Finite Group Databasebeta

← Group #294713

Character table — Group #294713

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111222222222222222244444444444444444444444444888888888888888888161616161616161616163232
order12222222444444444444444444444444448888888888888888224444444488888888444444888824
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111-1-1-1-1111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ61111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111111111-1-1
χ91111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1111-1-111-1-11-1
χ101111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11-1-1-111-1-111-11
χ111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-11111-1111-1-1-1-111-11
χ121111111111-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111111-1-1-11111-1-11-1
χ131111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-11-1-11111-1-1-11
χ141111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111-111-1-1-1-1111-1
χ151111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1111111-1-1-1-1-11-1-111-1-1111-1
χ161111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-11-111-1-111-1-1-11
χ1722222222222222-2-2-2-2-2-222-2-222-2-22222-2-200000000000000002200-2-200-2-200000000000000000000
χ1822222222222222-2-2-2-2-2-222-2-222-2-2-2-2-2-2-2-20000000000000000-2-20022002200000000000000000000
χ192222222222-2-2-2-22222-2-222-2-2-2-2222222-2-20000000000000000-2-200-2-2002200000000000000000000
χ202222222222-2-2-2-22222-2-222-2-2-2-222-2-2-2-2-2-2000000000000000022002200-2-200000000000000000000
χ2122222222-2-22222222222-2-222-2-2-2-20000-2-20000000000000000002200220000000000-2-20000000000
χ2222222222-2-22222222222-2-222-2-2-2-20000-2-2000000000000000000-2-200-2-20000000000220000000000
χ2322222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-2220000220000000000000000000000000000000000002-22-2000000
χ2422222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-222000022000000000000000000000000000000000000-22-22000000
χ2522222222-2-2-2-2-2-22222-2-2-2-2-2-222-2-20000220000000000000000000000000000000000002-2-22000000
χ2622222222-2-2-2-2-2-22222-2-2-2-2-2-222-2-2000022000000000000000000000000000000000000-222-2000000
χ2722222222-2-2-2-2-2-2-2-2-2-222-2-22222220000-2-20000000000000000002200-2-200000000002-20000000000
χ2822222222-2-2-2-2-2-2-2-2-2-222-2-22222220000-2-2000000000000000000-2-200220000000000-220000000000
χ29222-2-2-2-22002i2i−2i−2i2i2i−2i−2i2-2002-20000000000i2i2i2i2−i2−i2−i2−i22222−2−2−2−2002-2002i−2i0000000000000000i2−i22−200
χ30222-2-2-2-22002i2i−2i−2i2i2i−2i−2i2-2002-20000000000i2i2i2i2−i2−i2−i2−i22222−2−2−2−200-2200−2i2i0000000000000000−i2i2−2200
χ31222-2-2-2-22002i2i−2i−2i2i2i−2i−2i2-2002-20000000000−i2−i2−i2−i2i2i2i2i2−2−2−2−22222002-2002i−2i0000000000000000−i2i2−2200
χ32222-2-2-2-22002i2i−2i−2i2i2i−2i−2i2-2002-20000000000−i2−i2−i2−i2i2i2i2i2−2−2−2−2222200-2200−2i2i0000000000000000i2−i22−200
χ33222-2-2-2-2200−2i−2i2i2i−2i−2i2i2i2-2002-20000000000i2i2i2i2−i2−i2−i2−i2−2−2−2−22222002-200−2i2i0000000000000000i2−i2−2200
χ34222-2-2-2-2200−2i−2i2i2i−2i−2i2i2i2-2002-20000000000i2i2i2i2−i2−i2−i2−i2−2−2−2−2222200-22002i−2i0000000000000000−i2i22−200
χ35222-2-2-2-2200−2i−2i2i2i−2i−2i2i2i2-2002-20000000000−i2−i2−i2−i2i2i2i2i22222−2−2−2−2002-200−2i2i0000000000000000−i2i22−200
χ36222-2-2-2-2200−2i−2i2i2i−2i−2i2i2i2-2002-20000000000−i2−i2−i2−i2i2i2i2i22222−2−2−2−200-22002i−2i0000000000000000i2−i2−2200
χ3722-222-2-2-22-200002i−2i2i−2i002-200002i−2i22-2-20022−2−222−2−2i2i2−i2−i2i2i2−i2−i2000000002i−2i22−2−2i2i2−i2−i2000000000000
χ3822-222-2-2-22-200002i−2i2i−2i002-200002i−2i22-2-200−2−222−2−222−i2−i2i2i2−i2−i2i2i2000000002i−2i−2−222−i2−i2i2i2000000000000
χ3922-222-2-2-22-200002i−2i2i−2i002-200002i−2i-2-2220022−2−222−2−2i2i2−i2−i2i2i2−i2−i200000000−2i2i−2−222−i2−i2i2i2000000000000
χ4022-222-2-2-22-200002i−2i2i−2i002-200002i−2i-2-22200−2−222−2−222−i2−i2i2i2−i2−i2i2i200000000−2i2i22−2−2i2i2−i2−i2000000000000
χ4122-222-2-2-22-20000−2i2i−2i2i002-20000−2i2i22-2-20022−2−222−2−2−i2−i2i2i2−i2−i2i2i200000000−2i2i22−2−2−i2−i2i2i2000000000000
χ4222-222-2-2-22-20000−2i2i−2i2i002-20000−2i2i22-2-200−2−222−2−222i2i2−i2−i2i2i2−i2−i200000000−2i2i−2−222i2i2−i2−i2000000000000
χ4322-222-2-2-22-20000−2i2i−2i2i002-20000−2i2i-2-2220022−2−222−2−2−i2−i2i2i2−i2−i2i2i2000000002i−2i−2−222i2i2−i2−i2000000000000
χ4422-222-2-2-22-20000−2i2i−2i2i002-20000−2i2i-2-22200−2−222−2−222i2i2−i2−i2i2i2−i2−i2000000002i−2i22−2−2−i2−i2i2i2000000000000
χ452-222-22-2-22-22i−2i2i−2i000000-22002i−2i002i−2i2i−2i002−22−22−22−2i2−i2i2−i2i2−i2i2−i22-200000000i2−i2i2−i22−22−2000000000000
χ462-222-22-2-22-22i−2i2i−2i000000-22002i−2i002i−2i2i−2i00−22−22−22−22−i2i2−i2i2−i2i2−i2i22-200000000−i2i2−i2i2−22−22000000000000
χ472-222-22-2-22-22i−2i2i−2i000000-22002i−2i00−2i2i−2i2i002−22−22−22−2i2−i2i2−i2i2−i2i2−i2-2200000000−i2i2−i2i2−22−22000000000000
χ482-222-22-2-22-22i−2i2i−2i000000-22002i−2i00−2i2i−2i2i00−22−22−22−22−i2i2−i2i2−i2i2−i2i2-2200000000i2−i2i2−i22−22−2000000000000
χ492-222-22-2-22-2−2i2i−2i2i000000-2200−2i2i002i−2i2i−2i002−22−22−22−2−i2i2−i2i2−i2i2−i2i2-2200000000i2−i2i2−i2−22−22000000000000
χ502-222-22-2-22-2−2i2i−2i2i000000-2200−2i2i002i−2i2i−2i00−22−22−22−22i2−i2i2−i2i2−i2i2−i2-2200000000−i2i2−i2i22−22−2000000000000
χ512-222-22-2-22-2−2i2i−2i2i000000-2200−2i2i00−2i2i−2i2i002−22−22−22−2−i2i2−i2i2−i2i2−i2i22-200000000−i2i2−i2i22−22−2000000000000
χ522-222-22-2-22-2−2i2i−2i2i000000-2200−2i2i00−2i2i−2i2i00−22−22−22−22i2−i2i2−i2i2−i2i2−i22-200000000i2−i2i2−i2−22−22000000000000
χ532-2-22-2-22222000000002-2-2-2-2200002i−2i−2i2i2-22-2-222-2-220000000000002i−2i00002i−2i−2i2i0000000000000000
χ542-2-22-2-22222000000002-2-2-2-2200002i−2i−2i2i2-2-222-2-222-20000000000002i−2i0000−2i2i2i−2i0000000000000000
χ552-2-22-2-22222000000002-2-2-2-220000−2i2i2i−2i2-22-2-222-2-22000000000000−2i2i0000−2i2i2i−2i0000000000000000
χ562-2-22-2-22222000000002-2-2-2-220000−2i2i2i−2i2-2-222-2-222-2000000000000−2i2i00002i−2i−2i2i0000000000000000
χ572-2-22-2-2222200000000-22-2-22-200002i−2i−2i2i-22000000002-2-222-2-220000−2i2i00000000−2i2i2i−2i000000000000
χ582-2-22-2-2222200000000-22-2-22-200002i−2i−2i2i-2200000000-222-2-222-20000−2i2i000000002i−2i−2i2i000000000000
χ592-2-22-2-2222200000000-22-2-22-20000−2i2i2i−2i-22000000002-2-222-2-2200002i−2i000000002i−2i−2i2i000000000000
χ602-2-22-2-2222200000000-22-2-22-20000−2i2i2i−2i-2200000000-222-2-222-200002i−2i00000000−2i2i2i−2i000000000000
χ61444-4-4-4-44004i4i−4i−4i−4i−4i4i4i-4400-4400000000000000000000000000000000000000000000000000000000
χ62444-4-4-4-4400−4i−4i4i4i4i4i−4i−4i-4400-4400000000000000000000000000000000000000000000000000000000
χ6344-444-4-4-4-4400004i−4i4i−4i00-440000−4i4i0000000000000000000000000000000000000000000000000000
χ6444-444-4-4-4-440000−4i4i−4i4i00-4400004i−4i0000000000000000000000000000000000000000000000000000
χ6544-4-4-444-40000004-4-4400000000000000002i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ6644-4-4-444-40000004-4-440000000000000000−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ6744-4-4-444-4000000-444-400000000000000002i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ6844-4-4-444-4000000-444-40000000000000000−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ694-444-44-4-4-444i−4i4i−4i0000004-400−4i4i000000000000000000000000000000000000000000000000000000
χ704-444-44-4-4-44−4i4i−4i4i0000004-4004i−4i000000000000000000000000000000000000000000000000000000
χ714-44-44-44-4004-4-44000000000000000000002i−2i2i−2i−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000
χ724-44-44-44-4004-4-4400000000000000000000−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i−2i2i−2i2i000000000000000000000000000000
χ734-44-44-44-400-444-4000000000000000000002i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i000000000000000000000000000000
χ744-44-44-44-400-444-400000000000000000000−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000
χ754-4-44-4-444-4-4000000004-444-4400000000-440000000000000000000000000000000000000000000000
χ764-4-44-4-444-4-400000000-44444-4000000004-40000000000000000000000000000000000000000000000
χ774-4-4-444-4400000000004400-4-400000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000000
χ784-4-4-444-4400000000004400-4-40000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000000
χ794-4-4-444-440000000000-4-4004400000000000000000022−22−2222−222222−22000000000000000000000000000000
χ804-4-4-444-440000000000-4-40044000000000000000000−222222−2222−22−2222000000000000000000000000000000

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