Finite Group Databasebeta

← Group #396265

Character table — Group #396265

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222444444444444888888888888888888888888888888161616161616161616161616
order12222222222222222222444444444444222222224444444444444444444444444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-11111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1
χ911111111111111111111-1-1-1-1-1-1-1-11111-1-11111111111-1-1-1-111-1-11111-1-111-1-1-1-1-1-111-1-111-1-1
χ1011111111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-111-1-111
χ1111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-111-1-111
χ1211111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111111111-1-111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-111-1-111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1111111-1-1-1-111-1-1-1-11111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-111-1-1111111-1-1-1-11111-1-111-1-1-1-111
χ1722222222222-2-2-2-2-2-2-22-20000000022-2-2000000000000220000220000-2-22-2-2-2000000000000
χ1822222222222-2-2-2-2-2-2-22-20000000022-2-2000000000000-2-20000-2-20000222-222000000000000
χ1922222222222-2-2-2-2-2-2-22-200000000-2-222000000000000220000-2-20000-2-2-2222000000000000
χ2022222222222-2-2-2-2-2-2-22-200000000-2-222000000000000-2-2000022000022-22-2-2000000000000
χ2122222222-2-2-2222-2-2-2-2-220000000022-2-20000002222-2-20000-2-200000000-2200000000000000
χ2222222222-2-2-2222-2-2-2-2-220000000022-2-2000000-2-2-2-22200002200000000-2200000000000000
χ2322222222-2-2-2222-2-2-2-2-2200000000-2-22200000022-2-2220000-2-2000000002-200000000000000
χ2422222222-2-2-2222-2-2-2-2-2200000000-2-222000000-2-222-2-2000022000000002-200000000000000
χ2522222222-2-2-2-2-2-22222-2-22222-2-2-2-22222-2-2000000000000220000000000-2-200000000000000
χ2622222222-2-2-2-2-2-22222-2-22222-2-2-2-2-2-2-2-222000000000000-2-200000000002200000000000000
χ2722222222-2-2-2-2-2-22222-2-2-2-2-2-22222222222000000000000-2-20000000000-2-200000000000000
χ2822222222-2-2-2-2-2-22222-2-2-2-2-2-22222-2-2-2-2-2-20000000000002200000000002200000000000000
χ29222-22-2-2-222-22-2-22-22-2-222i2i−2i−2i2i2i−2i−2i00000022-2-20000000000000000000000002i−2i0000000000
χ30222-22-2-2-222-22-2-22-22-2-222i2i−2i−2i2i2i−2i−2i000000-2-222000000000000000000000000−2i2i0000000000
χ31222-22-2-2-222-22-2-22-22-2-22−2i−2i2i2i−2i−2i2i2i00000022-2-2000000000000000000000000−2i2i0000000000
χ32222-22-2-2-222-22-2-22-22-2-22−2i−2i2i2i−2i−2i2i2i000000-2-2220000000000000000000000002i−2i0000000000
χ33222-22-2-2-2-2-22-2222-22-22-22i2i−2i−2i−2i−2i2i2i0000000000000000000000002i2i−2i−2i000000002-200000000
χ34222-22-2-2-2-2-22-2222-22-22-22i2i−2i−2i−2i−2i2i2i000000000000000000000000−2i−2i2i2i00000000-2200000000
χ35222-22-2-2-2-2-22-2222-22-22-2−2i−2i2i2i2i2i−2i−2i0000000000000000000000002i2i−2i−2i00000000-2200000000
χ36222-22-2-2-2-2-22-2222-22-22-2−2i−2i2i2i2i2i−2i−2i000000000000000000000000−2i−2i2i2i000000002-200000000
χ372-2-222-22-22-2222-2-2-222-2-20000000000002-20000002i−2i2i−2i002-2002i−2i000000002i−2i000000000000
χ382-2-222-22-22-2222-2-2-222-2-20000000000002-2000000−2i2i−2i2i002-200−2i2i00000000−2i2i000000000000
χ392-2-222-22-22-2222-2-2-222-2-2000000000000-220000002i−2i2i−2i00-2200−2i2i00000000−2i2i000000000000
χ402-2-222-22-22-2222-2-2-222-2-2000000000000-22000000−2i2i−2i2i00-22002i−2i000000002i−2i000000000000
χ412-2-222-22-22-22-2-2222-2-2-222i−2i2i−2i2i−2i2i−2i00000000002-2000000002-22i−2i00000000−2i2i000000000000
χ422-2-222-22-22-22-2-2222-2-2-222i−2i2i−2i2i−2i2i−2i0000000000-2200000000-22−2i2i000000002i−2i000000000000
χ432-2-222-22-22-22-2-2222-2-2-22−2i2i−2i2i−2i2i−2i2i00000000002-2000000002-2−2i2i000000002i−2i000000000000
χ442-2-222-22-22-22-2-2222-2-2-22−2i2i−2i2i−2i2i−2i2i0000000000-2200000000-222i−2i00000000−2i2i000000000000
χ452-2-222-22-2-22-222-222-2-22-22i−2i2i−2i−2i2i−2i2i0000000000002i−2i−2i2i2-200000000002-20000000000000000
χ462-2-222-22-2-22-222-222-2-22-22i−2i2i−2i−2i2i−2i2i000000000000−2i2i2i−2i-220000000000-220000000000000000
χ472-2-222-22-2-22-222-222-2-22-2−2i2i−2i2i2i−2i2i−2i0000000000002i−2i−2i2i-220000000000-220000000000000000
χ482-2-222-22-2-22-222-222-2-22-2−2i2i−2i2i2i−2i2i−2i000000000000−2i2i2i−2i2-200000000002-20000000000000000
χ492-2-222-22-2-22-2-2-22-2-222220000000000002-200002-20000-22-22-220000002-20000000000000000
χ502-2-222-22-2-22-2-2-22-2-222220000000000002-20000-2200002-2-222-2000000-220000000000000000
χ512-2-222-22-2-22-2-2-22-2-22222000000000000-2200002-200002-22-2-22000000-220000000000000000
χ522-2-222-22-2-22-2-2-22-2-22222000000000000-220000-220000-222-22-20000002-20000000000000000
χ532-2-2-222-222-2-2-22-22-2-22222-2-222-2-22000000000000000000000000000000000000002-22-20000
χ542-2-2-222-222-2-2-22-22-2-22222-2-222-2-2200000000000000000000000000000000000000-22-220000
χ552-2-2-222-222-2-2-22-22-2-2222-222-2-222-2000000000000000000000000000000000000002-2-220000
χ562-2-2-222-222-2-2-22-22-2-2222-222-2-222-200000000000000000000000000000000000000-222-20000
χ572-2-2-222-22-2222-222-2-22-2-22-2-22-222-20000000000000000000000000000000000000000002i−2i2i−2i
χ582-2-2-222-22-2222-222-2-22-2-22-2-22-222-2000000000000000000000000000000000000000000−2i2i−2i2i
χ592-2-2-222-22-2222-222-2-22-2-2-222-22-2-220000000000000000000000000000000000000000002i−2i−2i2i
χ602-2-2-222-22-2222-222-2-22-2-2-222-22-2-22000000000000000000000000000000000000000000−2i2i2i−2i
χ61444-44-4-4-444-4-444-44-44-4-4000000000000000000000000000000000000000000000000000000
χ62444-44-4-4-4-4-444-4-4-44-4444000000000000000000000000000000000000000000000000000000
χ6344-44-44-4-400000000000000000000004i−4i002-22-2000000000000002i−2i2i−2i000000000000000000
χ6444-44-44-4-400000000000000000000004i−4i00-22-2200000000000000−2i2i−2i2i000000000000000000
χ6544-44-44-4-40000000000000000000000−4i4i002-22-200000000000000−2i2i−2i2i000000000000000000
χ6644-44-44-4-40000000000000000000000−4i4i00-22-22000000000000002i−2i2i−2i000000000000000000
χ6744-4-4-4-444000000000000000000004-400002-2-22000000000000002-2-22000000000000000000
χ6844-4-4-4-444000000000000000000004-40000-222-200000000000000-222-2000000000000000000
χ6944-4-4-4-44400000000000000000000-4400002-2-2200000000000000-222-2000000000000000000
χ7044-4-4-4-44400000000000000000000-440000-222-2000000000000002-2-22000000000000000000
χ714-4-4-444-444-4-44-44-444-44-4000000000000000000000000000000000000000000000000000000
χ724-4-4-444-44-444-44-4-444-4-44000000000000000000000000000000000000000000000000000000
χ738-888-8-8-88000000000000000000000000000000000000000000000000000000000000000000
χ748-88-8-888-8000000000000000000000000000000000000000000000000000000000000000000

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