Finite Group Databasebeta

← Group #274841

Character table — Group #274841

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222222244444488888888888888888888888881616161616161616161616163232
order12222222222244444444444444222244444888888888888888844448888888844
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ311111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ511111111111111111111111111-1-1-1-11-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ711111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111
χ811111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ911111111-1-1-1-11111111111-1-1-1-111-1-1-111-1-111-1-111-1-11111-1-1-1-111-1-111-1-111-1-11-1
χ1011111111-1-1-1-11111111111-1-1-1-111-1-1-111-1-111-1-111-1-1-1-1-1-11111-1-111-1-11111-1-1-11
χ1111111111-1-1-1-11111111111-1-1-1-111-1-1-111-1-1-1-111-1-1111111-1-1-1-111-1-1-1-111-1-111-11
χ1211111111-1-1-1-11111111111-1-1-1-111-1-1-111-1-1-1-111-1-111-1-1-1-11111-1-11111-1-1-1-1111-1
χ1311111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-11111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111-11
χ1411111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-11111-1-111-1-1-1-1-1-1111111-1-1-1-111-1-1111-1
χ1511111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-111-1-111-1-1111111-1-1-1-1-1-111-1-11111-1-11-1
χ1611111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-111-1-111-1-111-1-1-1-1111111-1-111-1-111-1-1-11
χ172222222222222-2-222-2-22-2-222-2-22222-2-2-2-2-2000000000000000000000000000000
χ182222222222222-2-222-2-22-2-222-2-2-2-2-2-2-22222000000000000000000000000000000
χ19222222222222-222-2-222-2-2-2-2-2220000-200002222-2-2-2-20000000000000000000000
χ20222222222222-222-2-222-2-2-2-2-2220000-20000-2-2-2-222220000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-222-2-2-2-20000200000000000000000000000000002i−2i2i−2i00
χ22222222222222-2-2-2-2-2-2-2-222-2-2-2-2000020000000000000000000000000000−2i2i−2i2i00
χ2322222222-2-2-2-22-2-222-2-22-2-2-2-22222-2-22-2-222000000000000000000000000000000
χ2422222222-2-2-2-22-2-222-2-22-2-2-2-222-2-222222-2-2000000000000000000000000000000
χ2522222222-2-2-2-2-222-2-222-2-2-222-2-200002000022-2-2-2-2220000000000000000000000
χ2622222222-2-2-2-2-222-2-222-2-2-222-2-2000020000-2-22222-2-20000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22222220000-200000000000000000000000000002i−2i−2i2i00
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22222220000-20000000000000000000000000000−2i2i2i−2i00
χ2922-2-2-22-2222-2-202200-2-2000002-200000000000002i−2i2i−2ii2i2−i2−i2i2i2−i2−i200002−22−2000000
χ3022-2-2-22-2222-2-202200-2-2000002-200000000000002i−2i2i−2i−i2−i2i2i2−i2−i2i2i20000−22−22000000
χ3122-2-2-22-2222-2-202200-2-2000002-20000000000000−2i2i−2i2ii2i2−i2−i2i2i2−i2−i20000−22−22000000
χ3222-2-2-22-2222-2-202200-2-2000002-20000000000000−2i2i−2i2i−i2−i2i2i2−i2−i2i2i200002−22−2000000
χ3322-2-2-22-22-2-22202200-2-200000-2200000000000002i−2i−2i2ii2i2−i2−i2−i2−i2i2i200002−2−22000000
χ3422-2-2-22-22-2-22202200-2-200000-2200000000000002i−2i−2i2i−i2−i2i2i2i2i2−i2−i20000−222−2000000
χ3522-2-2-22-22-2-22202200-2-200000-220000000000000−2i2i2i−2ii2i2−i2−i2−i2−i2i2i20000−222−2000000
χ3622-2-2-22-22-2-22202200-2-200000-220000000000000−2i2i2i−2i−i2−i2i2i2i2i2−i2−i200002−2−22000000
χ372-2-222-2-22000022-22-22-2-22-20000002-20002-20000000000002i−2i2i−2i2i−2i000000000000
χ382-2-222-2-22000022-22-22-2-22-20000002-20002-2000000000000−2i2i−2i2i−2i2i000000000000
χ392-2-222-2-22000022-22-22-2-22-2000000-22000-220000000000002i−2i2i−2i−2i2i000000000000
χ402-2-222-2-22000022-22-22-2-22-2000000-22000-22000000000000−2i2i−2i2i2i−2i000000000000
χ412-2-222-2-2200002-222-2-22-2-220000002-2000-22000000002i−2i2i−2i0000002i−2i0000000000
χ422-2-222-2-2200002-222-2-22-2-220000002-2000-2200000000−2i2i−2i2i000000−2i2i0000000000
χ432-2-222-2-2200002-222-2-22-2-22000000-220002-2000000002i−2i2i−2i000000−2i2i0000000000
χ442-2-222-2-2200002-222-2-22-2-22000000-220002-200000000−2i2i−2i2i0000002i−2i0000000000
χ454444-4-4-4-44-44-4400-4-4004004-400000000000000000000000000000000000000000
χ464444-4-4-4-44-44-4-4004400-400-4400000000000000000000000000000000000000000
χ474444-4-4-4-4-44-44400-4-400400-4400000000000000000000000000000000000000000
χ484444-4-4-4-4-44-44-4004400-4004-400000000000000000000000000000000000000000
χ4944-4-44-44-44-4-44000000000000000000000002i2−2i22i2−2i200000000000000000000000000
χ5044-4-44-44-44-4-4400000000000000000000000−2i22i2−2i22i200000000000000000000000000
χ5144-4-44-44-4-444-4000000000000000000000002i2−2i2−2i22i200000000000000000000000000
χ5244-4-44-44-4-444-400000000000000000000000−2i22i22i2−2i200000000000000000000000000
χ5344-4-4-44-4444-4-40-4-4004400000-44000000000000000000000000000000000000000
χ5444-4-4-44-44-4-4440-4-40044000004-4000000000000000000000000000000000000000
χ554-44-4-4-444000004-400-44000000000000000000000000000022−22−222200000000000000
χ564-44-4-4-444000004-400-440000000000000000000000000000−222222−2200000000000000
χ574-44-4-4-44400000-44004-400000000000000000000000022−22−2222000000000000000000
χ584-44-4-4-44400000-44004-4000000000000000000000000−222222−22000000000000000000
χ594-4-444-4-440000-44-4-444-44-440000000000000000000000000000000000000000000
χ604-4-444-4-440000-4-44-44-4444-40000000000000000000000000000000000000000000
χ614-4-44-444-40000400-4400-4000000000004i−4i00000000000000000000000000000000
χ624-4-44-444-40000400-4400-400000000000−4i4i00000000000000000000000000000000
χ634-4-44-444-40000-4004-40040000004-40000000000000000000000000000000000000
χ644-4-44-444-40000-4004-4004000000-440000000000000000000000000000000000000
χ658-88-888-8-8000000000000000000000000000000000000000000000000000000000

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