Finite Group Databasebeta

← Group #374162

Character table — Group #374162

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122222222222222222222222222224444444444444444888888888888888888888888888888881616161616161616
order12222222222222224444444444444444444422444444444444448888888888888888888888888888888822444444
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
χ5111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111
χ6111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1
χ7111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ91111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1-111-1-11-1
χ101111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-11-1-111-11
χ111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-11-1-111-11
χ121111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1-111-1-11-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii1-1-1-1111-1
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-1111-1-1-11
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-1111-1-1-11
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i1-1-1-1111-1
χ17111111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-111-1-1-1-111-1-1-1-111-1-111-1-111-1-111-1-111-1-111-1-111-1-111-1-1111-11-1-1-1
χ18111111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-111-1-1-1-111-1-1-1-111-1-111-1-111-1-111-1-1-1-111-1-111-1-111-1-111-1-1-11-1111
χ19111111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-111-1-111-1-111-1-11111-1-111-1-111-1-111-1-1-1-1-11-1111
χ20111111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-111-1-111-1-111-1-111-1-111-1-111-1-111-1-111111-11-1-1-1
χ21111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1111111-1-111-1-1-1-111-1-11111-1-111-1-1-1-111-1-11111-11-11-1-1
χ22111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1111111-1-111-1-1-1-111-1-111-1-111-1-11111-1-111-1-1-1-11-11-111
χ23111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-111-1-11111-1-111-1-111-1-111-1-1-1-111-1-111-1-11-11-111
χ24111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-111-1-11111-1-111-1-1-1-111-1-11111-1-111-1-111-11-11-1-1
χ25111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iii1-11-1-11-11
χ26111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−i-11-111-11-1
χ27111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iii-11-111-11-1
χ28111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i1-11-1-11-11
χ29111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1111111-1-1-1-1ii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−i1-1-111-1-11
χ30111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1111111-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iii-111-1-111-1
χ31111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1111111-1-1-1-1−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i-111-1-111-1
χ32111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1111111-1-1-1-1−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii1-1-111-1-11
χ3322222222-2-2-2-2222222-2-222222222-2-2-2-222-2-2-2-2-2-2-2-222-2-22222-2-20000000000000000000000000000000000000000
χ3422222222-2-2-2-2222222-2-22222-2-2-2-2222222-2-2-2-2-2-222-2-222-2-2-2-2220000000000000000000000000000000000000000
χ3522222222-2-2-2-22222-2-222-2-2-2-222222222-2-222-2-222-2-222-2-2-2-2-2-2220000000000000000000000000000000000000000
χ3622222222-2-2-2-22222-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-22222-2-2222222-2-20000000000000000000000000000000000000000
χ3722222222-2-2-2-2-2-2-2-222-2-2-2-2-2-22222-2-2-2-222-2-22222-2-2-2-22222-2-2220000000000000000000000000000000000000000
χ3822222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-2222222-2-222222222-2-2-2-222-2-20000000000000000000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-2-2-222222222222222-2-22222-2-2-2-2-2-222-2-222-2-20000000000000000000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-2-2-22222-2-22222-2-222-2-2220000000000000000000000000000000000000000
χ4122-222-2-2-222-2-200002-22-200002i2i−2i−2i2i2i−2i−2i2-22-200002i−2i00002i−2i0000002-2002-2002i−2i002i−2i000000000000000000000000
χ4222-222-2-2-222-2-200002-22-200002i2i−2i−2i2i2i−2i−2i2-22-200002i−2i00002i−2i000000-2200-2200−2i2i00−2i2i000000000000000000000000
χ4322-222-2-2-222-2-200002-22-20000−2i−2i2i2i−2i−2i2i2i2-22-20000−2i2i0000−2i2i0000002-2002-200−2i2i00−2i2i000000000000000000000000
χ4422-222-2-2-222-2-200002-22-20000−2i−2i2i2i−2i−2i2i2i2-22-20000−2i2i0000−2i2i000000-2200-22002i−2i002i−2i000000000000000000000000
χ4522-222-2-2-222-2-20000-22-2200002i2i−2i−2i−2i−2i2i2i-22-2200002i−2i0000−2i2i0000002i−2i00−2i2i00-22002-2000000000000000000000000
χ4622-222-2-2-222-2-20000-22-2200002i2i−2i−2i−2i−2i2i2i-22-2200002i−2i0000−2i2i000000−2i2i002i−2i002-200-22000000000000000000000000
χ4722-222-2-2-222-2-20000-22-220000−2i−2i2i2i2i2i−2i−2i-22-220000−2i2i00002i−2i0000002i−2i00−2i2i002-200-22000000000000000000000000
χ4822-222-2-2-222-2-20000-22-220000−2i−2i2i2i2i2i−2i−2i-22-220000−2i2i00002i−2i000000−2i2i002i−2i00-22002-2000000000000000000000000
χ4922-222-2-2-2-2-22200002-2-2200002i2i−2i−2i−2i−2i2i2i2-2-220000−2i2i00002i−2i00002-2002-2002i−2i002i−2i00000000000000000000000000
χ5022-222-2-2-2-2-22200002-2-2200002i2i−2i−2i−2i−2i2i2i2-2-220000−2i2i00002i−2i0000-2200-2200−2i2i00−2i2i00000000000000000000000000
χ5122-222-2-2-2-2-22200002-2-220000−2i−2i2i2i2i2i−2i−2i2-2-2200002i−2i0000−2i2i00002-2002-200−2i2i00−2i2i00000000000000000000000000
χ5222-222-2-2-2-2-22200002-2-220000−2i−2i2i2i2i2i−2i−2i2-2-2200002i−2i0000−2i2i0000-2200-22002i−2i002i−2i00000000000000000000000000
χ5322-222-2-2-2-2-2220000-222-200002i2i−2i−2i2i2i−2i−2i-222-20000−2i2i0000−2i2i00002i−2i00−2i2i00-22002-200000000000000000000000000
χ5422-222-2-2-2-2-2220000-222-200002i2i−2i−2i2i2i−2i−2i-222-20000−2i2i0000−2i2i0000−2i2i002i−2i002-200-2200000000000000000000000000
χ5522-222-2-2-2-2-2220000-222-20000−2i−2i2i2i−2i−2i2i2i-222-200002i−2i00002i−2i00002i−2i00−2i2i002-200-2200000000000000000000000000
χ5622-222-2-2-2-2-2220000-222-20000−2i−2i2i2i−2i−2i2i2i-222-200002i−2i00002i−2i0000−2i2i002i−2i00-22002-200000000000000000000000000
χ572-2-22-22-222-22-222-2-22-22222-2-200000000-22-2-22-22-200000000000000000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ582-2-22-22-222-22-222-2-22-22222-2-200000000-22-2-22-22-20000000000000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ592-2-22-22-222-22-222-2-2-22-2-2-2-222000000002-2222-2-2200000000000000000000000000002-22-2-22-220000000000000000
χ602-2-22-22-222-22-222-2-2-22-2-2-2-222000000002-2222-2-220000000000000000000000000000-22-222-22-20000000000000000
χ612-2-22-22-222-22-2-2-2222-222-2-22200000000-22-2-2-22-2200000000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ622-2-22-22-222-22-2-2-2222-222-2-22200000000-22-2-2-22-220000000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ632-2-22-22-222-22-2-2-222-22-2-222-2-2000000002-222-222-200000000000000000000000000002-2-22-222-20000000000000000
χ642-2-22-22-222-22-2-2-222-22-2-222-2-2000000002-222-222-20000000000000000000000000000-222-22-2-220000000000000000
χ652-2-22-22-22-22-2222-2-22-2-2-222-2-200000000-2222-22-220000000000000000000000000000000000002-22-22-22-200000000
χ662-2-22-22-22-22-2222-2-22-2-2-222-2-200000000-2222-22-22000000000000000000000000000000000000-22-22-22-2200000000
χ672-2-22-22-22-22-2222-2-2-2222-2-222000000002-2-2-2-222-20000000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i00000000
χ682-2-22-22-22-22-2222-2-2-2222-2-222000000002-2-2-2-222-2000000000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i00000000
χ692-2-22-22-22-22-22-2-2222-2-2-2-2-22200000000-22222-22-20000000000000000000000000000000000002-2-222-2-2200000000
χ702-2-22-22-22-22-22-2-2222-2-2-2-2-22200000000-22222-22-2000000000000000000000000000000000000-222-2-222-200000000
χ712-2-22-22-22-22-22-2-222-222222-2-2000000002-2-2-22-2-220000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000
χ722-2-22-22-22-22-22-2-222-222222-2-2000000002-2-2-22-2-22000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000
χ73444-4-4-4-4400004-44-4000000004i−4i4i−4i000000000000004i−4i000000000000000000000000000000000000000000000000
χ74444-4-4-4-4400004-44-400000000−4i4i−4i4i00000000000000−4i4i000000000000000000000000000000000000000000000000
χ75444-4-4-4-440000-44-44000000004i−4i4i−4i00000000000000−4i4i000000000000000000000000000000000000000000000000
χ76444-4-4-4-440000-44-4400000000−4i4i−4i4i000000000000004i−4i000000000000000000000000000000000000000000000000
χ7744-4-4-444-40000000000004i−4i4i−4i4-4-44000000000000000000004i−4i000000000000000000000000000000000000000000
χ7844-4-4-444-40000000000004i−4i4i−4i-444-400000000000000000000−4i4i000000000000000000000000000000000000000000
χ7944-4-4-444-4000000000000−4i4i−4i4i4-4-4400000000000000000000−4i4i000000000000000000000000000000000000000000
χ8044-4-4-444-4000000000000−4i4i−4i4i-444-4000000000000000000004i−4i000000000000000000000000000000000000000000
χ814-444-4-44-44-4-440000444-4000000000000-4-4-4400000000000000000000000000000000000000000000000000000000
χ824-444-4-44-44-4-440000-4-4-44000000000000444-400000000000000000000000000000000000000000000000000000000
χ834-444-4-44-4-444-4000044-44000000000000-4-44-400000000000000000000000000000000000000000000000000000000
χ844-444-4-44-4-444-40000-4-44-400000000000044-4400000000000000000000000000000000000000000000000000000000
χ854-44-444-4-40000000000004i−4i−4i4i00004i−4i4i−4i0000000000004-40000000000000000000000000000000000000000000000
χ864-44-444-4-40000000000004i−4i−4i4i0000−4i4i−4i4i000000000000-440000000000000000000000000000000000000000000000
χ874-44-444-4-4000000000000−4i4i4i−4i00004i−4i4i−4i000000000000-440000000000000000000000000000000000000000000000
χ884-44-444-4-4000000000000−4i4i4i−4i0000−4i4i−4i4i0000000000004-40000000000000000000000000000000000000000000000
χ894-4-4-44-44400004-4-440000000000004-4-440000000000000000004-40000000000000000000000000000000000000000
χ904-4-4-44-44400004-4-44000000000000-444-4000000000000000000-440000000000000000000000000000000000000000
χ914-4-4-44-4440000-444-40000000000004-4-44000000000000000000-440000000000000000000000000000000000000000
χ924-4-4-44-4440000-444-4000000000000-444-40000000000000000004-40000000000000000000000000000000000000000

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