Finite Group Databasebeta

← Group #275821

Character table — Group #275821

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444444444444444448888888844444888888888888888888882244888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
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
χ511111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1
χ9111111111-1-1-1-11111111-1-111-1-1111111111111-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-11-1
χ10111111111-1-1-1-11111111-1-111-1-1111111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-11
χ11111111111-1-1-1-11111111-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-111-11
χ12111111111-1-1-1-11111111-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-111-1-11-1
χ13111111111-1-1-1-11111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1111111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1-11
χ14111111111-1-1-1-11111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111-1
χ15111111111-1-1-1-11111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1111-1
χ16111111111-1-1-1-11111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1-111-1-1-1-11111-1-1-1-11111-1-11111-1-1-11
χ172222222222222-2-222-22-222-2-2-2-20000000022222222-20000-2-2-2-200000000000000000000000000
χ182222222222222-2-222-22-222-2-2-2-200000000-2-2-2-2-2-2-2-2-20000222200000000000000000000000000
χ19222222222-2-2-2-2-2-222-22-2-2-2-2-222000000002222-2-2-2-220000-2-22200000000000000000000000000
χ20222222222-2-2-2-2-2-222-22-2-2-2-2-22200000000-2-2-2-222222000022-2-200000000000000000000000000
χ2122222222-2222222-2-22-22-2-2-2-2222222-2-2-2-200000000-222-2-2000000000000000000000000000000
χ2222222222-2222222-2-22-22-2-2-2-222-2-2-2-2222200000000-2-2-222000000000000000000000000000000
χ2322222222-22222-2-2-2-2-2-2-2-2-222-2-2000000000000000020000000000002i2i−2i−2i2i2i−2i−2i00000000000000
χ2422222222-22222-2-2-2-2-2-2-2-2-222-2-200000000000000002000000000000−2i−2i2i2i−2i−2i2i2i00000000000000
χ2522222222-2-2-2-2-222-2-22-2222-2-2-2-22222-2-2-2-2000000002-2-222000000000000000000000000000000
χ2622222222-2-2-2-2-222-2-22-2222-2-2-2-2-2-2-2-2222200000000222-2-2000000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22222220000000000000000-20000000000002i2i−2i−2i−2i−2i2i2i00000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22222220000000000000000-2000000000000−2i−2i2i2i2i2i−2i−2i00000000000000
χ29222-2-2-22-2-222-2-2002-20202-20000000000002i2i−2i−2i2i2i−2i−2i000000000i2i2−i2−i200000000i2i2−i2−i200002−22−200
χ30222-2-2-22-2-222-2-2002-20202-20000000000002i2i−2i−2i2i2i−2i−2i000000000−i2−i2i2i200000000−i2−i2i2i20000−22−2200
χ31222-2-2-22-2-222-2-2002-20202-2000000000000−2i−2i2i2i−2i−2i2i2i000000000i2i2−i2−i200000000i2i2−i2−i20000−22−2200
χ32222-2-2-22-2-222-2-2002-20202-2000000000000−2i−2i2i2i−2i−2i2i2i000000000−i2−i2i2i200000000−i2−i2i2i200002−22−200
χ33222-2-2-22-2-2-2-222002-2020-220000000000002i2i−2i−2i−2i−2i2i2i000000000i2i2−i2−i200000000−i2−i2i2i200002−2−2200
χ34222-2-2-22-2-2-2-222002-2020-220000000000002i2i−2i−2i−2i−2i2i2i000000000−i2−i2i2i200000000i2i2−i2−i20000−222−200
χ35222-2-2-22-2-2-2-222002-2020-22000000000000−2i−2i2i2i2i2i−2i−2i000000000i2i2−i2−i200000000−i2−i2i2i20000−222−200
χ36222-2-2-22-2-2-2-222002-2020-22000000000000−2i−2i2i2i2i2i−2i−2i000000000−i2−i2i2i200000000i2i2−i2−i200002−2−2200
χ3722-22-2-2-22200002-2-2-222-2002-2002i2i−2i−2i2i2i−2i−2i000000000000000002-22-2000000000000002i−2i000000
χ3822-22-2-2-22200002-2-2-222-2002-2002i2i−2i−2i2i2i−2i−2i00000000000000000-22-2200000000000000−2i2i000000
χ3922-22-2-2-22200002-2-2-222-2002-200−2i−2i2i2i−2i−2i2i2i000000000000000002-22-200000000000000−2i2i000000
χ4022-22-2-2-22200002-2-2-222-2002-200−2i−2i2i2i−2i−2i2i2i00000000000000000-22-22000000000000002i−2i000000
χ4122-22-2-2-22-200002-2222-2-200-22002i2i−2i−2i−2i−2i2i2i000000000000000000000000000002i−2i2i−2i2-200000000
χ4222-22-2-2-22-200002-2222-2-200-22002i2i−2i−2i−2i−2i2i2i00000000000000000000000000000−2i2i−2i2i-2200000000
χ4322-22-2-2-22-200002-2222-2-200-2200−2i−2i2i2i2i2i−2i−2i000000000000000000000000000002i−2i2i−2i-2200000000
χ4422-22-2-2-22-200002-2222-2-200-2200−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000−2i2i−2i2i2-200000000
χ452-2-2-22-22202-22-22200-20-200002-22i−2i2i−2i00002−22−22−22−202i−2i002−22−20000i2−i2i2−i2i2−i2i2−i200000000000000
χ462-2-2-22-22202-22-22200-20-200002-22i−2i2i−2i0000−22−22−22−2202i−2i00−22−220000−i2i2−i2i2−i2i2−i2i200000000000000
χ472-2-2-22-22202-22-22200-20-200002-2−2i2i−2i2i00002−22−22−22−20−2i2i002−22−20000−i2i2−i2i2−i2i2−i2i200000000000000
χ482-2-2-22-22202-22-22200-20-200002-2−2i2i−2i2i0000−22−22−22−220−2i2i00−22−220000i2−i2i2−i2i2−i2i2−i200000000000000
χ492-2-2-22-22202-22-2-2-2002020000-2200002-22-22−22−22−22−20002-2−22−2200002−2−222−2−2200000000000000
χ502-2-2-22-22202-22-2-2-2002020000-2200002-22-2−22−22−22−220002-22−22−20000−222−2−222−200000000000000
χ512-2-2-22-22202-22-2-2-2002020000-220000-22-222−22−22−22−2000-22−22−220000−222−2−222−200000000000000
χ522-2-2-22-22202-22-2-2-2002020000-220000-22-22−22−22−22−22000-222−22−200002−2−222−2−2200000000000000
χ532-2-2-22-2220-22-222200-20-20000-222i−2i2i−2i00002−22−2−22−220−2i2i002−2−220000i2−i2i2−i2−i2i2−i2i200000000000000
χ542-2-2-22-2220-22-222200-20-20000-222i−2i2i−2i0000−22−222−22−20−2i2i00−222−20000−i2i2−i2i2i2−i2i2−i200000000000000
χ552-2-2-22-2220-22-222200-20-20000-22−2i2i−2i2i00002−22−2−22−2202i−2i002−2−220000−i2i2−i2i2i2−i2i2−i200000000000000
χ562-2-2-22-2220-22-222200-20-20000-22−2i2i−2i2i0000−22−222−22−202i−2i00−222−20000i2−i2i2−i2−i2i2−i2i200000000000000
χ572-2-2-22-2220-22-22-2-20020200002-200002-22-22−22−2−22−22000-22−222−200002−2−22−222−200000000000000
χ582-2-2-22-2220-22-22-2-20020200002-200002-22-2−22−222−22−2000-222−2−220000−222−22−2−2200000000000000
χ592-2-2-22-2220-22-22-2-20020200002-20000-22-222−22−2−22−220002-2−222−20000−222−22−2−2200000000000000
χ602-2-2-22-2220-22-22-2-20020200002-20000-22-22−22−222−22−20002-22−2−2200002−2−22−222−200000000000000
χ61444-4-4-44-4444-4-400-440-40-440000000000000000000000000000000000000000000000000000000
χ62444-4-4-44-44-4-44400-440-404-40000000000000000000000000000000000000000000000000000000
χ6344-44-4-4-4440000-44-4-4-44400-4400000000000000000000000000000000000000000000000000000
χ6444-44-4-4-44-40000-4444-4-44004-400000000000000000000000000000000000000000000000000000
χ6544-4-444-4-440000004-40-40000000000000000000000000000000000000000000022−22−22220000000000
χ6644-4-444-4-440000004-40-400000000000000000000000000000000000000000000−222222−220000000000
χ6744-4-444-4-4-4000000-4404000000000000000000000000000000002i2−2i2−2i22i20000000000000000000000
χ6844-4-444-4-4-4000000-440400000000000000000000000000000000−2i22i22i2−2i20000000000000000000000
χ694-44-4-44-44000004-400-4040000004-4-4400000000000000000000000000000000000000000000000
χ704-44-4-44-44000004-400-404000000-444-400000000000000000000000000000000000000000000000
χ714-44-4-44-4400000-440040-400000000004i−4i−4i4i0000000000000000000000000000000000000000000
χ724-44-4-44-4400000-440040-40000000000−4i4i4i−4i0000000000000000000000000000000000000000000
χ734-4-44-444-404-4-440000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000
χ744-4-44-444-404-4-44000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000
χ754-4-44-444-40-444-40000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000
χ764-4-44-444-40-444-4000000000000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000
χ778-8888-8-8-8000000000000000000000000000000000000000000000000000000000000000000000

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