Finite Group Databasebeta

← Group #346620

Character table — Group #346620

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444222222224444444444444422222444444444444888888888888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-111111111-1-1-1-1111-1-1-1-111-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-111111111-1-1-1-1111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111-1-1-1-111111111-1-1-1-11111111-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-11111-1-1
χ611111111111111111111-1-1-1-111111111-1-1-1-11111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111
χ811111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1
χ9111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-111-1-11-1
χ10111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-111-11
χ11111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-111-11
χ12111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-11111-1-11-1
χ13111111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-11
χ14111111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1111-1
χ15111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-11111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1111-1
χ16111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-11111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-11
χ172222222222-2-2222222-2-200002222-2-22200002222-2-2-2000000-2-200-2-20000000000000000000000
χ182222222222-2-2222222-2-20000-2-2-2-2-2-2220000-2-2-2-2-2-2-20000002200220000000000000000000000
χ192222222222-2-2-2-2-2-222-2-20000222222-2-20000-2-2-2-2-2-220000002200-2-20000000000000000000000
χ202222222222-2-2-2-2-2-222-2-20000-2-2-2-222-2-200002222-2-22000000-2-200220000000000000000000000
χ2122222222-2-2222222-2-2222222000022-2-222220000-2-2-20000-2-200-2-2000000000000000000000000
χ2222222222-2-2222222-2-222-2-2-2-2000022-2-2-2-2-2-20000-2-2-20000220022000000000000000000000000
χ2322222222-2-222-2-2-2-2-2-22222220000-2-222-2-2-2-20000-2-220000-2-20022000000000000000000000000
χ2422222222-2-222-2-2-2-2-2-222-2-2-2-20000-2-22222220000-2-2200002200-2-2000000000000000000000000
χ2522222222-2-2-2-22222-2-2-2-200000000-2-2-2-20000000022222-2-20000000022-2-2000000000000000000
χ2622222222-2-2-2-22222-2-2-2-200000000-2-2-2-200000000222-2-22200000000-2-222000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-20000000022220000000022-222-2-200000000-2-222000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-20000000022220000000022-2-2-2220000000022-2-2000000000000000000
χ29222-2-2-22-2002-22i2i−2i−2i002-222-2-200002i−2i002i2i−2i−2i00000000000000000000000i2i2−i2−i222−2−2i2−i22−2000000
χ30222-2-2-22-2002-22i2i−2i−2i002-222-2-200002i−2i002i2i−2i−2i00000000000000000000000−i2−i2i2i2−2−222−i2i2−22000000
χ31222-2-2-22-2002-22i2i−2i−2i002-2-2-22200002i−2i00−2i−2i2i2i00000000000000000000000i2i2−i2−i222−2−2−i2i2−22000000
χ32222-2-2-22-2002-22i2i−2i−2i002-2-2-22200002i−2i00−2i−2i2i2i00000000000000000000000−i2−i2i2i2−2−222i2−i22−2000000
χ33222-2-2-22-2002-2−2i−2i2i2i002-222-2-20000−2i2i00−2i−2i2i2i00000000000000000000000i2i2−i2−i2−2−222i2−i2−22000000
χ34222-2-2-22-2002-2−2i−2i2i2i002-222-2-20000−2i2i00−2i−2i2i2i00000000000000000000000−i2−i2i2i222−2−2−i2i22−2000000
χ35222-2-2-22-2002-2−2i−2i2i2i002-2-2-2220000−2i2i002i2i−2i−2i00000000000000000000000i2i2−i2−i2−2−222−i2i22−2000000
χ36222-2-2-22-2002-2−2i−2i2i2i002-2-2-2220000−2i2i002i2i−2i−2i00000000000000000000000−i2−i2i2i222−2−2i2−i2−22000000
χ3722-2-222-2-22-2002i−2i2i−2i2-200000022-2-2002i−2i00002i2i−2i−2i00000000000000000002−22−2i2−i2i2−i200002−2i2−i200
χ3822-2-222-2-22-2002i−2i2i−2i2-200000022-2-2002i−2i00002i2i−2i−2i0000000000000000000−22−22−i2i2−i2i20000−22−i2i200
χ3922-2-222-2-22-2002i−2i2i−2i2-2000000-2-222002i−2i0000−2i−2i2i2i00000000000000000002−22−2i2−i2i2−i20000−22−i2i200
χ4022-2-222-2-22-2002i−2i2i−2i2-2000000-2-222002i−2i0000−2i−2i2i2i0000000000000000000−22−22−i2i2−i2i200002−2i2−i200
χ4122-2-222-2-22-200−2i2i−2i2i2-200000022-2-200−2i2i0000−2i−2i2i2i00000000000000000002−22−2−i2i2−i2i200002−2−i2i200
χ4222-2-222-2-22-200−2i2i−2i2i2-200000022-2-200−2i2i0000−2i−2i2i2i0000000000000000000−22−22i2−i2i2−i20000−22i2−i200
χ4322-2-222-2-22-200−2i2i−2i2i2-2000000-2-22200−2i2i00002i2i−2i−2i00000000000000000002−22−2−i2i2−i2i20000−22i2−i200
χ4422-2-222-2-22-200−2i2i−2i2i2-2000000-2-22200−2i2i00002i2i−2i−2i0000000000000000000−22−22i2−i2i2−i200002−2−i2i200
χ452-2-2-2-22222-22-20000-22-2200002-22-200002-22-200002-20000000002-22-22-22-2000000000000000000
χ462-2-2-2-22222-22-20000-22-2200002-22-20000-22-2200002-2000000000-222-2-22-22000000000000000000
χ472-2-2-2-22222-22-20000-22-220000-22-2200002-22-200002-20000000002-2-22-22-22000000000000000000
χ482-2-2-2-22222-22-20000-22-220000-22-220000-22-2200002-2000000000-22-222-22-2000000000000000000
χ492-2-2-2-22222-2-220000-222-22-22-22-22-2000000000000-2202-22-22-20000-220000000000000000000000
χ502-2-2-2-22222-2-220000-222-22-22-2-22-22000000000000-220-22-222-200002-20000000000000000000000
χ512-2-2-2-22222-2-220000-222-2-22-222-22-2000000000000-220-22-22-220000-220000000000000000000000
χ522-2-2-2-22222-2-220000-222-2-22-22-22-22000000000000-2202-22-2-2200002-20000000000000000000000
χ532-2-2-2-2222-222-200002-2-220000000000002-22-22-22-2-2202-2-22002-2-22000000000000000000000000
χ542-2-2-2-2222-222-200002-2-220000000000002-22-2-22-22-220-222-200-22-22000000000000000000000000
χ552-2-2-2-2222-222-200002-2-22000000000000-22-222-22-2-220-222-2002-22-2000000000000000000000000
χ562-2-2-2-2222-222-200002-2-22000000000000-22-22-22-22-2202-2-2200-222-2000000000000000000000000
χ572-2-2-2-2222-22-2200002-22-22-22-20000000000002-22-22-200000-22-2200002-2-22000000000000000000
χ582-2-2-2-2222-22-2200002-22-22-22-2000000000000-22-222-200000-222-20000-222-2000000000000000000
χ592-2-2-2-2222-22-2200002-22-2-22-220000000000002-22-22-2000002-2-220000-222-2000000000000000000
χ602-2-2-2-2222-22-2200002-22-2-22-22000000000000-22-222-2000002-22-200002-2-22000000000000000000
χ61444-4-4-44-400-444i4i−4i−4i00-4400000000−4i4i00000000000000000000000000000000000000000000000
χ62444-4-4-44-400-44−4i−4i4i4i00-44000000004i−4i00000000000000000000000000000000000000000000000
χ6344-44-4-4-4400004-4-4400000000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000
χ6444-44-4-4-4400004-4-440000000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000
χ6544-44-4-4-440000-444-400000000000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000
χ6644-44-4-4-440000-444-40000000000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000
χ6744-4-444-4-4-44004i−4i4i−4i-44000000000000−4i4i000000000000000000000000000000000000000000000
χ6844-4-444-4-4-4400−4i4i−4i4i-440000000000004i−4i000000000000000000000000000000000000000000000
χ694-444-44-4-444000000-4-40000004-4-440000000000000000000000000000000000000000000000000
χ704-444-44-4-444000000-4-4000000-444-40000000000000000000000000000000000000000000000000
χ714-444-44-4-4-4-4000000440000000000000000004i−4i−4i4i0000000000000000000000000000000000000
χ724-444-44-4-4-4-400000044000000000000000000−4i4i4i−4i0000000000000000000000000000000000000
χ734-4-444-44-40044000000-4-40000000000004i−4i−4i4i00000000000000000000000000000000000000000
χ744-4-444-44-40044000000-4-4000000000000−4i4i4i−4i00000000000000000000000000000000000000000
χ754-4-444-44-400-4-4000000444-4-4400000000000000000000000000000000000000000000000000000
χ764-4-444-44-400-4-400000044-444-400000000000000000000000000000000000000000000000000000
χ778-88-88-8-88000000000000000000000000000000000000000000000000000000000000000000000

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