Finite Group Databasebeta

← Group #274113

Character table — Group #274113

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222222244444444444444444444448888888844444888888888888888888884444888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111111111111111-1-1-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1
χ911111111-1-1-1-111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11-1
χ1011111111-1-1-1-111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-11
χ1111111111-1-1-1-111111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1-1-111-11
χ1211111111-1-1-1-111111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-11111-1-11-1
χ1311111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-111-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-11
χ1411111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1111-1
χ1511111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-1111-1
χ1611111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1111111-1-1-1-1-1-1-1-1111111-1-111-1-1-11
χ1722222222222222-2-22-2-2222-2-22222-2-2-2-2-2-20000000022-2-2-2000000000000000000000000000000
χ1822222222222222-2-22-2-2222-2-2-2-2-2-22222-2-200000000-2-222-2000000000000000000000000000000
χ19222222222222-2-222-222-2-2-22200000000-2-2222222220000-2-2-2-2-200000000000000000000000000
χ20222222222222-2-222-222-2-2-22200000000-2-2-2-2-2-2-2-2-2-20000-2222200000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000022000000000000200002i2i−2i−2i2i2i−2i−2i000000000000000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000002200000000000020000−2i−2i2i2i−2i−2i2i2i000000000000000000
χ2322222222-2-2-2-222-2-22-2-22-2-2222222-2-2-2-2-2-200000000-2-2222000000000000000000000000000000
χ2422222222-2-2-2-222-2-22-2-22-2-222-2-2-2-22222-2-20000000022-2-22000000000000000000000000000000
χ2522222222-2-2-2-2-2-222-222-222-2-200000000-2-22222-2-2-2-200002-2-22200000000000000000000000000
χ2622222222-2-2-2-2-2-222-222-222-2-200000000-2-2-2-2-2-222220000222-2-200000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-222220000000022000000000000-200002i2i−2i−2i−2i−2i2i2i000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222220000000022000000000000-20000−2i−2i2i2i2i2i−2i−2i000000000000000000
χ292222-2-2-2-222-2-200220-2-20002-2000000000022-2-222-2-20000000000000000022−2−222−2−200002−22−200
χ302222-2-2-2-222-2-200220-2-20002-2000000000022-2-222-2-200000000000000000−2−222−2−2220000−22−2200
χ312222-2-2-2-222-2-200220-2-20002-20000000000-2-222-2-2220000000000000000022−2−222−2−20000−22−2200
χ322222-2-2-2-222-2-200220-2-20002-20000000000-2-222-2-22200000000000000000−2−222−2−22200002−22−200
χ332222-2-2-2-2-2-22200220-2-2000-22000000000022-2-2-2-2220000000000000000022−2−2−2−22200002−2−2200
χ342222-2-2-2-2-2-22200220-2-2000-22000000000022-2-2-2-22200000000000000000−2−22222−2−20000−222−200
χ352222-2-2-2-2-2-22200220-2-2000-220000000000-2-22222-2-20000000000000000022−2−2−2−2220000−222−200
χ362222-2-2-2-2-2-22200220-2-2000-220000000000-2-22222-2-200000000000000000−2−22222−2−200002−2−2200
χ3722-2-222-2-22-22-22200-200-22-20022-2-20000002−22−22−22−22-20002−22−22−22−22−22−2000000000000000000
χ3822-2-222-2-22-22-22200-200-22-20022-2-2000000−22−22−22−222-2000−22−22−22−22−22−22000000000000000000
χ3922-2-222-2-22-22-22200-200-22-200-2-2220000002−22−22−22−2-220002−22−2−22−22−22−22000000000000000000
χ4022-2-222-2-22-22-22200-200-22-200-2-222000000−22−22−22−22-22000−22−222−22−22−22−2000000000000000000
χ4122-2-222-2-22-22-2-2-2002002-220000002i2i−2i−2i002−22−22−22−2002i−2i0−22−22i2−i2−i2i2i2−i2−i2i2000000000000000000
χ4222-2-222-2-22-22-2-2-2002002-220000002i2i−2i−2i00−22−22−22−22002i−2i02−22−2−i2i2i2−i2−i2i2i2−i2000000000000000000
χ4322-2-222-2-22-22-2-2-2002002-22000000−2i−2i2i2i002−22−22−22−200−2i2i0−22−22−i2i2i2−i2−i2i2i2−i2000000000000000000
χ4422-2-222-2-22-22-2-2-2002002-22000000−2i−2i2i2i00−22−22−22−2200−2i2i02−22−2i2−i2−i2i2i2−i2−i2i2000000000000000000
χ4522-2-222-2-2-22-222200-200-2-220022-2-20000002−22−2−22−22-220002−2−222−22−2−22−22000000000000000000
χ4622-2-222-2-2-22-222200-200-2-220022-2-2000000−22−222−22−2-22000−222−2−22−222−22−2000000000000000000
χ4722-2-222-2-2-22-222200-200-2-2200-2-2220000002−22−2−22−222-20002−2−22−22−222−22−2000000000000000000
χ4822-2-222-2-2-22-222200-200-2-2200-2-222000000−22−222−22−22-2000−222−22−22−2−22−22000000000000000000
χ4922-2-222-2-2-22-22-2-20020022-20000002i2i−2i−2i002−22−2−22−2200−2i2i0−222−2i2−i2−i2i2−i2i2i2−i2000000000000000000
χ5022-2-222-2-2-22-22-2-20020022-20000002i2i−2i−2i00−22−222−22−200−2i2i02−2−22−i2i2i2−i2i2−i2−i2i2000000000000000000
χ5122-2-222-2-2-22-22-2-20020022-2000000−2i−2i2i2i002−22−2−22−22002i−2i0−222−2−i2i2i2−i2i2−i2−i2i2000000000000000000
χ5222-2-222-2-2-22-22-2-20020022-2000000−2i−2i2i2i00−22−222−22−2002i−2i02−2−22i2−i2−i2i2−i2i2i2−i2000000000000000000
χ532-2-222-2-2200002-22-222-2-200002i−2i2i−2i2i−2i2i−2i2-2000000000000000000000000000002i−2i2i−2i002-2000000
χ542-2-222-2-2200002-22-222-2-200002i−2i2i−2i2i−2i2i−2i2-200000000000000000000000000000−2i2i−2i2i00-22000000
χ552-2-222-2-2200002-22-222-2-20000−2i2i−2i2i−2i2i−2i2i2-2000000000000000000000000000002i−2i2i−2i00-22000000
χ562-2-222-2-2200002-22-222-2-20000−2i2i−2i2i−2i2i−2i2i2-200000000000000000000000000000−2i2i−2i2i002-2000000
χ572-2-222-2-2200002-2-222-22-200002i−2i2i−2i−2i2i−2i2i-2200000000000000000000000002i−2i2i−2i00002-200000000
χ582-2-222-2-2200002-2-222-22-200002i−2i2i−2i−2i2i−2i2i-220000000000000000000000000−2i2i−2i2i0000-2200000000
χ592-2-222-2-2200002-2-222-22-20000−2i2i−2i2i2i−2i2i−2i-2200000000000000000000000002i−2i2i−2i0000-2200000000
χ602-2-222-2-2200002-2-222-22-20000−2i2i−2i2i2i−2i2i−2i-220000000000000000000000000−2i2i−2i2i00002-200000000
χ614444-4-4-4-444-4-400-4-4044000-4400000000000000000000000000000000000000000000000000000
χ624444-4-4-4-4-4-44400-4-40440004-400000000000000000000000000000000000000000000000000000
χ6344-4-4-4-4444-4-44000000000000000000000022−22−222222−22−222200000000000000000000000000000000000
χ6444-4-4-4-4444-4-440000000000000000000000−222222−22−222222−2200000000000000000000000000000000000
χ6544-4-4-4-444-444-4000000000000000000000022−22−2222−222222−2200000000000000000000000000000000000
χ6644-4-4-4-444-444-40000000000000000000000−222222−2222−22−222200000000000000000000000000000000000
χ674-44-44-44-400004-400-400400004i−4i−4i4i0000000000000000000000000000000000000000000000000
χ684-44-44-44-400004-400-40040000−4i4i4i−4i0000000000000000000000000000000000000000000000000
χ694-44-44-44-40000-4400400-4000000004-4-44000000000000000000000000000000000000000000000
χ704-44-44-44-40000-4400400-400000000-444-4000000000000000000000000000000000000000000000
χ714-4-444-4-440000-444-4-44-44000000000000-440000000000000000000000000000000000000000000
χ724-4-444-4-440000-44-44-4-4440000000000004-40000000000000000000000000000000000000000000
χ734-4-44-444-40000004-40-44000000000000000000000000000000000000000000002i2−2i2−2i22i20000000000
χ744-4-44-444-40000004-40-4400000000000000000000000000000000000000000000−2i22i22i2−2i20000000000
χ754-4-44-444-4000000-4404-400000000000000000000000000000000000000002i2−2i2−2i22i200000000000000
χ764-4-44-444-4000000-4404-40000000000000000000000000000000000000000−2i22i22i2−2i200000000000000
χ778-88-8-88-88000000000000000000000000000000000000000000000000000000000000000000000

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