Finite Group Databasebeta

← Group #279306

Character table — Group #279306

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444222244444444448888888844444888888888888888888884444888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
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
χ511111111111111111111-1-1-1-1111111-1-1-1-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ611111111111111111111-1-1-1-1111111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-111
χ811111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1
χ911111111111-1-1-1-111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-11
χ1011111111111-1-1-1-111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-111-1-1111-1
χ1111111111111-1-1-1-111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111-1-1-1-1111-1
χ1211111111111-1-1-1-111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-11111-1-1-11
χ1311111111111-1-1-1-111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11-1
χ1411111111111-1-1-1-111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-111-11
χ1511111111111-1-1-1-111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-111111111-1-1111111-1-1-1-1-1-1-1-1-1-111-1-111-11
χ1611111111111-1-1-1-111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1-1-1-1-1-1111111-1-1-1-1111111-1-111-1-11-1
χ17222222222-2-22222222-2-22222-2-222-2-2-2-2-2-200000000-222-2-2000000000000000000000000000000
χ18222222222-2-22222222-2-2-2-2-2-2-2-222-2-2222200000000-2-2-222000000000000000000000000000000
χ19222222222-2-2-2-2-2-2222-2-22222-2-2-2-222-2-2-2-2000000002-2-222000000000000000000000000000000
χ20222222222-2-2-2-2-2-2222-2-2-2-2-2-2-2-2-2-222222200000000222-2-2000000000000000000000000000000
χ2122222222-2222222-2-2-2220000-2-2-2-222000022222222-200000000-2-2-2-20000000000000000000000
χ2222222222-2222222-2-2-2220000-2-2-2-2220000-2-2-2-2-2-2-2-2-20000000022220000000000000000000000
χ2322222222-222-2-2-2-2-2-2-2220000-2-222-2-200002222-2-2-2-2200000000-2-2220000000000000000000000
χ2422222222-222-2-2-2-2-2-2-2220000-2-222-2-20000-2-2-2-2222220000000022-2-20000000000000000000000
χ2522222222-2-2-22222-2-2-2-2-2000022-2-2-2-200000000000020000000000002i2i−2i−2i2i2i−2i−2i00000000000000
χ2622222222-2-2-22222-2-2-2-2-2000022-2-2-2-20000000000002000000000000−2i−2i2i2i−2i−2i2i2i00000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-20000222222000000000000-20000000000002i2i−2i−2i−2i−2i2i2i00000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-20000222222000000000000-2000000000000−2i−2i2i2i2i2i−2i−2i00000000000000
χ29222-2-22-2-222200002-2-2-2-222-2-22-2000022-2-2000000000000022-2-200000000000000002-200000000
χ30222-2-22-2-222200002-2-2-2-222-2-22-2000022-2-20000000000000-2-2220000000000000000-2200000000
χ31222-2-22-2-222200002-2-2-2-2-2-2222-20000-2-222000000000000022-2-20000000000000000-2200000000
χ32222-2-22-2-222200002-2-2-2-2-2-2222-20000-2-2220000000000000-2-22200000000000000002-200000000
χ33222-2-22-2-22-2-200002-2-22222-2-2-220000-2-222000000000000000000000000000002i2i−2i−2i002i−2i000000
χ34222-2-22-2-22-2-200002-2-22222-2-2-220000-2-22200000000000000000000000000000−2i−2i2i2i00−2i2i000000
χ35222-2-22-2-22-2-200002-2-222-2-222-22000022-2-2000000000000000000000000000002i2i−2i−2i00−2i2i000000
χ36222-2-22-2-22-2-200002-2-222-2-222-22000022-2-200000000000000000000000000000−2i−2i2i2i002i−2i000000
χ3722-2-22-22-22002i2i−2i−2i-2-22002-22-2002i−2i00000022−2−2i2i2−i2−i202i−2i0000002−2i2−i22−22−2i2−i2i2−i200000000000000
χ3822-2-22-22-22002i2i−2i−2i-2-22002-22-2002i−2i000000−2−222−i2−i2i2i202i−2i000000−22−i2i2−22−22−i2i2−i2i200000000000000
χ3922-2-22-22-22002i2i−2i−2i-2-2200-22-22002i−2i00000022−2−2i2i2−i2−i20−2i2i0000002−2i2−i2−22−22−i2i2−i2i200000000000000
χ4022-2-22-22-22002i2i−2i−2i-2-2200-22-22002i−2i000000−2−222−i2−i2i2i20−2i2i000000−22−i2i22−22−2i2−i2i2−i200000000000000
χ4122-2-22-22-2200−2i−2i2i2i-2-22002-22-200−2i2i00000022−2−2−i2−i2i2i20−2i2i0000002−2−i2i22−22−2−i2i2−i2i200000000000000
χ4222-2-22-22-2200−2i−2i2i2i-2-22002-22-200−2i2i000000−2−222i2i2−i2−i20−2i2i000000−22i2−i2−22−22i2−i2i2−i200000000000000
χ4322-2-22-22-2200−2i−2i2i2i-2-2200-22-2200−2i2i00000022−2−2−i2−i2i2i202i−2i0000002−2−i2i2−22−22i2−i2i2−i200000000000000
χ4422-2-22-22-2200−2i−2i2i2i-2-2200-22-2200−2i2i000000−2−222i2i2−i2−i202i−2i000000−22i2−i22−22−2−i2i2−i2i200000000000000
χ4522-2-22-22-2-2002i2i−2i−2i22-200000000−2i2i002i−2i2i−2i22−2−2i2i2−i2−i20002-20000−22−i2i2i2−i2−i2i2−222−200000000000000
χ4622-2-22-22-2-2002i2i−2i−2i22-200000000−2i2i002i−2i2i−2i−2−222−i2−i2i2i20002-200002−2i2−i2−i2i2i2−i22−2−2200000000000000
χ4722-2-22-22-2-2002i2i−2i−2i22-200000000−2i2i00−2i2i−2i2i22−2−2i2i2−i2−i2000-220000−22−i2i2−i2i2i2−i22−2−2200000000000000
χ4822-2-22-22-2-2002i2i−2i−2i22-200000000−2i2i00−2i2i−2i2i−2−222−i2−i2i2i2000-2200002−2i2−i2i2−i2−i2i2−222−200000000000000
χ4922-2-22-22-2-200−2i−2i2i2i22-2000000002i−2i002i−2i2i−2i22−2−2−i2−i2i2i2000-220000−22i2−i2i2−i2−i2i22−2−2200000000000000
χ5022-2-22-22-2-200−2i−2i2i2i22-2000000002i−2i002i−2i2i−2i−2−222i2i2−i2−i2000-2200002−2−i2i2−i2i2i2−i2−222−200000000000000
χ5122-2-22-22-2-200−2i−2i2i2i22-2000000002i−2i00−2i2i−2i2i22−2−2−i2−i2i2i20002-20000−22i2−i2−i2i2i2−i2−222−200000000000000
χ5222-2-22-22-2-200−2i−2i2i2i22-2000000002i−2i00−2i2i−2i2i−2−222i2i2−i2−i20002-200002−2−i2i2i2−i2−i2i22−2−2200000000000000
χ532-2-2222-2-202-22i−2i2i−2i0002-2000000002i−2i00002i−2i2i−2i2-22-2000002−22−2000000000000i2−i2i2−i20000i2−i22−200
χ542-2-2222-2-202-22i−2i2i−2i0002-2000000002i−2i00002i−2i2i−2i2-22-200000−22−22000000000000−i2i2−i2i20000−i2i2−2200
χ552-2-2222-2-202-22i−2i2i−2i0002-2000000002i−2i0000−2i2i−2i2i-22-22000002−22−2000000000000i2−i2i2−i20000−i2i2−2200
χ562-2-2222-2-202-22i−2i2i−2i0002-2000000002i−2i0000−2i2i−2i2i-22-2200000−22−22000000000000−i2i2−i2i20000i2−i22−200
χ572-2-2222-2-202-2−2i2i−2i2i0002-200000000−2i2i00002i−2i2i−2i-22-22000002−22−2000000000000−i2i2−i2i20000i2−i2−2200
χ582-2-2222-2-202-2−2i2i−2i2i0002-200000000−2i2i00002i−2i2i−2i-22-2200000−22−22000000000000i2−i2i2−i20000−i2i22−200
χ592-2-2222-2-202-2−2i2i−2i2i0002-200000000−2i2i0000−2i2i−2i2i2-22-2000002−22−2000000000000−i2i2−i2i20000−i2i22−200
χ602-2-2222-2-202-2−2i2i−2i2i0002-200000000−2i2i0000−2i2i−2i2i2-22-200000−22−22000000000000i2−i2i2−i20000i2−i2−2200
χ61444-4-44-4-4-4440000-444-4-40000-44000000000000000000000000000000000000000000000000000
χ62444-4-44-4-4-4-4-40000-4444400004-4000000000000000000000000000000000000000000000000000
χ6344-44-4-4-444000000-44-4004-4-4400000000000000000000000000000000000000000000000000000
χ6444-44-4-4-444000000-44-400-444-400000000000000000000000000000000000000000000000000000
χ6544-44-4-4-44-40000004-440000000000004i−4i−4i4i0000000000000000000000000000000000000000000
χ6644-44-4-4-44-40000004-44000000000000−4i4i4i−4i0000000000000000000000000000000000000000000
χ674-44-44-4-440004-4-4400000000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000
χ684-44-44-4-440004-4-440000000000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000
χ694-44-44-4-44000-444-400000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000
χ704-44-44-4-44000-444-40000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000
χ714-4-4444-4-40-444i−4i4i−4i000-4400000000−4i4i00000000000000000000000000000000000000000000000
χ724-4-4444-4-40-44−4i4i−4i4i000-44000000004i−4i00000000000000000000000000000000000000000000000
χ734-4-4-4-444404-40000000-4400000000000000000000000000022−22−222200000000000000000000000000
χ744-4-4-4-444404-40000000-44000000000000000000000000000−222222−2200000000000000000000000000
χ754-4-4-4-44440-4400000004-4000000000000000000000000000000000000000000022−22−22220000000000
χ764-4-4-4-44440-4400000004-40000000000000000000000000000000000000000000−222222−220000000000
χ778-888-8-88-8000000000000000000000000000000000000000000000000000000000000000000000

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