Finite Group Databasebeta

← Group #299855

Character table — Group #299855

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size1111222222444444444488888888888881616161616161616161616161616161616163232
order12224444442444888888224488888888822244444888888888844
χ111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1
χ41111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111
χ511111111111111111111-1-1-1-111111111111-1-1-111-1-1-1-1-1-1-11111-1-1
χ611111111111111111111-1-1-1-1111111111-1-1111-1-11-1-1-1-1-1-1-1-1-1-111
χ711111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-111-111-1-111-1-1-1-111
χ811111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1111-1-1111-1-1111111-1-1
χ911111111111111-1-1-1-1-1-11111-11111-1-1-1-11-11-111-1-111-1-1-1-111-1-1-11
χ1011111111111111-1-1-1-1-1-11111-11111-1-1-1-1-11-11-1-11111-1-1-1-1-1-1111-1
χ1111111111111111-1-1-1-1-1-11111-1-1-1-1-111111-11-111-1-1-1-1-1-111-1-1111-1
χ1211111111111111-1-1-1-1-1-11111-1-1-1-1-11111-11-11-1-111-1-1-1-11111-1-1-11
χ1311111111111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1-11-11-11-1-1111111-1-11-1
χ1411111111111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-11-11-1-1-11111-1-111-11
χ1511111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11-11-111111-1-1-1-111-11
χ1611111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-11-11-11111-1-111-1-11-1
χ172222222-2-22-2-22-22222-2-20000-2000000002-2000-220000000000000
χ182222222-2-22-2-22-22222-2-20000-200000000-220002-20000000000000
χ192222222-2-22-2-22-2-2-2-2-222000020000000022000-2-20000000000000
χ202222222-2-22-2-22-2-2-2-2-2220000200000000-2-2000220000000000000
χ2122222-2-2222-22-2-222-2-2220000-2000000000022-200-2000000000000
χ2222222-2-2222-22-2-222-2-2220000-20000000000-2-22002000000000000
χ2322222-2-2222-22-2-2-2-222-2-20000200000000002-2-2002000000000000
χ2422222-2-2222-22-2-2-2-222-2-2000020000000000-22200-2000000000000
χ2522222-2-2-2-222-2-2222-2-2-2-22-22-220000000000000000002-200000000
χ2622222-2-2-2-222-2-2222-2-2-2-2-22-222000000000000000000-2200000000
χ2722222-2-2-2-222-2-22-2-222222-22-2-2000000000000000000-2200000000
χ2822222-2-2-2-222-2-22-2-22222-22-22-20000000000000000002-200000000
χ292222-22222-2-2-2-2200000022-2-2022-2-20000000000002-20000000000
χ302222-22222-2-2-2-2200000022-2-20-2-222000000000000-220000000000
χ312222-22222-2-2-2-22000000-2-222022-2-2000000000000-220000000000
χ322222-22222-2-2-2-22000000-2-2220-2-2220000000000002-20000000000
χ332222-2-2-2-2-2-2-22220000002-2-220000022-2-20000000000002-2000000
χ342222-2-2-2-2-2-2-22220000002-2-2200000-2-222000000000000-22000000
χ352222-2-2-2-2-2-2-2222000000-222-20000022-2-2000000000000-22000000
χ362222-2-2-2-2-2-2-2222000000-222-200000-2-2220000000000002-2000000
χ374444-444-4-4-444-4-4000000000000000000000000000000000000000
χ384444-4-4-444-44-44-4000000000000000000000000000000000000000
χ3944-4-4-400004000000004-40000000000000000000000000002i−2i2i−2i00
χ4044-4-4-400004000000004-4000000000000000000000000000−2i2i−2i2i00
χ4144-4-4-40000400000000-440000000000000000000000000002i−2i−2i2i00
χ4244-4-4-40000400000000-44000000000000000000000000000−2i2i2i−2i00
χ434-44-404-400000002i2−2i22i2−2i20000000002i2−2i22-22-200000000000000000000
χ444-44-404-400000002i2−2i22i2−2i2000000000−2i22i2-22-2200000000000000000000
χ454-44-404-40000000−2i22i2−2i22i20000000002i2−2i2-22-2200000000000000000000
χ464-44-404-40000000−2i22i2−2i22i2000000000−2i22i22-22-200000000000000000000
χ474-44-40-4400000002i2−2i2−2i22i200000002i2−2i2002-2-2200000000000000000000
χ484-44-40-4400000002i2−2i2−2i22i20000000−2i22i200-222-200000000000000000000
χ494-44-40-440000000−2i22i22i2−2i200000002i2−2i200-222-200000000000000000000
χ504-44-40-440000000−2i22i22i2−2i20000000−2i22i2002-2-2200000000000000000000
χ5188-8-880000-80000000000000000000000000000000000000000000
χ528-8-880008-800000000000000000000000000000000000000000000
χ538-8-88000-8800000000000000000000000000000000000000000000

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