Finite Group Databasebeta

← Group #346640

Character table — Group #346640

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444222222222244444444444422222244444444444888888888888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-11-1-111-1-1-1-1111111111111-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-11-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-111111-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ61111111111111111111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-11-1-1-1-1111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-11-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1
χ9111111111111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11-1
χ10111111111111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-11
χ11111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-11111111111-1-1-1-111-1-1-1-111-11
χ12111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1111111-1-1-1-11111-1-11111-1-11-1
χ13111111111111-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-11111-1-1-11
χ14111111111111-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-1-1-1111-1
χ15111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1111-1
χ16111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-11
χ172222222222-2-2222222-2-2-2-2222200002222220000-2-2-2-2000000-200-2-20000000000000000000000
χ182222222222-2-2222222-2-2-2-2-2-2-2-2000022-2-2-2-20000-2-222000000-200220000000000000000000000
χ192222222222-2-2-2-2-2-222-2-22222220000-2-2-2-2-2-20000-2-222000000200-2-20000000000000000000000
χ202222222222-2-2-2-2-2-222-2-222-2-2-2-20000-2-222220000-2-2-2-2000000200220000000000000000000000
χ2122222222-2-2222222-2-2222200002222-2-200002222-2-2000000-2-2-2-2-2000000000000000000000000
χ2222222222-2-2222222-2-222220000-2-2-2-2-2-20000-2-2-2-2-2-200000022-222000000000000000000000000
χ2322222222-2-222-2-2-2-2-2-222-2-200002222220000-2-2-2-2-2-2000000222-2-2000000000000000000000000
χ2422222222-2-222-2-2-2-2-2-222-2-20000-2-2-2-22200002222-2-2000000-2-2222000000000000000000000000
χ2522222222-2-2-2-22222-2-2-2-2-2-200000000-2-200000000220022-2-2002000022-2-2000000000000000000
χ2622222222-2-2-2-22222-2-2-2-2-2-200000000-2-2000000002200-2-2220020000-2-222000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-222000000002200000000220022-2-200-20000-2-222000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2220000000022000000002200-2-22200-2000022-2-2000000000000000000
χ29222-2-2-22-22-2002i2i−2i−2i2-2000022-2-200002i−2i2i2i−2i−2i00000000000000000000000i2i2−i2−i222−2−2i2−i22−2000000
χ30222-2-2-22-22-2002i2i−2i−2i2-2000022-2-200002i−2i2i2i−2i−2i00000000000000000000000−i2−i2i2i2−2−222−i2i2−22000000
χ31222-2-2-22-22-2002i2i−2i−2i2-20000-2-22200002i−2i−2i−2i2i2i00000000000000000000000i2i2−i2−i222−2−2−i2i2−22000000
χ32222-2-2-22-22-2002i2i−2i−2i2-20000-2-22200002i−2i−2i−2i2i2i00000000000000000000000−i2−i2i2i2−2−222i2−i22−2000000
χ33222-2-2-22-22-200−2i−2i2i2i2-2000022-2-20000−2i2i−2i−2i2i2i00000000000000000000000i2i2−i2−i2−2−222i2−i2−22000000
χ34222-2-2-22-22-200−2i−2i2i2i2-2000022-2-20000−2i2i−2i−2i2i2i00000000000000000000000−i2−i2i2i222−2−2−i2i22−2000000
χ35222-2-2-22-22-200−2i−2i2i2i2-20000-2-2220000−2i2i2i2i−2i−2i00000000000000000000000i2i2−i2−i2−2−222−i2i22−2000000
χ36222-2-2-22-22-200−2i−2i2i2i2-20000-2-2220000−2i2i2i2i−2i−2i00000000000000000000000−i2−i2i2i222−2−2i2−i2−22000000
χ3722-22-2-2-2200222-22-200-2-22-2000022-2-200000022-2-20000000000000000000i2−i2i2−i2i2−i2i2−i20000i2−i2i2−i200
χ3822-22-2-2-2200222-22-200-2-22-2000022-2-200000022-2-20000000000000000000−i2i2−i2i2−i2i2−i2i20000−i2i2−i2i200
χ3922-22-2-2-2200222-22-200-2-22-20000-2-222000000-2-2220000000000000000000i2−i2i2−i2i2−i2i2−i20000−i2i2−i2i200
χ4022-22-2-2-2200222-22-200-2-22-20000-2-222000000-2-2220000000000000000000−i2i2−i2i2−i2i2−i2i20000i2−i2i2−i200
χ4122-22-2-2-220022-22-2200-2-2-22000022-2-2000000-2-2220000000000000000000i2−i2i2−i2−i2i2−i2i20000i2−i2−i2i200
χ4222-22-2-2-220022-22-2200-2-2-22000022-2-2000000-2-2220000000000000000000−i2i2−i2i2i2−i2i2−i20000−i2i2i2−i200
χ4322-22-2-2-220022-22-2200-2-2-220000-2-22200000022-2-20000000000000000000i2−i2i2−i2−i2i2−i2i20000−i2i2i2−i200
χ4422-22-2-2-220022-22-2200-2-2-220000-2-22200000022-2-20000000000000000000−i2i2−i2i2i2−i2i2−i20000i2−i2−i2i200
χ452-2-2-22-2222-22-20000-222-20000000000002-22-22-22-22-22-22-22-22-2000000000000000000000000000
χ462-2-2-22-2222-22-20000-222-20000000000002-22-2-22-222-22-2-22-22-22000000000000000000000000000
χ472-2-2-22-2222-22-20000-222-2000000000000-22-222-22-22-2-22-22-222-2000000000000000000000000000
χ482-2-2-22-2222-22-20000-222-2000000000000-22-22-22-222-2-222-22-2-22000000000000000000000000000
χ492-2-2-22-2222-2-220000-22-220000002-22-2002-22-20000-22-2200000002-2002-22-2000000000000000000
χ502-2-2-22-2222-2-220000-22-220000002-22-200-22-220000-222-200000002-200-22-22000000000000000000
χ512-2-2-22-2222-2-220000-22-22000000-22-22002-22-20000-22-220000000-2200-22-22000000000000000000
χ522-2-2-22-2222-2-220000-22-22000000-22-2200-22-220000-222-20000000-22002-22-2000000000000000000
χ532-2-2-22-222-222-200002-22-2002-22-200000000002-22-2-22000000-220002-22-2-22000000000000000000
χ542-2-2-22-222-222-200002-22-2002-22-20000000000-22-22-220000002-20002-2-222-2000000000000000000
χ552-2-2-22-222-222-200002-22-200-22-2200000000002-22-2-22000000-22000-22-222-2000000000000000000
χ562-2-2-22-222-222-200002-22-200-22-220000000000-22-22-220000002-2000-222-2-22000000000000000000
χ572-2-2-22-222-22-2200002-2-22002-22-22-22-200000000002-2002-2-22000-22-220000000000000000000000
χ582-2-2-22-222-22-2200002-2-22002-22-2-22-2200000000002-200-222-20002-2-220000000000000000000000
χ592-2-2-22-222-22-2200002-2-2200-22-222-22-200000000002-200-222-2000-222-20000000000000000000000
χ602-2-2-22-222-22-2200002-2-2200-22-22-22-2200000000002-2002-2-220002-22-20000000000000000000000
χ61444-4-4-44-4-44004i4i−4i−4i-44000000000000−4i4i000000000000000000000000000000000000000000000
χ62444-4-4-44-4-4400−4i−4i4i4i-440000000000004i−4i000000000000000000000000000000000000000000000
χ6344-44-4-4-4400-4-44-44-40044-440000000000000000000000000000000000000000000000000000000
χ6444-44-4-4-4400-4-4-44-4400444-40000000000000000000000000000000000000000000000000000000
χ6544-4-444-4-400004i−4i−4i4i00000000000000000000000000000000000000000002-2-22−2i2i2i−2i0000000000
χ6644-4-444-4-400004i−4i−4i4i0000000000000000000000000000000000000000000-222-22i−2i−2i2i0000000000
χ6744-4-444-4-40000−4i4i4i−4i00000000000000000000000000000000000000000002-2-222i−2i−2i2i0000000000
χ6844-4-444-4-40000−4i4i4i−4i0000000000000000000000000000000000000000000-222-2−2i2i2i−2i0000000000
χ694-44-4-44-44004-4000000-4400000000000000004-4-440000000000000000000000000000000000000
χ704-44-4-44-44004-4000000-440000000000000000-444-40000000000000000000000000000000000000
χ714-44-4-44-4400-440000004-40000004-4-4400000000000000000000000000000000000000000000000
χ724-44-4-44-4400-440000004-4000000-444-400000000000000000000000000000000000000000000000
χ734-4-44-444-444000000-4-4000000000000004i−4i−4i4i00000000000000000000000000000000000000000
χ744-4-44-444-444000000-4-400000000000000−4i4i4i−4i00000000000000000000000000000000000000000
χ754-4-44-444-4-4-40000004400004-4-44000000000000000000000000000000000000000000000000000
χ764-4-44-444-4-4-4000000440000-444-4000000000000000000000000000000000000000000000000000
χ778-8888-8-8-8000000000000000000000000000000000000000000000000000000000000000000000

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