Finite Group Databasebeta

← Group #173842

Character table — Group #173842

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size1111111144444444444488888888888881616161616161616161616161616161616163232
order12222222444444444444222222444444444444488888888888844
χ111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-1111-1-1-1-11-1-11-1-11111-1-1-1-11111-1-1
χ41111111111111111111111-1-1-1-1111-1-1-1-11-1-11-1-1-1-1-1-11111-1-1-1-111
χ511111111111111111111-1-111-1-11-1-111-1-1-11-1-11-111111111-1-1-1-1-1-1
χ611111111111111111111-1-111-1-11-1-111-1-1-11-1-11-1-1-1-1-1-1-1-1-1111111
χ711111111111111111111-1-1-1-1111-1-1-1-111-1-11-1-111111-1-1-1-1-1-1-1-111
χ811111111111111111111-1-1-1-1111-1-1-1-111-1-11-1-11-1-1-1-111111111-1-1
χ9111111111-1-1-1-1-1-111111111111-1-1-1-1-1-1-11-11-11-111-1-111-1-111-1-11-1
χ10111111111-1-1-1-1-1-111111111111-1-1-1-1-1-1-11-11-11-1-1-111-1-111-1-111-11
χ11111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1111111-1-1-1111-1-1-1-11111-1-1-11
χ12111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1111111-1-1-11-1-11111-1-1-1-1111-1
χ13111111111-1-1-1-1-1-111111-1-111-1-1-111-1-111-1-1-111111-1-111-1-1-1-111-11
χ14111111111-1-1-1-1-1-111111-1-111-1-1-111-1-111-1-1-1111-1-111-1-11111-1-11-1
χ15111111111-1-1-1-1-1-111111-1-1-1-111-11111-1-1-1111-1-111-1-1-1-111-1-1111-1
χ16111111111-1-1-1-1-1-111111-1-1-1-111-11111-1-1-1111-1-1-1-11111-1-111-1-1-11
χ1722222222222-2-2-2-2-2-2-2-22002200200-2-2000200-2000000000000000
χ1822222222222-2-2-2-2-2-2-2-2200-2-20020022000-2002000000000000000
χ19222222222-2-22222-2-2-2-22002200-20022000-200-2000000000000000
χ20222222222-2-22222-2-2-2-2200-2-200-200-2-20002002000000000000000
χ2122222222-22222-2-222-2-2-2000022-200002200-200-200000000000000
χ2222222222-22222-2-222-2-2-20000-2-2-20000-2-200200200000000000000
χ2322222222-222-2-222-2-222-2220000-2220000-200-20000000000000000
χ2422222222-222-2-222-2-222-2-2-20000-2-2-2000020020000000000000000
χ2522222222-2-2-222-2-2-2-222-22200002-2-20000-20020000000000000000
χ2622222222-2-2-222-2-2-2-222-2-2-200002220000200-20000000000000000
χ2722222222-2-2-2-2-22222-2-2-200002220000-2-200-200200000000000000
χ2822222222-2-2-2-2-22222-2-2-20000-2-2200002200200-200000000000000
χ2922-22-2-2-2202i−2i2i−2i002-200000002-2000002i−2i0000000000i2−i22−2i2−i22−200
χ3022-22-2-2-2202i−2i2i−2i002-200000002-2000002i−2i0000000000−i2i2−22−i2i2−2200
χ3122-22-2-2-2202i−2i2i−2i002-20000000-2200000−2i2i0000000000i2−i22−2−i2i2−2200
χ3222-22-2-2-2202i−2i2i−2i002-20000000-2200000−2i2i0000000000−i2i2−22i2−i22−200
χ3322-22-2-2-220−2i2i−2i2i002-200000002-200000−2i2i0000000000i2−i2−22i2−i2−2200
χ3422-22-2-2-220−2i2i−2i2i002-200000002-200000−2i2i0000000000−i2i22−2−i2i22−200
χ3522-22-2-2-220−2i2i−2i2i002-20000000-22000002i−2i0000000000i2−i2−22−i2i22−200
χ3622-22-2-2-220−2i2i−2i2i002-20000000-22000002i−2i0000000000−i2i22−2i2−i2−2200
χ3744-44-4-4-4404i−4i−4i4i00-44000000000000000000000000000000000000
χ3844-44-4-4-440−4i4i4i−4i00-44000000000000000000000000000000000000
χ3944-4-444-4-4000004i−4i0000000000000000000000002-22i−2i0000000000
χ4044-4-444-4-4000004i−4i000000000000000000000000-22−2i2i0000000000
χ4144-4-444-4-400000−4i4i0000000000000000000000002-2−2i2i0000000000
χ4244-4-444-4-400000−4i4i000000000000000000000000-222i−2i0000000000
χ434-4444-4-4-440000000000-4004-400000000000000000000000000000
χ444-4444-4-4-440000000000-400-4400000000000000000000000000000
χ454-4444-4-4-4-4000000000040000000004i−4i0000000000000000000000
χ464-4444-4-4-4-400000000004000000000−4i4i0000000000000000000000
χ474-4-4-44-4440000000004-4000000004-4000000000000000000000000
χ484-4-4-44-4440000000004-400000000-44000000000000000000000000
χ494-4-4-44-444000000000-4404-40000000000000000000000000000000
χ504-4-4-44-444000000000-440-440000000000000000000000000000000
χ51888-8-8-88-8000000000000000000000000000000000000000000000
χ528-88-8-88-88000000000000000000000000000000000000000000000
χ538-8-88-888-8000000000000000000000000000000000000000000000

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