Finite Group Databasebeta

← Group #346643

Character table — Group #346643

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444222222444444444444444444444444444444444888888888888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-11-1-111-1-1-1-111111111-1-1-1-11111-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-11-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1
χ91111111111-1-1-1-1111111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-11111-1-1-1-11111-1-1-1-111-1-111-1-11-1
χ101111111111-1-1-1-1111111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-11111-1-1-1-1-1-1-1-11111-1-111-1-111-11
χ111111111111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-111-1-111111111-1-1-1-111-1-1-1-111-11
χ121111111111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-111-1-11111-1-1-1-11111-1-11111-1-11-1
χ131111111111-1-1-1-1111111-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-11
χ141111111111-1-1-1-1111111-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1111-1
χ151111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1111-1
χ161111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-11
χ1722222222222222-2-222-2-22222222222-2-200000000-2-2-2-2000000-2-2-2000000000000000000000000
χ1822222222222222-2-222-2-222-2-2-2-2-2-2-2-2-2-200000000-2-222000000-222000000000000000000000000
χ192222222222-2-2-2-2-2-222-2-2-2-22222-2-2-2-22200000000-2-2220000002-2-2000000000000000000000000
χ202222222222-2-2-2-2-2-222-2-2-2-2-2-2-2-222222200000000-2-2-2-2000000222000000000000000000000000
χ2122222222-2-2222222-2-222-2-2000000002222222222-2-200-2-20000-200-2-20000000000000000000000
χ2222222222-2-2222222-2-222-2-20000000022-2-2-2-2-2-2-2-2-2-200220000-200220000000000000000000000
χ2322222222-2-22222-2-2-2-2-2-2-2-200000000-2-20000000022000022-2-22000022-2-2000000000000000000
χ2422222222-2-22222-2-2-2-2-2-2-2-200000000-2-200000000220000-2-22220000-2-222000000000000000000
χ2522222222-2-2-2-2-2-222-2-2222200000000-2-22222-2-2-2-2-2-200220000200-2-20000000000000000000000
χ2622222222-2-2-2-2-2-222-2-2222200000000-2-2-2-2-2-22222-2-200-2-20000200220000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22200000000220000000022000022-2-2-20000-2-222000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222000000002200000000220000-2-222-2000022-2-2000000000000000000
χ29222-22-2-2-22222-2-200-2-2002-222-2-222-2-20000000000000000000000000000022−2−222−2−22−22−2000000
χ30222-22-2-2-22222-2-200-2-2002-222-2-222-2-200000000000000000000000000000−2−222−2−222−22−22000000
χ31222-22-2-2-22222-2-200-2-2002-2-2-222-2-2220000000000000000000000000000022−2−222−2−2−22−22000000
χ32222-22-2-2-22222-2-200-2-2002-2-2-222-2-22200000000000000000000000000000−2−222−2−2222−22−2000000
χ33222-22-2-2-222-2-22200-2-200-2222-2-2-2-2220000000000000000000000000000022−2−2−2−2222−2−22000000
χ34222-22-2-2-222-2-22200-2-200-2222-2-2-2-22200000000000000000000000000000−2−22222−2−2−222−2000000
χ35222-22-2-2-222-2-22200-2-200-22-2-22222-2-20000000000000000000000000000022−2−2−2−222−222−2000000
χ36222-22-2-2-222-2-22200-2-200-22-2-22222-2-200000000000000000000000000000−2−22222−2−22−2−22000000
χ3722-22-2-2-22002i−2i2i−2i2-2002-200000000002i−2i2i2i−2i−2i22-2-200000000000000000002−22−2i2−i2i2−i20000i2−i22−200
χ3822-22-2-2-22002i−2i2i−2i2-2002-200000000002i−2i2i2i−2i−2i22-2-20000000000000000000−22−22−i2i2−i2i20000−i2i2−2200
χ3922-22-2-2-22002i−2i2i−2i2-2002-200000000002i−2i−2i−2i2i2i-2-22200000000000000000002−22−2i2−i2i2−i20000−i2i2−2200
χ4022-22-2-2-22002i−2i2i−2i2-2002-200000000002i−2i−2i−2i2i2i-2-2220000000000000000000−22−22−i2i2−i2i20000i2−i22−200
χ4122-22-2-2-2200−2i2i−2i2i2-2002-20000000000−2i2i2i2i−2i−2i-2-22200000000000000000002−22−2−i2i2−i2i20000i2−i2−2200
χ4222-22-2-2-2200−2i2i−2i2i2-2002-20000000000−2i2i2i2i−2i−2i-2-2220000000000000000000−22−22i2−i2i2−i20000−i2i22−200
χ4322-22-2-2-2200−2i2i−2i2i2-2002-20000000000−2i2i−2i−2i2i2i22-2-200000000000000000002−22−2−i2i2−i2i20000−i2i22−200
χ4422-22-2-2-2200−2i2i−2i2i2-2002-20000000000−2i2i−2i−2i2i2i22-2-20000000000000000000−22−22i2−i2i2−i20000i2−i2−2200
χ452-2-2-22-2222-200002-22-2-220000002-22-2002-22-200002-22-20000000002-22-22-2000000000000000000
χ462-2-2-22-2222-200002-22-2-220000002-22-200-22-2200002-22-2000000000-22-22-22000000000000000000
χ472-2-2-22-2222-200002-22-2-22000000-22-22002-22-200002-2-220000000002-2-22-22000000000000000000
χ482-2-2-22-2222-200002-22-2-22000000-22-2200-22-2200002-2-22000000000-222-22-2000000000000000000
χ492-2-2-22-2222-20000-222-22-20000002-22-20000002-22-2-22-222-22-22-2000000000000000000000000000
χ502-2-2-22-2222-20000-222-22-20000002-22-2000000-22-22-22-22-22-22-22000000000000000000000000000
χ512-2-2-22-2222-20000-222-22-2000000-22-220000002-22-2-222-22-2-22-22000000000000000000000000000
χ522-2-2-22-2222-20000-222-22-2000000-22-22000000-22-22-222-2-222-22-2000000000000000000000000000
χ532-2-2-22-222-2200002-2-22-22002-22-20000002-22-20000-2200002-2-2202-2-220000000000000000000000
χ542-2-2-22-222-2200002-2-22-22002-22-2000000-22-220000-220000-222-202-22-20000000000000000000000
χ552-2-2-22-222-2200002-2-22-2200-22-220000002-22-20000-220000-222-20-22-220000000000000000000000
χ562-2-2-22-222-2200002-2-22-2200-22-22000000-22-220000-2200002-2-220-222-20000000000000000000000
χ572-2-2-22-222-220000-22-222-2002-22-200000000002-22-22-200-2200000-22002-2-22000000000000000000
χ582-2-2-22-222-220000-22-222-2002-22-20000000000-22-222-2002-200000-2200-222-2000000000000000000
χ592-2-2-22-222-220000-22-222-200-22-2200000000002-22-22-200-22000002-200-222-2000000000000000000
χ602-2-2-22-222-220000-22-222-200-22-220000000000-22-222-2002-2000002-2002-2-22000000000000000000
χ61444-44-4-4-4-4-444-4-4004400-440000000000000000000000000000000000000000000000000000000
χ62444-44-4-4-4-4-4-4-4440044004-40000000000000000000000000000000000000000000000000000000
χ6344-44-4-4-44004i−4i4i−4i-4400-440000000000−4i4i000000000000000000000000000000000000000000000
χ6444-44-4-4-4400−4i4i−4i4i-4400-4400000000004i−4i000000000000000000000000000000000000000000000
χ6544-4-4-444-4004i−4i−4i4i0000000000000000000000000000000000000000000002-2-222i−2i−2i2i0000000000
χ6644-4-4-444-4004i−4i−4i4i000000000000000000000000000000000000000000000-222-2−2i2i2i−2i0000000000
χ6744-4-4-444-400−4i4i4i−4i0000000000000000000000000000000000000000000002-2-22−2i2i2i−2i0000000000
χ6844-4-4-444-400−4i4i4i−4i000000000000000000000000000000000000000000000-222-22i−2i−2i2i0000000000
χ694-44-4-44-440000004400-4-40000000000004i−4i−4i4i00000000000000000000000000000000000000000
χ704-44-4-44-440000004400-4-4000000000000−4i4i4i−4i00000000000000000000000000000000000000000
χ714-44-4-44-44000000-4-4004400000000000000004-4-440000000000000000000000000000000000000
χ724-44-4-44-44000000-4-400440000000000000000-444-40000000000000000000000000000000000000
χ734-4-4444-4-44-4000000-44000000004-4-4400000000000000000000000000000000000000000000000
χ744-4-4444-4-44-4000000-4400000000-444-400000000000000000000000000000000000000000000000
χ754-4-4444-4-4-440000004-400004-4-44000000000000000000000000000000000000000000000000000
χ764-4-4444-4-4-440000004-40000-444-4000000000000000000000000000000000000000000000000000
χ778-888-8-88-8000000000000000000000000000000000000000000000000000000000000000000000

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