Finite Group Databasebeta

← Group #270947

Character table — Group #270947

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111222222222222222244444444444444444444444444888888888888888888161616161616161616163232
order12222222222244444444444422224444448888888888888888224444444488888888444444888824
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
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
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-11111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ6111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111111111-1-1
χ911111111-1-1-1-111111-1-1-1-11111111-1-11-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-111-1-111-1-11-1
χ1011111111-1-1-1-111111-1-1-1-11111111-1-11-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-11-1-111-1-111-11
χ1111111111-1-1-1-111111-1-1-1-11111111-1-11-1-11-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-111111-111-1-1-1-111-11
χ1211111111-1-1-1-111111-1-1-1-11111111-1-11-1-11-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1-1-11111-11-1-11111-1-11-1
χ1311111111-1-1-1-111111-1-1-1-1111-1-1-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111111-1-1-11111-1-1-11
χ1411111111-1-1-1-111111-1-1-1-1111-1-1-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1111-1-1-1-1111-1
χ1511111111-1-1-1-111111-1-1-1-1111-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-1111111111111-1-111-1-11111-1-1-1-11-1-1-111-1-1111-1
χ1611111111-1-1-1-111111-1-1-1-1111-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1111-1-111-1-1-11
χ1722222222222222-2-2-2-2-2-2-222-2222222-2-2-2-200000000000000002200-2-2-2-20000000000000000000000
χ1822222222222222-2-2-2-2-2-2-222-2-2-2-2-222-2-2-2-20000000000000000-2-20022220000000000000000000000
χ19222222222222-2-22222222-2-220000-2-2-2-2-2-20000000000000000002200002200000000-2-20000000000
χ20222222222222-2-22222222-2-220000-2-2-2-2-2-2000000000000000000-2-20000-2-200000000220000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-20000-2-222220000000000000000000000000000000000002-22-2000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-20000-2-22222000000000000000000000000000000000000-22-22000000
χ2322222222-2-2-2-222-2-2-2222222-22222-2-2-222-20000000000000000-2-200-2-2220000000000000000000000
χ2422222222-2-2-2-222-2-2-2222222-2-2-2-2-2-2-2-222-20000000000000000220022-2-20000000000000000000000
χ2522222222-2-2-2-2-2-2222-2-2-2-2-2-22000022-222-2000000000000000000220000-2-200000000-220000000000
χ2622222222-2-2-2-2-2-2222-2-2-2-2-2-22000022-222-2000000000000000000-2-2000022000000002-20000000000
χ2722222222-2-2-2-2-2-2-2-2-22222-2-2-20000222-2-220000000000000000000000000000000000002-2-22000000
χ2822222222-2-2-2-2-2-2-2-2-22222-2-2-20000222-2-22000000000000000000000000000000000000-222-2000000
χ29222-22-2-2-222-2-2-2-2000000022022-2-22-20000i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i22-200000000i2i2−i2−i2i2i2−i2−i2000000000000
χ30222-22-2-2-222-2-2-2-2000000022022-2-22-20000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i22-200000000−i2−i2i2i2−i2−i2i2i2000000000000
χ31222-22-2-2-222-2-2-2-20000000220-2-2222-20000i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2-2200000000−i2−i2i2i2−i2−i2i2i2000000000000
χ32222-22-2-2-222-2-2-2-20000000220-2-2222-20000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2-2200000000i2i2−i2−i2i2i2−i2−i2000000000000
χ33222-22-2-2-2-2-222-2-2000000022022-2-2-220000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i2-2200000000i2i2−i2−i2−i2−i2i2i2000000000000
χ34222-22-2-2-2-2-222-2-2000000022022-2-2-220000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i2-2200000000−i2−i2i2i2i2i2−i2−i2000000000000
χ35222-22-2-2-2-2-222-2-20000000220-2-222-220000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i22-200000000−i2−i2i2i2i2i2−i2−i2000000000000
χ36222-22-2-2-2-2-222-2-20000000220-2-222-220000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i22-200000000i2i2−i2−i2−i2−i2i2i2000000000000
χ372-222-2-22-200002-20002i2i−2i−2i2-202-22-20002i−2i022−2−222−2−2i2i2−i2−i2i2i2−i2−i20000002i−2i002−22−2i2−i2i2−i2000000000000
χ382-222-2-22-200002-20002i2i−2i−2i2-202-22-20002i−2i0−2−222−2−222−i2−i2i2i2−i2−i2i2i20000002i−2i00−22−22−i2i2−i2i2000000000000
χ392-222-2-22-200002-20002i2i−2i−2i2-20-22-220002i−2i022−2−222−2−2i2i2−i2−i2i2i2−i2−i2000000−2i2i00−22−22−i2i2−i2i2000000000000
χ402-222-2-22-200002-20002i2i−2i−2i2-20-22-220002i−2i0−2−222−2−222−i2−i2i2i2−i2−i2i2i2000000−2i2i002−22−2i2−i2i2−i2000000000000
χ412-222-2-22-200002-2000−2i−2i2i2i2-202-22-2000−2i2i022−2−222−2−2−i2−i2i2i2−i2−i2i2i2000000−2i2i002−22−2−i2i2−i2i2000000000000
χ422-222-2-22-200002-2000−2i−2i2i2i2-202-22-2000−2i2i0−2−222−2−222i2i2−i2−i2i2i2−i2−i2000000−2i2i00−22−22i2−i2i2−i2000000000000
χ432-222-2-22-200002-2000−2i−2i2i2i2-20-22-22000−2i2i022−2−222−2−2−i2−i2i2i2−i2−i2i2i20000002i−2i00−22−22i2−i2i2−i2000000000000
χ442-222-2-22-200002-2000−2i−2i2i2i2-20-22-22000−2i2i0−2−222−2−222i2i2−i2−i2i2i2−i2−i20000002i−2i002−22−2−i2i2−i2i2000000000000
χ452-22-2-22-220000-2222-200002-2-22-2-2200200-22i2i−2i−2i−2i−2i2i2i0000000000002-200002i−2i−2i2i0000000000000000
χ462-22-2-22-220000-2222-200002-2-22-2-2200200-2−2i−2i2i2i2i2i−2i−2i0000000000002-20000−2i2i2i−2i0000000000000000
χ472-22-2-22-220000-2222-200002-2-2-222-200200-22i2i−2i−2i−2i−2i2i2i000000000000-220000−2i2i2i−2i0000000000000000
χ482-22-2-22-220000-2222-200002-2-2-222-200200-2−2i−2i2i2i2i2i−2i−2i000000000000-2200002i−2i−2i2i0000000000000000
χ492-22-2-22-220000-22-2-2200002-222-2-2200-20020000000022-2-2-2-2220000-22000000002-2-22000000000000
χ502-22-2-22-220000-22-2-2200002-222-2-2200-200200000000-2-22222-2-20000-2200000000-222-2000000000000
χ512-22-2-22-220000-22-2-2200002-22-222-200-20020000000022-2-2-2-22200002-200000000-222-2000000000000
χ522-22-2-22-220000-22-2-2200002-22-222-200-200200000000-2-22222-2-200002-2000000002-2-22000000000000
χ532-2-2-22-2222-22-2002-2-22-22-200200000000002−22−22−22−22−22−22−22−2002-200002-2000000000000002−22−200
χ542-2-2-22-2222-22-2002-2-22-22-200200000000002−22−22−22−22−22−22−22−200-220000-2200000000000000−22−2200
χ552-2-2-22-2222-22-2002-2-22-22-20020000000000−22−22−22−22−22−22−22−22002-200002-200000000000000−22−2200
χ562-2-2-22-2222-22-2002-2-22-22-20020000000000−22−22−22−22−22−22−22−2200-220000-22000000000000002−22−200
χ572-2-2-22-222-22-22002-2-2-22-2200200000000002−22−22−22−2−22−22−22−22002-20000-22000000000000002−2−2200
χ582-2-2-22-222-22-22002-2-2-22-2200200000000002−22−22−22−2−22−22−22−2200-2200002-200000000000000−222−200
χ592-2-2-22-222-22-22002-2-2-22-220020000000000−22−22−22−222−22−22−22−2002-20000-2200000000000000−222−200
χ602-2-2-22-222-22-22002-2-2-22-220020000000000−22−22−22−222−22−22−22−200-2200002-2000000000000002−2−2200
χ61444-44-4-4-444-4-4440000000-4-400000-4400000000000000000000000000000000000000000000000000
χ62444-44-4-4-4-4-444440000000-4-4000004-400000000000000000000000000000000000000000000000000
χ6344-44-4-4-440000004-44000000-400000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000000
χ6444-44-4-4-440000004-44000000-40000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000000
χ6544-44-4-4-44000000-44-4000000400000000000000000022−22−2222−222222−22000000000000000000000000000000
χ6644-44-4-4-44000000-44-40000004000000000000000000−222222−2222−22−2222000000000000000000000000000000
χ6744-4-4-444-40000000004i−4i−4i4i00000000000002-2-222-2-222i−2i−2i2i2i−2i−2i2i000000000000000000000000000000
χ6844-4-4-444-40000000004i−4i−4i4i0000000000000-222-2-222-2−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000
χ6944-4-4-444-4000000000−4i4i4i−4i00000000000002-2-222-2-22−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000
χ7044-4-4-444-4000000000−4i4i4i−4i0000000000000-222-2-222-22i−2i−2i2i2i−2i−2i2i000000000000000000000000000000
χ714-444-4-44-40000-440004i4i−4i−4i-4400000000−4i4i00000000000000000000000000000000000000000000000
χ724-444-4-44-40000-44000−4i−4i4i4i-44000000004i−4i00000000000000000000000000000000000000000000000
χ734-44-4-44-4400004-444-40000-44-4000000-40040000000000000000000000000000000000000000000000
χ744-44-4-44-4400004-4-4-440000-444000000400-40000000000000000000000000000000000000000000000
χ754-4-4444-4-44-4-4400000000000000000000002i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i000000000000000000000000000000
χ764-4-4444-4-44-4-440000000000000000000000−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000
χ774-4-4444-4-4-444-400000000000000000000002i−2i2i−2i−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000
χ784-4-4444-4-4-444-40000000000000000000000−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i−2i2i−2i2i000000000000000000000000000000
χ794-4-4-44-4444-44-400-444-44-4400-400000000000000000000000000000000000000000000000000000000
χ804-4-4-44-444-44-4400-4444-44-400-400000000000000000000000000000000000000000000000000000000

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