Finite Group Databasebeta

← Group #240258

Character table — Group #240258

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111111111111222222222222222244444444444444444444888888888888888888888888888888881616161616161616
order12222222444444442222444444444444444488888888888888882222444488888888888888888888888844444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-11111111-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-11111111-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111
χ1111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-11111111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-111
χ1211111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-11111111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ1311111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ1411111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ1511111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ1611111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111
χ17222222222222222222222-2-2-2-2-2-2222-2-2-2-2-2-22222-2-2-2-22222-2-2-2-20000000000000000000000000000000000000000
χ18222222222222222222222-2-2-2-2-2-2222-2-2-2-2-2-2-2-2-2-22222-2-2-2-222220000000000000000000000000000000000000000
χ192222222222222222-2-2-2-2-2222222-2-2-222-2-2-2-2000000000000000022-2-2-2-22200000000000000000000000000000000
χ202222222222222222-2-2-2-2-2222222-2-2-222-2-2-2-20000000000000000-2-22222-2-200000000000000000000000000000000
χ212222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ2322222222-2-2-2-2-2-2-2-22222-222-2-2-2-2-2-2-222-2-22200000000000000002222-2-2-2-200000000000000000000000000000000
χ2422222222-2-2-2-2-2-2-2-22222-222-2-2-2-2-2-2-222-2-2220000000000000000-2-2-2-2222200000000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-2-22222-2-2-2-2-222-2-20000000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ2622222222-2-2-2-2-2-2-2-22222-2-2-22222-2-2-2-2-222-2-2000000000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22-2-22222222-2-2-2-2222222-2-2-2-2-2-2-2-222220000000000000000000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22-2-22222222-2-2-2-222-2-2-2-222222222-2-2-2-20000000000000000000000000000000000000000
χ29222-2-22-2-22222-2-2-2-222-2-2-20000002-22000000000022-2-2000022-2-20000000000000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200000000
χ30222-2-22-2-22222-2-2-2-222-2-2-20000002-22000000000022-2-2000022-2-20000000000000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200000000
χ31222-2-22-2-22222-2-2-2-222-2-2-20000002-220000000000-2-2220000-2-2220000000000000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200000000
χ32222-2-22-2-22222-2-2-2-222-2-2-20000002-220000000000-2-2220000-2-2220000000000000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200000000
χ33222-2-22-2-2-2-2-2-22222-2-222-20000002-22000000000022-2-20000-2-2220000000000000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i200000000
χ34222-2-22-2-2-2-2-2-22222-2-222-20000002-22000000000022-2-20000-2-2220000000000000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i200000000
χ35222-2-22-2-2-2-2-2-22222-2-222-20000002-220000000000-2-222000022-2-20000000000000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i200000000
χ36222-2-22-2-2-2-2-2-22222-2-222-20000002-220000000000-2-222000022-2-20000000000000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i200000000
χ3722-22-2-22-22i2i−2i−2i2i2i−2i−2i000002-22i2i−2i−2i0002-20000i2i2−i2−i2i2−i2i2−i222−2−22−22−2002-22i−2i002−22−2i2−i2i2−i2000000000000000000000000
χ3822-22-2-22-22i2i−2i−2i2i2i−2i−2i000002-22i2i−2i−2i0002-20000i2i2−i2−i2i2−i2i2−i222−2−22−22−200-22−2i2i00−22−22−i2i2−i2i2000000000000000000000000
χ3922-22-2-22-22i2i−2i−2i2i2i−2i−2i000002-22i2i−2i−2i0002-20000−i2−i2i2i2−i2i2−i2i2−2−222−22−22002-22i−2i00−22−22−i2i2−i2i2000000000000000000000000
χ4022-22-2-22-22i2i−2i−2i2i2i−2i−2i000002-22i2i−2i−2i0002-20000−i2−i2i2i2−i2i2−i2i2−2−222−22−2200-22−2i2i002−22−2i2−i2i2−i2000000000000000000000000
χ4122-22-2-22-22i2i−2i−2i2i2i−2i−2i00000-22−2i−2i2i2i000-220000i2i2−i2−i2−i2i2−i2i222−2−2−22−222-200002i−2ii2−i2−i2i2−222−2000000000000000000000000
χ4222-22-2-22-22i2i−2i−2i2i2i−2i−2i00000-22−2i−2i2i2i000-220000i2i2−i2−i2−i2i2−i2i222−2−2−22−22-220000−2i2i−i2i2i2−i22−2−22000000000000000000000000
χ4322-22-2-22-22i2i−2i−2i2i2i−2i−2i00000-22−2i−2i2i2i000-220000−i2−i2i2i2i2−i2i2−i2−2−2222−22−22-200002i−2i−i2i2i2−i22−2−22000000000000000000000000
χ4422-22-2-22-22i2i−2i−2i2i2i−2i−2i00000-22−2i−2i2i2i000-220000−i2−i2i2i2i2−i2i2−i2−2−2222−22−2-220000−2i2ii2−i2−i2i2−222−2000000000000000000000000
χ4522-22-2-22-2−2i−2i2i2i−2i−2i2i2i000002-2−2i−2i2i2i0002-20000i2i2−i2−i2i2−i2i2−i2−2−222−22−22002-2−2i2i00−22−22i2−i2i2−i2000000000000000000000000
χ4622-22-2-22-2−2i−2i2i2i−2i−2i2i2i000002-2−2i−2i2i2i0002-20000i2i2−i2−i2i2−i2i2−i2−2−222−22−2200-222i−2i002−22−2−i2i2−i2i2000000000000000000000000
χ4722-22-2-22-2−2i−2i2i2i−2i−2i2i2i000002-2−2i−2i2i2i0002-20000−i2−i2i2i2−i2i2−i2i222−2−22−22−2002-2−2i2i002−22−2−i2i2−i2i2000000000000000000000000
χ4822-22-2-22-2−2i−2i2i2i−2i−2i2i2i000002-2−2i−2i2i2i0002-20000−i2−i2i2i2−i2i2−i2i222−2−22−22−200-222i−2i00−22−22i2−i2i2−i2000000000000000000000000
χ4922-22-2-22-2−2i−2i2i2i−2i−2i2i2i00000-222i2i−2i−2i000-220000i2i2−i2−i2−i2i2−i2i2−2−2222−22−22-20000−2i2ii2−i2−i2i22−2−22000000000000000000000000
χ5022-22-2-22-2−2i−2i2i2i−2i−2i2i2i00000-222i2i−2i−2i000-220000i2i2−i2−i2−i2i2−i2i2−2−2222−22−2-2200002i−2i−i2i2i2−i2−222−2000000000000000000000000
χ5122-22-2-22-2−2i−2i2i2i−2i−2i2i2i00000-222i2i−2i−2i000-220000−i2−i2i2i2i2−i2i2−i222−2−2−22−222-20000−2i2i−i2i2i2−i2−222−2000000000000000000000000
χ5222-22-2-22-2−2i−2i2i2i−2i−2i2i2i00000-222i2i−2i−2i000-220000−i2−i2i2i2i2−i2i2−i222−2−2−22−22-2200002i−2ii2−i2−i2i22−2−22000000000000000000000000
χ532-2-2222-2-22-22-22-22-22-22-220000002-2-20000002i−2i2i−2i00002i−2i2i−2i000000000000000000002−22−22−22−2i2−i2i2−i2i2−i2i2−i200000000
χ542-2-2222-2-22-22-22-22-22-22-220000002-2-20000002i−2i2i−2i00002i−2i2i−2i00000000000000000000−22−22−22−22−i2i2−i2i2−i2i2−i2i200000000
χ552-2-2222-2-22-22-22-22-22-22-220000002-2-2000000−2i2i−2i2i0000−2i2i−2i2i000000000000000000002−22−22−22−2−i2i2−i2i2−i2i2−i2i200000000
χ562-2-2222-2-22-22-22-22-22-22-220000002-2-2000000−2i2i−2i2i0000−2i2i−2i2i00000000000000000000−22−22−22−22i2−i2i2−i2i2−i2i2−i200000000
χ572-2-2222-2-2-22-22-22-22-22-2220000002-2-20000002i−2i2i−2i0000−2i2i−2i2i000000000000000000002−22−2−22−22i2−i2i2−i2−i2i2−i2i200000000
χ582-2-2222-2-2-22-22-22-22-22-2220000002-2-20000002i−2i2i−2i0000−2i2i−2i2i00000000000000000000−22−222−22−2−i2i2−i2i2i2−i2i2−i200000000
χ592-2-2222-2-2-22-22-22-22-22-2220000002-2-2000000−2i2i−2i2i00002i−2i2i−2i000000000000000000002−22−2−22−22−i2i2−i2i2i2−i2i2−i200000000
χ602-2-2222-2-2-22-22-22-22-22-2220000002-2-2000000−2i2i−2i2i00002i−2i2i−2i00000000000000000000−22−222−22−2i2−i2i2−i2−i2i2−i2i200000000
χ612-2-2-2-22222-22-2-22-222-2-22-2222-22-222-2-2-22-22-2000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ622-2-2-2-22222-22-2-22-222-2-22-2222-22-222-2-2-22-22-200000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ632-2-2-2-22222-22-2-22-222-2-22-2-2-2-22-2222-222-22-2200000000000000000000000000000000000000002-2-222-2-2200000000
χ642-2-2-2-22222-22-2-22-222-2-22-2-2-2-22-2222-222-22-220000000000000000000000000000000000000000-222-2-222-200000000
χ652-2-2-2-22222-22-2-22-22-222-22222-22-2-2-22-2-2-22-220000000000000000000000000000000000000000000000002i−2i2i−2i0000
χ662-2-2-2-22222-22-2-22-22-222-22222-22-2-2-22-2-2-22-22000000000000000000000000000000000000000000000000−2i2i−2i2i0000
χ672-2-2-2-22222-22-2-22-22-222-22-2-2-22-22-2-22222-22-200000000000000000000000000000000000000000000000000002-22-2
χ682-2-2-2-22222-22-2-22-22-222-22-2-2-22-22-2-22222-22-20000000000000000000000000000000000000000000000000000-22-22
χ692-2-2-2-2222-22-222-22-22-2-22222-22-22-2-22-2-2-222-20000000000000000000000000000000000000000000000002i−2i−2i2i0000
χ702-2-2-2-2222-22-222-22-22-2-22222-22-22-2-22-2-2-222-2000000000000000000000000000000000000000000000000−2i2i2i−2i0000
χ712-2-2-2-2222-22-222-22-22-2-222-2-22-22-2-2-22222-2-2200000000000000000000000000000000000000000000000000002-2-22
χ722-2-2-2-2222-22-222-22-22-2-222-2-22-22-2-2-22222-2-220000000000000000000000000000000000000000000000000000-222-2
χ732-2-2-2-2222-22-222-22-2-222-2-222-22-2222-2-2-22-2-22000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ742-2-2-2-2222-22-222-22-2-222-2-222-22-2222-2-2-22-2-2200000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ752-2-2-2-2222-22-222-22-2-222-2-2-2-22-22-222-222-222-200000000000000000000000000000000000000002-2-22-222-200000000
χ762-2-2-2-2222-22-222-22-2-222-2-2-2-22-22-222-222-222-20000000000000000000000000000000000000000-222-22-2-2200000000
χ77444-4-44-4-44444-4-4-4-4-4-4444000000-44-400000000000000000000000000000000000000000000000000000000000000
χ78444-4-44-4-4-4-4-4-4444444-4-44000000-44-400000000000000000000000000000000000000000000000000000000000000
χ7944-4-44-4-444i4i−4i−4i−4i−4i4i4i0000000000000000000000002i2−2i2−2i22i2000022−22−22220000000000000000000000000000000000000000
χ8044-4-44-4-444i4i−4i−4i−4i−4i4i4i000000000000000000000000−2i22i22i2−2i20000−222222−220000000000000000000000000000000000000000
χ8144-4-44-4-44−4i−4i4i4i4i4i−4i−4i0000000000000000000000002i2−2i2−2i22i20000−222222−220000000000000000000000000000000000000000
χ8244-4-44-4-44−4i−4i4i4i4i4i−4i−4i000000000000000000000000−2i22i22i2−2i2000022−22−22220000000000000000000000000000000000000000
χ834-444-4-4-444i−4i−4i4i4i−4i−4i4i0000000000000000000022−22−22220000−2i22i22i2−2i200000000000000000000000000000000000000000000
χ844-444-4-4-444i−4i−4i4i4i−4i−4i4i00000000000000000000−222222−2200002i2−2i2−2i22i200000000000000000000000000000000000000000000
χ854-444-4-4-44−4i4i4i−4i−4i4i4i−4i0000000000000000000022−22−222200002i2−2i2−2i22i200000000000000000000000000000000000000000000
χ864-444-4-4-44−4i4i4i−4i−4i4i4i−4i00000000000000000000−222222−220000−2i22i22i2−2i200000000000000000000000000000000000000000000
χ874-44-44-44-44i−4i−4i4i−4i4i4i−4i000004-44i−4i−4i4i000-44000000000000000000000000000000000000000000000000000000000000
χ884-44-44-44-44i−4i−4i4i−4i4i4i−4i00000-44−4i4i4i−4i0004-4000000000000000000000000000000000000000000000000000000000000
χ894-44-44-44-4−4i4i4i−4i4i−4i−4i4i000004-4−4i4i4i−4i000-44000000000000000000000000000000000000000000000000000000000000
χ904-44-44-44-4−4i4i4i−4i4i−4i−4i4i00000-444i−4i−4i4i0004-4000000000000000000000000000000000000000000000000000000000000
χ914-4-4444-4-44-44-44-44-4-44-44-4000000-44400000000000000000000000000000000000000000000000000000000000000
χ924-4-4444-4-4-44-44-44-444-44-4-4000000-44400000000000000000000000000000000000000000000000000000000000000

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