Finite Group Databasebeta

← Group #287754

Character table — Group #287754

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444444444888888888888888844444444488888888888888884444888822
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ911111111-1-1-1-111111111-1-111-1-11111-1-1-1-111111111-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-11-1
χ1011111111-1-1-1-111111111-1-111-1-11111-1-1-1-111111111-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-11
χ1111111111-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-11111-1-1-11
χ1211111111-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-111-1-1-1-1111-1
χ1311111111-1-1-1-111111111-1-111-1-1-1-1-1-1111111111111-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-11
χ1411111111-1-1-1-111111111-1-111-1-1-1-1-1-1111111111111-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-11-1
χ1511111111-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-111-1-1111-1
χ1611111111-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-11111-1-111-1-1-11
χ172222222222222-222-2-22-222-2-2-2-20000000000000000-222-2-222-2-200000000000000000000000000
χ182222222222222-222-2-22-222-2-2-2-20000000000000000-2-2-222-2-22200000000000000000000000000
χ19222222222222-22-2-222-22-2-2-2-2222222222200000000-200000000000000000000-2-2-2-20000000000
χ20222222222222-22-2-222-22-2-2-2-222-2-2-2-2-2-2-2-200000000-20000000000000000000022220000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-222-2-2000000002i2i2i2i−2i−2i−2i−2i2000000002i2i−2i−2i0000000000000000000000
χ22222222222222-2-2-2-2-2-2-2-2-2-222-2-200000000−2i−2i−2i−2i2i2i2i2i200000000−2i−2i2i2i0000000000000000000000
χ2322222222-2-2-2-22-222-2-22-2-2-2-2-2220000000000000000222-2-2-2-22200000000000000000000000000
χ2422222222-2-2-2-22-222-2-22-2-2-2-2-22200000000000000002-2-22222-2-200000000000000000000000000
χ2522222222-2-2-2-2-22-2-222-2222-2-2-2-22222-2-2-2-200000000200000000000000000000-2-2220000000000
χ2622222222-2-2-2-2-22-2-222-2222-2-2-2-2-2-2-2-222220000000020000000000000000000022-2-20000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222222000000002i2i2i2i−2i−2i−2i−2i-200000000−2i−2i2i2i0000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222222200000000−2i−2i−2i−2i2i2i2i2i-2000000002i2i−2i−2i0000000000000000000000
χ29222-22-2-2-222-2-220-2-200202-20000i2i2−i2−i2i2i2−i2−i222−2−222−2−20002i−2i002i−2i2−22−200000000i2−i2i2−i20000000000
χ30222-22-2-2-222-2-220-2-200202-20000i2i2−i2−i2i2i2−i2−i2−2−222−2−222000−2i2i00−2i2i−22−2200000000i2−i2i2−i20000000000
χ31222-22-2-2-222-2-220-2-200202-20000−i2−i2i2i2−i2−i2i2i222−2−222−2−2000−2i2i00−2i2i2−22−200000000−i2i2−i2i20000000000
χ32222-22-2-2-222-2-220-2-200202-20000−i2−i2i2i2−i2−i2i2i2−2−222−2−2220002i−2i002i−2i−22−2200000000−i2i2−i2i20000000000
χ33222-22-2-2-222-2-2-202200-20-220000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i202-2002-200i2−i2−i2i200000000−i2i2−i2i20000000000
χ34222-22-2-2-222-2-2-202200-20-220000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20-2200-2200−i2i2i2−i200000000−i2i2−i2i20000000000
χ35222-22-2-2-222-2-2-202200-20-220000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20-2200-2200i2−i2−i2i200000000i2−i2i2−i20000000000
χ36222-22-2-2-222-2-2-202200-20-220000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i202-2002-200−i2i2i2−i200000000i2−i2i2−i20000000000
χ37222-22-2-2-2-2-22220-2-20020-220000i2i2−i2−i2−i2−i2i2i222−2−222−2−20002i−2i00−2i2i−22−2200000000i2−i2−i2i20000000000
χ38222-22-2-2-2-2-22220-2-20020-220000i2i2−i2−i2−i2−i2i2i2−2−222−2−222000−2i2i002i−2i2−22−200000000i2−i2−i2i20000000000
χ39222-22-2-2-2-2-22220-2-20020-220000−i2−i2i2i2i2i2−i2−i222−2−222−2−2000−2i2i002i−2i−22−2200000000−i2i2i2−i20000000000
χ40222-22-2-2-2-2-22220-2-20020-220000−i2−i2i2i2i2i2−i2−i2−2−222−2−2220002i−2i00−2i2i2−22−200000000−i2i2i2−i20000000000
χ41222-22-2-2-2-2-222-202200-202-20000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i202-200-2200−i2i2i2−i200000000−i2i2i2−i20000000000
χ42222-22-2-2-2-2-222-202200-202-20000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20-22002-200i2−i2−i2i200000000−i2i2i2−i20000000000
χ43222-22-2-2-2-2-222-202200-202-20000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20-22002-200−i2i2i2−i200000000i2−i2−i2i20000000000
χ44222-22-2-2-2-2-222-202200-202-20000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i202-200-2200i2−i2−i2i200000000i2−i2−i2i20000000000
χ4522-2-2-222-22-22-202002-20-200002-22-22-22-22-2000000000000000000000i2i2−i2−i2i2i2−i2−i200000000i2−i2i2−i200
χ4622-2-2-222-22-22-202002-20-200002-22-22-22-22-2000000000000000000000−i2−i2i2i2−i2−i2i2i200000000−i2i2−i2i200
χ4722-2-2-222-22-22-202002-20-200002-2-22-22-22-22000000000000000000000i2i2−i2−i2i2i2−i2−i200000000−i2i2−i2i200
χ4822-2-2-222-22-22-202002-20-200002-2-22-22-22-22000000000000000000000−i2−i2i2i2−i2−i2i2i200000000i2−i2i2−i200
χ4922-2-2-222-2-22-2202002-20-20000-222-22-2-22-22000000000000000000000i2i2−i2−i2−i2−i2i2i200000000i2−i2−i2i200
χ5022-2-2-222-2-22-2202002-20-20000-222-22-2-22-22000000000000000000000−i2−i2i2i2i2i2−i2−i200000000−i2i2i2−i200
χ5122-2-2-222-2-22-2202002-20-20000-22-22-222-22-2000000000000000000000i2i2−i2−i2−i2−i2i2i200000000−i2i2i2−i200
χ5222-2-2-222-2-22-2202002-20-20000-22-22-222-22-2000000000000000000000−i2−i2i2i2i2i2−i2−i200000000i2−i2−i2i200
χ532-2-2-222-220000222-2-22-2-2002-200000000002i−2i2i−2i2i−2i2i−2i000000000000000002-22-20000002i−2i000000
χ542-2-2-222-220000222-2-22-2-2002-200000000002i−2i2i−2i2i−2i2i−2i00000000000000000-22-22000000−2i2i000000
χ552-2-2-222-220000222-2-22-2-2002-20000000000−2i2i−2i2i−2i2i−2i2i000000000000000002-22-2000000−2i2i000000
χ562-2-2-222-220000222-2-22-2-2002-20000000000−2i2i−2i2i−2i2i−2i2i00000000000000000-22-220000002i−2i000000
χ572-2-2-222-220000-2-2-222-222002-200000000002-22-2-22-2200000000000002-22-2000000002-200000000
χ582-2-2-222-220000-2-2-222-222002-200000000002-22-2-22-220000000000000-22-2200000000-2200000000
χ592-2-2-222-220000-2-2-222-222002-20000000000-22-222-22-200000000000002-22-200000000-2200000000
χ602-2-2-222-220000-2-2-222-222002-20000000000-22-222-22-20000000000000-22-22000000002-200000000
χ6144-44-4-4-444-4-44000000000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000000000000000
χ6244-44-4-4-444-4-4400000000000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000000000000000
χ6344-44-4-4-44-444-4000000000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000000000000000000
χ6444-44-4-4-44-444-400000000000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000000000000000000
χ6544-4-4-444-44-44-40-400-44040000-44000000000000000000000000000000000000000000000000000
χ6644-4-4-444-4-44-440-400-440400004-4000000000000000000000000000000000000000000000000000
χ674-444-44-4-400000400-4-4040000000000000000000000000000000000000002i2−2i2−2i22i200000000000000
χ684-444-44-4-400000400-4-404000000000000000000000000000000000000000−2i22i22i2−2i200000000000000
χ694-444-44-4-400000-400440-4000000000000000000000000000000000002i2−2i2−2i22i2000000000000000000
χ704-444-44-4-400000-400440-400000000000000000000000000000000000−2i22i22i2−2i2000000000000000000
χ714-4-444-44-4000040-4400-40000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000
χ724-4-444-44-4000040-4400-4000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000
χ734-4-444-44-40000-404-400400000000000000022−22−2222−222222−2200000000000000000000000000000000000
χ744-4-444-44-40000-404-4004000000000000000−222222−2222−22−222200000000000000000000000000000000000
χ754-4-4-444-4400004-44-44-4-4400-4400000000000000000000000000000000000000000000000000000
χ764-4-4-444-440000-44-44-444-400-4400000000000000000000000000000000000000000000000000000
χ778-88-8-8-888000000000000000000000000000000000000000000000000000000000000000000000

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