1-1111-1
χ15111111111-1-1-1-1-1-111111-1-1-111-1-11111-1-1-1111-1-111-1-1-1-111-1-1111-1
χ16111111111-1-1-1-1-1-111111-1-1-111-1-11111-1-1-1111-1-1-1-11111-1-111-1-1-11
χ1722222222222-2-2-2-2-2-2-2-22222-2-2000000000200-2000000000000000
χ1822222222222-2-2-2-2-2-2-2-22-2-2222000000000-2002000000000000000
χ19222222222-2-22222-2-2-2-2222-222000000000-200-2000000000000000
χ20222222222-2-22222-2-2-2-22-2-2-2-2-20000000002002000000000000000
χ2122222222-22222-2-2-2-222-200-20022220000-200-20000000000000000
χ2222222222-22222-2-2-2-222-200-200-2-2-2-2000020020000000000000000
χ2322222222-222-2-22222-2-2-200-2000000222200-200-200000000000000
χ2422222222-222-2-22222-2-2-200-2000000-2-2-2-200200200000000000000
χ2522222222-2-2-222-2-222-2-2-200200000022-2-200-200200000000000000
χ2622222222-2-2-222-2-222-2-2-2002000000-2-22200200-200000000000000
χ2722222222-2-2-2-2-222-2-222-20020022-2-20000-20020000000000000000
χ2822222222-2-2-2-2-222-2-222-200200-2-2220000200-20000000000000000
χ2922-22-2-2-2202i−2i2i−2i00002-20000002i−2i2-200000000002−2i2−i20000i2−i22−200
χ3022-22-2-2-2202i−2i2i−2i00002-20000002i−2i2-20000000000−22−i2i20000−i2i2−2200
χ3122-22-2-2-2202i−2i2i−2i00002-2000000−2i2i-2200000000002−2i2−i20000−i2i2−2200
χ3222-22-2-2-2202i−2i2i−2i00002-2000000−2i2i-220000000000−22−i2i20000i2−i22−200
χ3322-22-2-2-220−2i2i−2i2i00002-20000002i−2i-2200000000002−2−i2i20000i2−i2−2200
χ3422-22-2-2-220−2i2i−2i2i00002-20000002i−2i-220000000000−22i2−i20000−i2i22−200
χ3522-22-2-2-220−2i2i−2i2i00002-2000000−2i2i2-200000000002−2−i2i20000−i2i22−200
χ3622-22-2-2-220−2i2i−2i2i00002-2000000−2i2i2-20000000000−22i2−i20000i2−i2−2200
χ3744-44-4-4-4404i−4i−4i4i0000-440000000000000000000000000000000000
χ3844-44-4-4-440−4i4i4i−4i0000-440000000000000000000000000000000000
χ3944-4-444-4-440000000000-44-40000000000000000000000000000000
χ4044-4-444-4-440000000000-4-440000000000000000000000000000000
χ4144-4-444-4-4-4000000000040004i−4i0000000000000000000000000000
χ4244-4-444-4-4-400000000004000−4i4i0000000000000000000000000000
χ434-44-44-4-4400000004-4000000000000004i−4i00000000000000000000
χ444-44-44-4-4400000004-400000000000000−4i4i00000000000000000000
χ454-44-44-4-440000000-440000000000004i−4i0000000000000000000000
χ464-44-44-4-440000000-44000000000000−4i4i0000000000000000000000
χ474-4-444-44-4000004i−4i00000000000000000000000000002i−2i2-2000000
χ484-4-444-44-4000004i−4i0000000000000000000000000000−2i2i-22000000
χ494-4-444-44-400000−4i4i00000000000000000000000000002i−2i-22000000
χ504-4-444-44-400000−4i4i0000000000000000000000000000−2i2i2-2000000
χ51888-8-8-88-8000000000000000000000000000000000000000000000
χ528-888-88-8-8000000000000000000000000000000000000000000000
χ538-8-8-8-8888000000000000000000000000000000000000000000000

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