Finite Group Databasebeta

← Group #287751

Character table — Group #287751

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444444444888888888888888844444444488888888888888882244888822
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
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
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1
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
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111
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
χ911111111111-1-1-1-111111-1-1-1-1111111-1-1-1-111111111-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11-1
χ1011111111111-1-1-1-111111-1-1-1-1111111-1-1-1-111111111-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111-11
χ1111111111111-1-1-1-111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-111-1-111-1-1-11
χ1211111111111-1-1-1-111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-111-1-1111-1
χ1311111111111-1-1-1-111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-111-1-111-11
χ1411111111111-1-1-1-111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11-1
χ1511111111111-1-1-1-111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-111-1-1-1-111-1-1-1-1111-1
χ1611111111111-1-1-1-111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111111-1-11111-1-1-11
χ17222222222-2-2222222-22-222-2-2-2-22222222200000000-20000000000000000-2-2-2-200000000000000
χ18222222222-2-2222222-22-222-2-2-2-2-2-2-2-2-2-2-2-200000000-20000000000000000222200000000000000
χ19222222222-2-2-2-2-2-222-22-2-2-222-2-22222-2-2-2-20000000020000000000000000-2-22200000000000000
χ20222222222-2-2-2-2-2-222-22-2-2-222-2-2-2-2-2-22222000000002000000000000000022-2-200000000000000
χ2122222222-2222222-2-22-22-2-222-2-20000000000000000-222-2-222-2-200000000000000000000000000
χ2222222222-2222222-2-22-22-2-222-2-20000000000000000-2-2-222-2-22200000000000000000000000000
χ2322222222-222-2-2-2-2-2-22-2222-2-2-2-20000000000000000222-2-2-2-22200000000000000000000000000
χ2422222222-222-2-2-2-2-2-22-2222-2-2-2-200000000000000002-2-22222-2-200000000000000000000000000
χ2522222222-2-2-22222-2-2-2-2-2-2-2-2-222000000002i2i2i2i−2i−2i−2i−2i2000000002i2i−2i−2i0000000000000000000000
χ2622222222-2-2-22222-2-2-2-2-2-2-2-2-22200000000−2i−2i−2i−2i2i2i2i2i200000000−2i−2i2i2i0000000000000000000000
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
χ29222-2-22-2-220022-2-22-20-202-2000022-2-222-2-2000000000000000000000i2i2−i2−i20000i2i2−i2−i20000i2−i2i2−i200
χ30222-2-22-2-220022-2-22-20-202-2000022-2-222-2-2000000000000000000000−i2−i2i2i20000−i2−i2i2i20000−i2i2−i2i200
χ31222-2-22-2-220022-2-22-20-202-20000-2-222-2-222000000000000000000000i2i2−i2−i20000i2i2−i2−i20000−i2i2−i2i200
χ32222-2-22-2-220022-2-22-20-202-20000-2-222-2-222000000000000000000000−i2−i2i2i20000−i2−i2i2i20000i2−i2i2−i200
χ33222-2-22-2-2200-2-2222-20-20-22000022-2-2-2-222000000000000000000000i2i2−i2−i20000−i2−i2i2i20000i2−i2−i2i200
χ34222-2-22-2-2200-2-2222-20-20-22000022-2-2-2-222000000000000000000000−i2−i2i2i20000i2i2−i2−i20000−i2i2i2−i200
χ35222-2-22-2-2200-2-2222-20-20-220000-2-22222-2-2000000000000000000000i2i2−i2−i20000−i2−i2i2i20000−i2i2i2−i200
χ36222-2-22-2-2200-2-2222-20-20-220000-2-22222-2-2000000000000000000000−i2−i2i2i20000i2i2−i2−i20000i2−i2−i2i200
χ3722-2-2-2-22222-20000-222-2-200002-2000000002i2i−2i−2i2i2i−2i−2i00000000000002-22-200000000002i−2i000000
χ3822-2-2-2-22222-20000-222-2-200002-2000000002i2i−2i−2i2i2i−2i−2i0000000000000-22-220000000000−2i2i000000
χ3922-2-2-2-22222-20000-222-2-200002-200000000−2i−2i2i2i−2i−2i2i2i00000000000002-22-20000000000−2i2i000000
χ4022-2-2-2-22222-20000-222-2-200002-200000000−2i−2i2i2i−2i−2i2i2i0000000000000-22-2200000000002i−2i000000
χ4122-2-2-2-222-2-2200002-2-22200002-20000000022-2-2-2-2220000000000000000000002-22-22-200000000
χ4222-2-2-2-222-2-2200002-2-22200002-20000000022-2-2-2-222000000000000000000000-22-22-2200000000
χ4322-2-2-2-222-2-2200002-2-22200002-200000000-2-22222-2-20000000000000000000002-22-2-2200000000
χ4422-2-2-2-222-2-2200002-2-22200002-200000000-2-22222-2-2000000000000000000000-22-222-200000000
χ452-2-22-222-20222-22-200-20-2002-2002−22−22−22−2i2−i2i2−i2i2−i2i2−i20002i−2i002i−2ii2−i2i2−i200002−22−200000000000000
χ462-2-22-222-20222-22-200-20-2002-2002−22−22−22−2−i2i2−i2i2−i2i2−i2i2000−2i2i00−2i2i−i2i2−i2i200002−22−200000000000000
χ472-2-22-222-20222-22-200-20-2002-200−22−22−22−22i2−i2i2−i2i2−i2i2−i2000−2i2i00−2i2ii2−i2i2−i20000−22−2200000000000000
χ482-2-22-222-20222-22-200-20-2002-200−22−22−22−22−i2i2−i2i2−i2i2−i2i20002i−2i002i−2i−i2i2−i2i20000−22−2200000000000000
χ492-2-22-222-2022-22-2200-20-200-22002−22−2−22−22i2−i2i2−i2i2−i2i2−i20002i−2i00−2i2i−i2i2−i2i200002−2−2200000000000000
χ502-2-22-222-2022-22-2200-20-200-22002−22−2−22−22−i2i2−i2i2−i2i2−i2i2000−2i2i002i−2ii2−i2i2−i200002−2−2200000000000000
χ512-2-22-222-2022-22-2200-20-200-2200−22−222−22−2i2−i2i2−i2i2−i2i2−i2000−2i2i002i−2i−i2i2−i2i20000−222−200000000000000
χ522-2-22-222-2022-22-2200-20-200-2200−22−222−22−2−i2i2−i2i2−i2i2−i2i20002i−2i00−2i2ii2−i2i2−i20000−222−200000000000000
χ532-2-22-222-20-2-22-22-20020200-22002−22−22−22−22−22−2−22−2202-2002-2002−2−220000−22−2200000000000000
χ542-2-22-222-20-2-22-22-20020200-22002−22−22−22−2−22−222−22−20-2200-2200−222−20000−22−2200000000000000
χ552-2-22-222-20-2-22-22-20020200-2200−22−22−22−222−22−2−22−220-2200-22002−2−2200002−22−200000000000000
χ562-2-22-222-20-2-22-22-20020200-2200−22−22−22−22−22−222−22−202-2002-200−222−200002−22−200000000000000
χ572-2-22-222-20-2-2-22-2200202002-2002−22−2−22−222−22−2−22−2202-200-2200−222−20000−222−200000000000000
χ582-2-22-222-20-2-2-22-2200202002-2002−22−2−22−22−22−222−22−20-22002-2002−2−220000−222−200000000000000
χ592-2-22-222-20-2-2-22-2200202002-200−22−222−22−22−22−2−22−220-22002-200−222−200002−2−2200000000000000
χ602-2-22-222-20-2-2-22-2200202002-200−22−222−22−2−22−222−22−202-200-22002−2−2200002−2−2200000000000000
χ61444-4-44-4-4-40044-4-4-44040-440000000000000000000000000000000000000000000000000000000
χ62444-4-44-4-4-400-4-444-440404-40000000000000000000000000000000000000000000000000000000
χ6344-444-4-4-44000000-4-4040000000000000000000000000000000000002i2−2i2−2i22i2000000000000000000
χ6444-444-4-4-44000000-4-404000000000000000000000000000000000000−2i22i22i2−2i2000000000000000000
χ6544-444-4-4-4-4000000440-4000000000000000000000000000000000000000000002i2−2i2−2i22i20000000000
χ6644-444-4-4-4-4000000440-400000000000000000000000000000000000000000000−2i22i22i2−2i20000000000
χ6744-4-4-4-4444-440000-44-4-440000-44000000000000000000000000000000000000000000000000000
χ6844-4-4-4-444-44-400004-444-40000-44000000000000000000000000000000000000000000000000000
χ694-44-44-44-404-4000000-4040000000000000022−22−222222−22−222200000000000000000000000000000000000
χ704-44-44-44-404-4000000-40400000000000000−222222−22−222222−2200000000000000000000000000000000000
χ714-44-44-44-40-4400000040-4000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000
χ724-44-44-44-40-4400000040-400000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000
χ734-4-4-444-440004-4-440000000000022−22−222222−22−22220000000000000000000000000000000000000000000
χ744-4-4-444-440004-4-4400000000000−222222−22−222222−220000000000000000000000000000000000000000000
χ754-4-4-444-44000-444-40000000000022−22−2222−222222−220000000000000000000000000000000000000000000
χ764-4-4-444-44000-444-400000000000−222222−2222−22−22220000000000000000000000000000000000000000000
χ778-888-8-8-88000000000000000000000000000000000000000000000000000000000000000000000

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