Finite Group Databasebeta

← Group #275255

Character table — Group #275255

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444224444444444448888888844444888888888888888888884444888844
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
χ51111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1
χ9111111111-1-1-1-11111111-1-11111111111-1-11111-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11-1
χ10111111111-1-1-1-11111111-1-11111111111-1-11111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111-11
χ11111111111-1-1-1-11111111-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-111-11
χ12111111111-1-1-1-11111111-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-11-1
χ13111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1111111-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-11
χ14111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111-1
χ15111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-11111-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1111-1
χ16111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-11111-1-111-1-1-1-11111-1-1-1-1111111-1-111-1-1-11
χ172222222222222-2-222-2-22-2-22222-2-2-2-2-2-22200000000-222-2-2000000000000000000000000000000
χ182222222222222-2-222-2-22-2-2-2-2-2-22222-2-22200000000-2-2-222000000000000000000000000000000
χ19222222222-2-2-2-2-2-222-2-22222222-2-2-2-2-2-2-2-2000000002-2-222000000000000000000000000000000
χ20222222222-2-2-2-2-2-222-2-2222-2-2-2-22222-2-2-2-200000000222-2-2000000000000000000000000000000
χ2122222222-2222222-2-222-22200000000-2-2-2-222222222-20000-2-2-2-200000000000000000000000000
χ2222222222-2222222-2-222-22200000000-2-2-2-2-2-2-2-2-2-2-2-2-20000222200000000000000000000000000
χ2322222222-22222-2-2-2-2-2-2-2-2-20000000022-2-20000000020000000000002i2i−2i−2i2i2i−2i−2i00000000000000
χ2422222222-22222-2-2-2-2-2-2-2-2-20000000022-2-2000000002000000000000−2i−2i2i2i−2i−2i2i2i00000000000000
χ2522222222-2-2-2-2-222-2-222-2-2-200000000-2-2222222-2-2-2-220000-2-22200000000000000000000000000
χ2622222222-2-2-2-2-222-2-222-2-2-200000000-2-222-2-2-2-222222000022-2-200000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22200000000222200000000-20000000000002i2i−2i−2i−2i−2i2i2i00000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22200000000222200000000-2000000000000−2i−2i2i2i2i2i−2i−2i00000000000000
χ29222-2-2-22-2-200002-22-22-22002i2i−2i−2i2i2i−2i−2i2-2000000000000000000000000000000022-2-2002i−2i000000
χ30222-2-2-22-2-200002-22-22-22002i2i−2i−2i2i2i−2i−2i2-20000000000000000000000000000000-2-22200−2i2i000000
χ31222-2-2-22-2-200002-22-22-2200−2i−2i2i2i−2i−2i2i2i2-2000000000000000000000000000000022-2-200−2i2i000000
χ32222-2-2-22-2-200002-22-22-2200−2i−2i2i2i−2i−2i2i2i2-20000000000000000000000000000000-2-222002i−2i000000
χ33222-2-2-22-2-20000-222-2-222002i2i−2i−2i−2i−2i2i2i-22000000000000000000022-2-20000000000002i−2i00000000
χ34222-2-2-22-2-20000-222-2-222002i2i−2i−2i−2i−2i2i2i-220000000000000000000-2-222000000000000−2i2i00000000
χ35222-2-2-22-2-20000-222-2-22200−2i−2i2i2i2i2i−2i−2i-22000000000000000000022-2-2000000000000−2i2i00000000
χ36222-2-2-22-2-20000-222-2-22200−2i−2i2i2i2i2i−2i−2i-220000000000000000000-2-2220000000000002i−2i00000000
χ3722-222-2-2-2022-2-2-2-2002202-200000000000022-2-222-2-2000000000i2−i2i2−i200000000i2−i2i2−i20000i2−i2i2−i200
χ3822-222-2-2-2022-2-2-2-2002202-200000000000022-2-222-2-2000000000−i2i2−i2i200000000−i2i2−i2i20000−i2i2−i2i200
χ3922-222-2-2-2022-2-2-2-2002202-2000000000000-2-222-2-222000000000i2−i2i2−i200000000i2−i2i2−i20000−i2i2−i2i200
χ4022-222-2-2-2022-2-2-2-2002202-2000000000000-2-222-2-222000000000−i2i2−i2i200000000−i2i2−i2i20000i2−i2i2−i200
χ4122-222-2-2-20-2-222-2-200220-2200000000000022-2-2-2-222000000000i2−i2i2−i200000000−i2i2−i2i20000i2−i2−i2i200
χ4222-222-2-2-20-2-222-2-200220-2200000000000022-2-2-2-222000000000−i2i2−i2i200000000i2−i2i2−i20000−i2i2i2−i200
χ4322-222-2-2-20-2-222-2-200220-22000000000000-2-22222-2-2000000000i2−i2i2−i200000000−i2i2−i2i20000−i2i2i2−i200
χ4422-222-2-2-20-2-222-2-200220-22000000000000-2-22222-2-2000000000−i2i2−i2i200000000i2−i2i2−i20000i2−i2−i2i200
χ452-222-2-2-2222i−2i2i−2i00-2-20020000002-22-2002i−2i2−22−2i2−i2i2−i20002i−2i2−2i2−i200002−22−2i2−i2i2−i200000000000000
χ462-222-2-2-2222i−2i2i−2i00-2-20020000002-22-2002i−2i−22−22−i2i2−i2i20002i−2i−22−i2i20000−22−22−i2i2−i2i200000000000000
χ472-222-2-2-2222i−2i2i−2i00-2-2002000000-22-22002i−2i2−22−2i2−i2i2−i2000−2i2i2−2i2−i20000−22−22−i2i2−i2i200000000000000
χ482-222-2-2-2222i−2i2i−2i00-2-2002000000-22-22002i−2i−22−22−i2i2−i2i2000−2i2i−22−i2i200002−22−2i2−i2i2−i200000000000000
χ492-222-2-2-222−2i2i−2i2i00-2-20020000002-22-200−2i2i2−22−2−i2i2−i2i2000−2i2i2−2−i2i200002−22−2−i2i2−i2i200000000000000
χ502-222-2-2-222−2i2i−2i2i00-2-20020000002-22-200−2i2i−22−22i2−i2i2−i2000−2i2i−22i2−i20000−22−22i2−i2i2−i200000000000000
χ512-222-2-2-222−2i2i−2i2i00-2-2002000000-22-2200−2i2i2−22−2−i2i2−i2i20002i−2i2−2−i2i20000−22−22i2−i2i2−i200000000000000
χ522-222-2-2-222−2i2i−2i2i00-2-2002000000-22-2200−2i2i−22−22i2−i2i2−i20002i−2i−22i2−i200002−22−2−i2i2−i2i200000000000000
χ532-222-2-2-22-22i−2i2i−2i002200-2002i−2i2i−2i000000−2i2i2−22−2i2−i2i2−i202-200−22−i2i20000i2−i2−i2i2−222−200000000000000
χ542-222-2-2-22-22i−2i2i−2i002200-2002i−2i2i−2i000000−2i2i−22−22−i2i2−i2i202-2002−2i2−i20000−i2i2i2−i22−2−2200000000000000
χ552-222-2-2-22-22i−2i2i−2i002200-200−2i2i−2i2i000000−2i2i2−22−2i2−i2i2−i20-2200−22−i2i20000−i2i2i2−i22−2−2200000000000000
χ562-222-2-2-22-22i−2i2i−2i002200-200−2i2i−2i2i000000−2i2i−22−22−i2i2−i2i20-22002−2i2−i20000i2−i2−i2i2−222−200000000000000
χ572-222-2-2-22-2−2i2i−2i2i002200-2002i−2i2i−2i0000002i−2i2−22−2−i2i2−i2i20-2200−22i2−i20000i2−i2−i2i22−2−2200000000000000
χ582-222-2-2-22-2−2i2i−2i2i002200-2002i−2i2i−2i0000002i−2i−22−22i2−i2i2−i20-22002−2−i2i20000−i2i2i2−i2−222−200000000000000
χ592-222-2-2-22-2−2i2i−2i2i002200-200−2i2i−2i2i0000002i−2i2−22−2−i2i2−i2i202-200−22i2−i20000−i2i2i2−i2−222−200000000000000
χ602-222-2-2-22-2−2i2i−2i2i002200-200−2i2i−2i2i0000002i−2i−22−22i2−i2i2−i202-2002−2−i2i20000i2−i2−i2i22−2−2200000000000000
χ61444-4-4-44-4400004-4-444-4-40000000000-44000000000000000000000000000000000000000000000
χ62444-4-4-44-440000-44-44-44-400000000004-4000000000000000000000000000000000000000000000
χ6344-444-4-4-4044-4-44400-4-40-440000000000000000000000000000000000000000000000000000000
χ6444-444-4-4-40-4-4444400-4-404-40000000000000000000000000000000000000000000000000000000
χ6544-4-4-44-44000004-400-44000000000000000000000000000000002i2−2i2−2i22i20000000000000000000000
χ6644-4-4-44-44000004-400-4400000000000000000000000000000000−2i22i22i2−2i20000000000000000000000
χ6744-4-4-44-4400000-44004-4000000000000000000000000000000000000000000002i2−2i2−2i22i20000000000
χ6844-4-4-44-4400000-44004-400000000000000000000000000000000000000000000−2i22i22i2−2i20000000000
χ694-44-444-4-440000004-400-4004-4-44000000000000000000000000000000000000000000000000000
χ704-44-444-4-440000004-400-400-444-4000000000000000000000000000000000000000000000000000
χ714-44-444-4-4-4000000-440040000004i−4i−4i4i00000000000000000000000000000000000000000000000
χ724-44-444-4-4-4000000-44004000000−4i4i4i−4i00000000000000000000000000000000000000000000000
χ734-4-44-444-404i−4i−4i4i00000000000000000000022−22−22222i2−2i2−2i22i200000000000000000000000000000000000
χ744-4-44-444-404i−4i−4i4i000000000000000000000−222222−22−2i22i22i2−2i200000000000000000000000000000000000
χ754-4-44-444-40−4i4i4i−4i00000000000000000000022−22−2222−2i22i22i2−2i200000000000000000000000000000000000
χ764-4-44-444-40−4i4i4i−4i000000000000000000000−222222−222i2−2i2−2i22i200000000000000000000000000000000000
χ778-8-8-88-888000000000000000000000000000000000000000000000000000000000000000000000

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