Finite Group Databasebeta

← Group #349516

Character table — Group #349516

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444222244444444444444444444444444444444444888888888888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1
χ41111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111-1-1-1-11-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ611111111111111111111-1-1-1-11-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111-1-1-1-11-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1111111111111-1-1-1-1-1-1-1-111
χ811111111111111111111-1-1-1-11-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111111111-1-1
χ91111111111-1-1-1-111111111111-1-1-1-1-1-11111-1-1-1-1-1-11-111-1-1111111-1-1-1-1-1-11111-1-1-1-111-1-111-1-11-1
χ101111111111-1-1-1-111111111111-1-1-1-1-1-11111-1-1-1-1-1-11-111-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-11
χ111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-11111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-11
χ121111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-11-1
χ131111111111-1-1-1-1111111-1-1-1-111111-1-11111-1-1-1-1-1-11-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-11
χ141111111111-1-1-1-1111111-1-1-1-111111-1-11111-1-1-1-1-1-11-111-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1111-1
χ151111111111-1-1-1-1111111-1-1-1-111111-1-1-1-1-1-1-1-111111-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-1111-1
χ161111111111-1-1-1-1111111-1-1-1-111111-1-1-1-1-1-1-1-111111-1-1-111-1-1111111-1-1-1-1-1-1-1-1111111-1-111-1-1-11
χ1722222222222222-2-222-2-22222-22222220000-2-20000-2-20000-2-20000-2-20000000000000000000000
χ1822222222222222-2-222-2-2-2-2-2-2-2-2-2-2-2220000-2-20000-2-20000220000220000000000000000000000
χ192222222222-2-2-2-2-2-222-2-22222-2-2-2-2-2-2-20000220000-220000-2-20000220000000000000000000000
χ202222222222-2-2-2-2-2-222-2-2-2-2-2-2-22222-2-20000220000-220000220000-2-20000000000000000000000
χ2122222222-2-2222222-2-2220000-20000-2-22222222222-2-2-2-2-2-2000000000000000000000000000000
χ2222222222-2-2222222-2-2220000-20000-2-2-2-2-2-222-2-2-2-2-2-22222000000000000000000000000000000
χ2322222222-2-22222-2-2-2-2-2-2000020000-2-20000-2-200002200000022-2-20022-2-2000000000000000000
χ2422222222-2-22222-2-2-2-2-2-2000020000-2-20000-2-2000022000000-2-22200-2-222000000000000000000
χ2522222222-2-2-2-2-2-222-2-2220000-20000222222-2-2-2-2-2-2-22-2-222000000000000000000000000000000
χ2622222222-2-2-2-2-2-222-2-2220000-2000022-2-2-2-2-2-22222-2222-2-2000000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-20000200002200002200002-200000022-2-200-2-222000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-20000200002200002200002-2000000-2-2220022-2-2000000000000000000
χ29222-2-2-22-222000022-2-2-2-222-2-2200000022-2-2000000-202-2002-22-22-2000000000000000000000000
χ30222-2-2-22-222000022-2-2-2-222-2-22000000-2-222000000-20-22002-2-22-22000000000000000000000000
χ31222-2-2-22-222000022-2-2-2-2-2-222200000022-2-2000000-202-200-22-22-22000000000000000000000000
χ32222-2-2-22-222000022-2-2-2-2-2-2222000000-2-222000000-20-2200-222-22-2000000000000000000000000
χ33222-2-2-22-2220000-2-2-2-22222-2-2-20000000000002i2i−2i−2i20002i−2i-220000002i−2i2i−2i000000000000000000
χ34222-2-2-22-2220000-2-2-2-22222-2-2-2000000000000−2i−2i2i2i2000−2i2i-22000000−2i2i−2i2i000000000000000000
χ35222-2-2-22-2220000-2-2-2-222-2-222-20000000000002i2i−2i−2i20002i−2i2-2000000−2i2i−2i2i000000000000000000
χ36222-2-2-22-2220000-2-2-2-222-2-222-2000000000000−2i−2i2i2i2000−2i2i2-20000002i−2i2i−2i000000000000000000
χ37222-2-2-22-2-2-200002222-2-20000-22i2i−2i−2i0022-2-200000020-22000000002i−2i2i−2i−2i2i000000000000000000
χ38222-2-2-22-2-2-200002222-2-20000-22i2i−2i−2i00-2-222000000202-2000000002i−2i−2i2i2i−2i000000000000000000
χ39222-2-2-22-2-2-200002222-2-20000-2−2i−2i2i2i0022-2-200000020-2200000000−2i2i−2i2i2i−2i000000000000000000
χ40222-2-2-22-2-2-200002222-2-20000-2−2i−2i2i2i00-2-222000000202-200000000−2i2i2i−2i−2i2i000000000000000000
χ41222-2-2-22-2-2-20000-2-22222000022i2i−2i−2i000000002i2i−2i−2i-2000−2i2i002-2-22−2i2i0000000000000000000000
χ42222-2-2-22-2-2-20000-2-22222000022i2i−2i−2i00000000−2i−2i2i2i-20002i−2i00-222-2−2i2i0000000000000000000000
χ43222-2-2-22-2-2-20000-2-2222200002−2i−2i2i2i000000002i2i−2i−2i-2000−2i2i00-222-22i−2i0000000000000000000000
χ44222-2-2-22-2-2-20000-2-2222200002−2i−2i2i2i00000000−2i−2i2i2i-20002i−2i002-2-222i−2i0000000000000000000000
χ4522-22-2-2-222-22i2i−2i−2i002-2002-22-202i−2i2i−2i2i−2i000000000000000000000000000022−2−2i2i2−i2−i22−2i2−i2000000
χ4622-22-2-2-222-22i2i−2i−2i002-2002-22-202i−2i2i−2i2i−2i0000000000000000000000000000−2−222−i2−i2i2i2−22−i2i2000000
χ4722-22-2-2-222-22i2i−2i−2i002-200-22-220−2i2i−2i2i2i−2i000000000000000000000000000022−2−2i2i2−i2−i2−22−i2i2000000
χ4822-22-2-2-222-22i2i−2i−2i002-200-22-220−2i2i−2i2i2i−2i0000000000000000000000000000−2−222−i2−i2i2i22−2i2−i2000000
χ4922-22-2-2-222-2−2i−2i2i2i002-2002-22-20−2i2i−2i2i−2i2i000000000000000000000000000022−2−2−i2−i2i2i22−2−i2i2000000
χ5022-22-2-2-222-2−2i−2i2i2i002-2002-22-20−2i2i−2i2i−2i2i0000000000000000000000000000−2−222i2i2−i2−i2−22i2−i2000000
χ5122-22-2-2-222-2−2i−2i2i2i002-200-22-2202i−2i2i−2i−2i2i000000000000000000000000000022−2−2−i2−i2i2i2−22i2−i2000000
χ5222-22-2-2-222-2−2i−2i2i2i002-200-22-2202i−2i2i−2i−2i2i0000000000000000000000000000−2−222i2i2−i2−i22−2−i2i2000000
χ532-2-22-222-2002i−2i2i−2i2-2002-2000000000002-22-22i−2i2i−2i2i−2i0000000000000000002−22−2i2−i2i2−i200002−2i2−i200
χ542-2-22-222-2002i−2i2i−2i2-2002-2000000000002-22-22i−2i2i−2i2i−2i000000000000000000−22−22−i2i2−i2i20000−22−i2i200
χ552-2-22-222-2002i−2i2i−2i2-2002-200000000000-22-222i−2i−2i2i−2i2i0000000000000000002−22−2i2−i2i2−i20000−22−i2i200
χ562-2-22-222-2002i−2i2i−2i2-2002-200000000000-22-222i−2i−2i2i−2i2i000000000000000000−22−22−i2i2−i2i200002−2i2−i200
χ572-2-22-222-200−2i2i−2i2i2-2002-2000000000002-22-2−2i2i−2i2i−2i2i0000000000000000002−22−2−i2i2−i2i200002−2−i2i200
χ582-2-22-222-200−2i2i−2i2i2-2002-2000000000002-22-2−2i2i−2i2i−2i2i000000000000000000−22−22i2−i2i2−i20000−22i2−i200
χ592-2-22-222-200−2i2i−2i2i2-2002-200000000000-22-22−2i2i2i−2i2i−2i0000000000000000002−22−2−i2i2−i2i20000−22i2−i200
χ602-2-22-222-200−2i2i−2i2i2-2002-200000000000-22-22−2i2i2i−2i2i−2i000000000000000000−22−22i2−i2i2−i200002−2−i2i200
χ6144-44-4-4-44-444i4i−4i−4i00-4400000000000−4i4i0000000000000000000000000000000000000000000000
χ6244-44-4-4-44-44−4i−4i4i4i00-44000000000004i−4i0000000000000000000000000000000000000000000000
χ6344-4-444-4-44-4000000-44004-4-4400000000000000000000000000000000000000000000000000000
χ6444-4-444-4-44-4000000-4400-444-400000000000000000000000000000000000000000000000000000
χ6544-4-444-4-4-440000004-400000004-4-44000000000000000000000000000000000000000000000000
χ6644-4-444-4-4-440000004-40000000-444-4000000000000000000000000000000000000000000000000
χ674-4444-4-4-4004-4-440000000000000000000000000000000000000000000002-2-222-2-220000000000
χ684-4444-4-4-4004-4-44000000000000000000000000000000000000000000000-222-2-222-20000000000
χ694-4444-4-4-400-444-40000000000000000000000000000000000000000000002-2-22-222-20000000000
χ704-4444-4-4-400-444-4000000000000000000000000000000000000000000000-222-22-2-220000000000
χ714-4-44-444-4004i−4i4i−4i-4400-44000000000000000−4i4i0000000000000000000000000000000000000000
χ724-4-44-444-400−4i4i−4i4i-4400-440000000000000004i−4i0000000000000000000000000000000000000000
χ734-4-4-44-4440000004-400-44000000000004-4-44000000000000000000000000000000000000000000
χ744-4-4-44-4440000004-400-4400000000000-444-4000000000000000000000000000000000000000000
χ754-4-4-44-444000000-44004-4000000000000000004-4-44000000000000000000000000000000000000
χ764-4-4-44-444000000-44004-400000000000000000-444-4000000000000000000000000000000000000
χ778-88-8-88-88000000000000000000000000000000000000000000000000000000000000000000000

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