Finite Group Databasebeta

← Group #274686

Character table — Group #274686

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444222222444444448888888822444888888888888888888884444888824
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
χ51111111111111111111111-1-1-1-11111-1-1-1-111111111-1-11-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ61111111111111111111111-1-1-1-11111-1-1-1-111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1
χ9111111111-1-1-1-11111111-1-1111111-1-111111111-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11-1
χ10111111111-1-1-1-11111111-1-1111111-1-111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111-11
χ11111111111-1-1-1-11111111-1-1111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-111-11
χ12111111111-1-1-1-11111111-1-1111111-1-11111-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-11-1
χ13111111111-1-1-1-11111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-11111-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-11
χ14111111111-1-1-1-11111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-11111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111-1
χ15111111111-1-1-1-11111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-111-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1111-1
χ16111111111-1-1-1-11111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-111-1-111-1-1-1-11111-1-1-1-1111111-1-111-1-1-11
χ172222222222222-2-222-2-22-2-22222-2-222-2-2-2-200000000-2-2-222000000000000000000000000000000
χ182222222222222-2-222-2-22-2-2-2-2-2-2-2-22222220000000022-2-2-2000000000000000000000000000000
χ19222222222-2-2-2-2-2-222-2-22222222-2-2-2-2-2-2-2-200000000222-2-2000000000000000000000000000000
χ20222222222-2-2-2-2-2-222-2-2222-2-2-2-2-2-2-2-2222200000000-2-2222000000000000000000000000000000
χ2122222222-2222222-2-222-2220000-2-2-2-200002222222200-200-2-2-2-200000000000000000000000000
χ2222222222-2222222-2-222-2220000-2-2-2-20000-2-2-2-2-2-2-2-200-200222200000000000000000000000000
χ2322222222-22222-2-2-2-2-2-2-2-2-2000022-2-200000000000000200000000002i2i−2i−2i2i2i−2i−2i00000000000000
χ2422222222-22222-2-2-2-2-2-2-2-2-2000022-2-20000000000000020000000000−2i−2i2i2i−2i−2i2i2i00000000000000
χ2522222222-2-2-2-2-222-2-222-2-2-20000-2-22200002222-2-2-2-200200-2-22200000000000000000000000000
χ2622222222-2-2-2-2-222-2-222-2-2-20000-2-2220000-2-2-2-222220020022-2-200000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2220000222200000000000000-200000000002i2i−2i−2i−2i−2i2i2i00000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2220000222200000000000000-20000000000−2i−2i2i2i2i2i−2i−2i00000000000000
χ29222-22-2-2-222i2i−2i−2i00-2-2002000000002i−2i2i2i−2i−2i22−2−2i2i2−i2−i22-20002−2i2−i20000i2−i2i2−i22−22−200000000000000
χ30222-22-2-2-222i2i−2i−2i00-2-2002000000002i−2i2i2i−2i−2i−2−222−i2−i2i2i22-2000−22−i2i20000−i2i2−i2i2−22−2200000000000000
χ31222-22-2-2-222i2i−2i−2i00-2-2002000000002i−2i−2i−2i2i2i22−2−2i2i2−i2−i2-220002−2i2−i20000−i2i2−i2i2−22−2200000000000000
χ32222-22-2-2-222i2i−2i−2i00-2-2002000000002i−2i−2i−2i2i2i−2−222−i2−i2i2i2-22000−22−i2i20000i2−i2i2−i22−22−200000000000000
χ33222-22-2-2-22−2i−2i2i2i00-2-200200000000−2i2i2i2i−2i−2i22−2−2−i2−i2i2i2-220002−2−i2i20000i2−i2i2−i2−22−2200000000000000
χ34222-22-2-2-22−2i−2i2i2i00-2-200200000000−2i2i2i2i−2i−2i−2−222i2i2−i2−i2-22000−22i2−i20000−i2i2−i2i22−22−200000000000000
χ35222-22-2-2-22−2i−2i2i2i00-2-200200000000−2i2i−2i−2i2i2i22−2−2−i2−i2i2i22-20002−2−i2i20000−i2i2−i2i22−22−200000000000000
χ36222-22-2-2-22−2i−2i2i2i00-2-200200000000−2i2i−2i−2i2i2i−2−222i2i2−i2−i22-2000−22i2−i20000i2−i2i2−i2−22−2200000000000000
χ37222-22-2-2-2-22i2i−2i−2i002200-20022-2-200−2i2i000022−2−2i2i2−i2−i20002i−2i−22−i2i200002−2−22−i2i2i2−i200000000000000
χ38222-22-2-2-2-22i2i−2i−2i002200-20022-2-200−2i2i0000−2−222−i2−i2i2i20002i−2i2−2i2−i20000−222−2i2−i2−i2i200000000000000
χ39222-22-2-2-2-22i2i−2i−2i002200-200-2-22200−2i2i000022−2−2i2i2−i2−i2000−2i2i−22−i2i20000−222−2i2−i2−i2i200000000000000
χ40222-22-2-2-2-22i2i−2i−2i002200-200-2-22200−2i2i0000−2−222−i2−i2i2i2000−2i2i2−2i2−i200002−2−22−i2i2i2−i200000000000000
χ41222-22-2-2-2-2−2i−2i2i2i002200-20022-2-2002i−2i000022−2−2−i2−i2i2i2000−2i2i−22i2−i200002−2−22i2−i2−i2i200000000000000
χ42222-22-2-2-2-2−2i−2i2i2i002200-20022-2-2002i−2i0000−2−222i2i2−i2−i2000−2i2i2−2−i2i20000−222−2−i2i2i2−i200000000000000
χ43222-22-2-2-2-2−2i−2i2i2i002200-200-2-222002i−2i000022−2−2−i2−i2i2i20002i−2i−22i2−i20000−222−2−i2i2i2−i200000000000000
χ44222-22-2-2-2-2−2i−2i2i2i002200-200-2-222002i−2i0000−2−222i2i2−i2−i20002i−2i2−2−i2i200002−2−22i2−i2−i2i200000000000000
χ4522-2-2-22-2202-22-22200-2-202-20000000000002i−2i2i−2i2i−2i2i−2i000000000i2i2−i2−i200000000i2i2−i2−i200002−22−200
χ4622-2-2-22-2202-22-22200-2-202-20000000000002i−2i2i−2i2i−2i2i−2i000000000−i2−i2i2i200000000−i2−i2i2i20000−22−2200
χ4722-2-2-22-2202-22-22200-2-202-2000000000000−2i2i−2i2i−2i2i−2i2i000000000i2i2−i2−i200000000i2i2−i2−i20000−22−2200
χ4822-2-2-22-2202-22-22200-2-202-2000000000000−2i2i−2i2i−2i2i−2i2i000000000−i2−i2i2i200000000−i2−i2i2i200002−22−200
χ4922-2-2-22-220-22-222200-2-20-220000000000002i−2i2i−2i−2i2i−2i2i000000000i2i2−i2−i200000000−i2−i2i2i200002−2−2200
χ5022-2-2-22-220-22-222200-2-20-220000000000002i−2i2i−2i−2i2i−2i2i000000000−i2−i2i2i200000000i2i2−i2−i20000−222−200
χ5122-2-2-22-220-22-222200-2-20-22000000000000−2i2i−2i2i2i−2i2i−2i000000000i2i2−i2−i200000000−i2−i2i2i20000−222−200
χ5222-2-2-22-220-22-222200-2-20-22000000000000−2i2i−2i2i2i−2i2i−2i000000000−i2−i2i2i200000000i2i2−i2−i200002−2−2200
χ532-222-2-2-22200002-22-22-2-2002-22-22-2002-22-2000000000000000000000000000002i−2i2i−2i002i−2i000000
χ542-222-2-2-22200002-22-22-2-2002-22-22-2002-22-200000000000000000000000000000−2i2i−2i2i00−2i2i000000
χ552-222-2-2-22200002-22-22-2-200-22-222-200-22-22000000000000000000000000000002i−2i2i−2i00−2i2i000000
χ562-222-2-2-22200002-22-22-2-200-22-222-200-22-2200000000000000000000000000000−2i2i−2i2i002i−2i000000
χ572-222-2-2-2220000-222-2-22-2002-22-2-2200-22-22000000000000000002i−2i2i−2i0000000000002i−2i00000000
χ582-222-2-2-2220000-222-2-22-2002-22-2-2200-22-2200000000000000000−2i2i−2i2i000000000000−2i2i00000000
χ592-222-2-2-2220000-222-2-22-200-22-22-22002-22-2000000000000000002i−2i2i−2i000000000000−2i2i00000000
χ602-222-2-2-2220000-222-2-22-200-22-22-22002-22-200000000000000000−2i2i−2i2i0000000000002i−2i00000000
χ6144-44-4-44-404i−4i−4i4i0000000000000000000002i2−2i2−2i22i2−222222−2200000000000000000000000000000000000
χ6244-44-4-44-404i−4i−4i4i000000000000000000000−2i22i22i2−2i222−22−222200000000000000000000000000000000000
χ6344-44-4-44-40−4i4i4i−4i0000000000000000000002i2−2i2−2i22i222−22−222200000000000000000000000000000000000
χ6444-44-4-44-40−4i4i4i−4i000000000000000000000−2i22i22i2−2i2−222222−2200000000000000000000000000000000000
χ6544-4-4-44-4404-44-4-4-400440-440000000000000000000000000000000000000000000000000000000
χ6644-4-4-44-440-44-44-4-4004404-40000000000000000000000000000000000000000000000000000000
χ674-444-4-4-44-400004-4-444-44000000-440000000000000000000000000000000000000000000000000
χ684-444-4-4-44-40000-44-44-4440000004-40000000000000000000000000000000000000000000000000
χ694-44-4-444-44000000-4400-400000000004i−4i−4i4i0000000000000000000000000000000000000000000
χ704-44-4-444-44000000-4400-40000000000−4i4i4i−4i0000000000000000000000000000000000000000000
χ714-44-4-444-4-40000004-4004004-4-44000000000000000000000000000000000000000000000000000
χ724-44-4-444-4-40000004-400400-444-4000000000000000000000000000000000000000000000000000
χ734-4-4-44-444000004-400-440000000000000000000000000000000000000000000022−22−22220000000000
χ744-4-4-44-444000004-400-4400000000000000000000000000000000000000000000−222222−220000000000
χ754-4-4-44-44400000-44004-40000000000000000000000000000000022−22−22220000000000000000000000
χ764-4-4-44-44400000-44004-400000000000000000000000000000000−222222−220000000000000000000000
χ778-8-8888-8-8000000000000000000000000000000000000000000000000000000000000000000000

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