Finite Group Databasebeta

← Group #346617

Character table — Group #346617

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222222244444444222222224444444444444444444444444444444888888888888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ611111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-111
χ811111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111111111-1-1
χ911111111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11-1
χ1011111111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-11
χ1111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-111111111-1-1-1-111-1-1-1-111-11
χ1211111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-11111-1-1-1-11111-1-11111-1-11-1
χ1311111111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-11
χ1411111111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1111-1
χ1511111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-111-11111-1-1-1-11111-1-1-1-1-1-111-1-1111-1
χ1611111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-111-11111-1-1-1-1-1-1-1-1111111-1-111-1-1-11
χ1722222222222222-2-222-2-22222222222-2-200000000-2-2-2-2-2-20000-200000000000000000000000000
χ1822222222222222-2-222-2-2-2-2-2-2-2-2-2-222-2-200000000-2-222220000-200000000000000000000000000
χ19222222222222-2-222-2-22200000000-2-22222222222-2-20000-2-2-2-2-200000000000000000000000000
χ20222222222222-2-222-2-22200000000-2-222-2-2-2-2-2-2-2-2-2-200002222-200000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-200000000-2-2-2-2000000002200000000222-2-222-2-2000000000000000000
χ22222222222222-2-2-2-2-2-2-2-200000000-2-2-2-20000000022000000002-2-222-2-222000000000000000000
χ2322222222-2-2-2-222-2-222-2-22222-2-2-2-2-2-22200000000-2-2-2-2220000200000000000000000000000000
χ2422222222-2-2-2-222-2-222-2-2-2-2-2-22222-2-22200000000-2-222-2-20000200000000000000000000000000
χ2522222222-2-2-2-2-2-222-2-2220000000022-2-22222-2-2-2-2-2-20000-2-222200000000000000000000000000
χ2622222222-2-2-2-2-2-222-2-2220000000022-2-2-2-2-2-22222-2-2000022-2-2200000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2000000002222000000002200000000-222-2-2-2-222000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2000000002222000000002200000000-2-2-22222-2-2000000000000000000
χ29222-2-2-22-222-2-200-2-2002200000000002-22i2i−2i−2i2i2i−2i−2i000000000000000000022−2−222−2−20000i2−i2i2−i200
χ30222-2-2-22-222-2-200-2-2002200000000002-22i2i−2i−2i2i2i−2i−2i0000000000000000000−2−222−2−2220000−i2i2−i2i200
χ31222-2-2-22-222-2-200-2-2002200000000002-2−2i−2i2i2i−2i−2i2i2i000000000000000000022−2−222−2−20000−i2i2−i2i200
χ32222-2-2-22-222-2-200-2-2002200000000002-2−2i−2i2i2i−2i−2i2i2i0000000000000000000−2−222−2−2220000i2−i2i2−i200
χ33222-2-2-22-2-2-22200-2-200220000000000-222i2i−2i−2i−2i−2i2i2i000000000000000000022−2−2−2−2220000i2−i2−i2i200
χ34222-2-2-22-2-2-22200-2-200220000000000-222i2i−2i−2i−2i−2i2i2i0000000000000000000−2−22222−2−20000−i2i2i2−i200
χ35222-2-2-22-2-2-22200-2-200220000000000-22−2i−2i2i2i2i2i−2i−2i000000000000000000022−2−2−2−2220000−i2i2i2−i200
χ36222-2-2-22-2-2-22200-2-200220000000000-22−2i−2i2i2i2i2i−2i−2i0000000000000000000−2−22222−2−20000i2−i2−i2i200
χ3722-2-222-2-22-22-2-2-200220022-2-222-2-22-200000000000000000000000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000
χ3822-2-222-2-22-22-2-2-200220022-2-222-2-22-200000000000000000000000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000
χ3922-2-222-2-22-22-2-2-2002200-2-222-2-2222-200000000000000000000000000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2000000
χ4022-2-222-2-22-22-2-2-2002200-2-222-2-2222-200000000000000000000000000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2000000
χ4122-2-222-2-2-22-22-2-200220022-2-2-2-222-2200000000000000000000000000000i2−i2i2−i2−i2i2−i2i2i2−i2−i2i2000000
χ4222-2-222-2-2-22-22-2-200220022-2-2-2-222-2200000000000000000000000000000−i2i2−i2i2i2−i2i2−i2−i2i2i2−i2000000
χ4322-2-222-2-2-22-22-2-2002200-2-22222-2-2-2200000000000000000000000000000i2−i2i2−i2−i2i2−i2i2−i2i2i2−i2000000
χ4422-2-222-2-2-22-22-2-2002200-2-22222-2-2-2200000000000000000000000000000−i2i2−i2i2i2−i2i2−i2i2−i2−i2i2000000
χ452-2-2-2-222200002-22-22-22-200002-22-2000000002-22-22-2002-2002-202-22-20000000000000000000000
χ462-2-2-2-222200002-22-22-22-200002-22-200000000-22-222-2002-200-220-22-220000000000000000000000
χ472-2-2-2-222200002-22-22-22-20000-22-22000000002-22-22-200-22002-20-22-220000000000000000000000
χ482-2-2-2-222200002-22-22-22-20000-22-2200000000-22-222-200-2200-2202-22-20000000000000000000000
χ492-2-2-2-222200002-2-222-2-2200002-22-200002-22-20000-2200-222-200000002-22-2000000000000000000
χ502-2-2-2-222200002-2-222-2-2200002-22-20000-22-220000-2200-22-220000000-22-22000000000000000000
χ512-2-2-2-222200002-2-222-2-220000-22-2200002-22-20000-22002-22-20000000-22-22000000000000000000
χ522-2-2-2-222200002-2-222-2-220000-22-220000-22-220000-22002-2-2200000002-22-2000000000000000000
χ532-2-2-2-22220000-222-2-222-22-22-20000000000002-22-2-222-20000-22000002-2-22000000000000000000
χ542-2-2-2-22220000-222-2-222-22-22-2000000000000-22-22-222-200002-200000-222-2000000000000000000
χ552-2-2-2-22220000-222-2-222-2-22-220000000000002-22-2-22-220000-2200000-222-2000000000000000000
χ562-2-2-2-22220000-222-2-222-2-22-22000000000000-22-22-22-2200002-2000002-2-22000000000000000000
χ572-2-2-2-22220000-22-22-22-222-22-2000000002-22-200002-2-2200-220002-2-220000000000000000000000
χ582-2-2-2-22220000-22-22-22-222-22-200000000-22-2200002-2-22002-2000-222-20000000000000000000000
χ592-2-2-2-22220000-22-22-22-22-22-22000000002-22-200002-22-200-22000-222-20000000000000000000000
χ602-2-2-2-22220000-22-22-22-22-22-2200000000-22-2200002-22-2002-20002-2-220000000000000000000000
χ61444-4-4-44-444-4-4004400-4-40000000000-44000000000000000000000000000000000000000000000
χ62444-4-4-44-4-4-444004400-4-400000000004-4000000000000000000000000000000000000000000000
χ6344-44-4-4-444-4-44000000000000000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000
χ6444-44-4-4-444-4-4400000000000000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000
χ6544-44-4-4-44-444-4000000000000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000
χ6644-44-4-4-44-444-400000000000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000
χ6744-4-444-4-44-44-44400-4-40000000000-4400000000000000000000000000000000000000000000000
χ6844-4-444-4-4-44-444400-4-400000000004-400000000000000000000000000000000000000000000000
χ694-444-44-4-400004-400-44004-4-4400000000000000000000000000000000000000000000000000000
χ704-444-44-4-400004-400-4400-444-400000000000000000000000000000000000000000000000000000
χ714-444-44-4-40000-44004-40000004-4-440000000000000000000000000000000000000000000000000
χ724-444-44-4-40000-44004-4000000-444-40000000000000000000000000000000000000000000000000
χ734-4-444-44-40000004-400-440000000000004i−4i−4i4i00000000000000000000000000000000000000000
χ744-4-444-44-40000004-400-44000000000000−4i4i4i−4i00000000000000000000000000000000000000000
χ754-4-444-44-4000000-44004-400000000000000004i−4i−4i4i0000000000000000000000000000000000000
χ764-4-444-44-4000000-44004-40000000000000000−4i4i4i−4i0000000000000000000000000000000000000
χ778-88-88-8-88000000000000000000000000000000000000000000000000000000000000000000000

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