Finite Group Databasebeta

← Group #375651

Character table — Group #375651

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122222222222222222222222222224444444444444444888888888888888888888888888888881616161616161616
order12222222222244444444444444444444444444444444444444448888888888888888888888888888888844444444
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
χ511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1
χ611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111
χ711111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111
χ811111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1
χ91111111111111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1
χ101111111111111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111
χ111111111111111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-111
χ121111111111111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111
χ141111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111
χ17111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1ii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−i1-11-11-11-1
χ18111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1ii−i−iii−i−iii−i−iii−i−i−i−iii−i−iii−i−iii−i−iii-11-11-11-11
χ19111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1−i−iii−i−iii−i−iii−i−iiiii−i−iii−i−iii−i−iii−i−i-11-11-11-11
χ20111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii1-11-11-11-1
χ21111111111111-1-1-1-11111-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-11111-1-111-1-1-1-111-1-1111-11-1-11-11
χ22111111111111-1-1-1-11111-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-111-1-111-1-11111-1-111-1-1-11-111-11-1
χ23111111111111-1-1-1-11111-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-111-1-111-1-111-1-1-1-111-1-111-11-111-11-1
χ24111111111111-1-1-1-11111-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-111-1-1-1-111-1-11111-1-111-1-11-11-1-11-11
χ25111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iii1-1-111-1-11
χ26111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−i-111-1-111-1
χ27111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iii-111-1-111-1
χ28111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i1-1-111-1-11
χ29111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-11111-1-111-1-1-1-111-1-11111-1-111-1-1-1-111-1-11111-1-11-1-11-111-1
χ30111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-11111-1-111-1-1-1-111-1-11111-1-1-1-11111-1-111-1-1-1-111-111-11-1-11
χ31111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-11111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111-1-11111-1-1-111-11-1-11
χ32111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-11111-1-1-1-11111-1-111-1-1-1-111-1-11111-1-111-1-1-1-1111-1-11-111-1
χ3322222222-2-2-2-222222222222222-2-2-2-2-2-2-2-222-2-2-2-222-2-2-2-222-2-2220000000000000000000000000000000000000000
χ3422222222-2-2-2-222222222-2-2-2-2-2-222222222-2-2-2-2-2-222-2-222-2-222-2-20000000000000000000000000000000000000000
χ3522222222-2-2-2-22222-2-2-2-22222222222-2-2-2-222-2-222-2-222-2-2-2-222-2-20000000000000000000000000000000000000000
χ3622222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-222-2-2222222-2-2220000000000000000000000000000000000000000
χ3722222222-2-2-2-2-2-2-2-222222222-2-222222222-2-222-2-2-2-222-2-222-2-2-2-20000000000000000000000000000000000000000
χ3822222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-222220000000000000000000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-22222-2-2222222-2-2-2-2-2-222220000000000000000000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2-2-222222222-2-22222-2-2-2-20000000000000000000000000000000000000000
χ4122-2-222-2-222-2-200002i2i−2i−2i00002-22i2i−2i−2i22-2-22-2002i−2i00000000002i−2i0000000000000000002i−2i002-22i−2i002-20000000000
χ4222-2-222-2-222-2-200002i2i−2i−2i00002-22i2i−2i−2i22-2-22-2002i−2i00000000002i−2i000000000000000000−2i2i00-22−2i2i00-220000000000
χ4322-2-222-2-222-2-200002i2i−2i−2i0000-22−2i−2i2i2i-2-222-22002i−2i0000000000−2i2i0000000000000000002-200−2i2i-22002i−2i0000000000
χ4422-2-222-2-222-2-200002i2i−2i−2i0000-22−2i−2i2i2i-2-222-22002i−2i0000000000−2i2i000000000000000000-22002i−2i2-200−2i2i0000000000
χ4522-2-222-2-222-2-20000−2i−2i2i2i00002-2−2i−2i2i2i22-2-22-200−2i2i0000000000−2i2i0000000000000000002i−2i00-222i−2i00-220000000000
χ4622-2-222-2-222-2-20000−2i−2i2i2i00002-2−2i−2i2i2i22-2-22-200−2i2i0000000000−2i2i000000000000000000−2i2i002-2−2i2i002-20000000000
χ4722-2-222-2-222-2-20000−2i−2i2i2i0000-222i2i−2i−2i-2-222-2200−2i2i00000000002i−2i0000000000000000002-2002i−2i-2200−2i2i0000000000
χ4822-2-222-2-222-2-20000−2i−2i2i2i0000-222i2i−2i−2i-2-222-2200−2i2i00000000002i−2i000000000000000000-2200−2i2i2-2002i−2i0000000000
χ4922-2-222-2-2-2-22200002i2i−2i−2i00002-2−2i−2i2i2i-2-2222-200−2i2i00000000002i−2i00000000000000002-2002i−2i00002-2002i−2i00000000
χ5022-2-222-2-2-2-22200002i2i−2i−2i00002-2−2i−2i2i2i-2-2222-200−2i2i00000000002i−2i0000000000000000-2200−2i2i0000-2200−2i2i00000000
χ5122-2-222-2-2-2-22200002i2i−2i−2i0000-222i2i−2i−2i22-2-2-2200−2i2i0000000000−2i2i00000000000000002i−2i00-220000−2i2i002-200000000
χ5222-2-222-2-2-2-22200002i2i−2i−2i0000-222i2i−2i−2i22-2-2-2200−2i2i0000000000−2i2i0000000000000000−2i2i002-200002i−2i00-2200000000
χ5322-2-222-2-2-2-2220000−2i−2i2i2i00002-22i2i−2i−2i-2-2222-2002i−2i0000000000−2i2i00000000000000002-200−2i2i00002-200−2i2i00000000
χ5422-2-222-2-2-2-2220000−2i−2i2i2i00002-22i2i−2i−2i-2-2222-2002i−2i0000000000−2i2i0000000000000000-22002i−2i0000-22002i−2i00000000
χ5522-2-222-2-2-2-2220000−2i−2i2i2i0000-22−2i−2i2i2i22-2-2-22002i−2i00000000002i−2i00000000000000002i−2i002-20000−2i2i00-2200000000
χ5622-2-222-2-2-2-2220000−2i−2i2i2i0000-22−2i−2i2i2i22-2-2-22002i−2i00000000002i−2i0000000000000000−2i2i00-2200002i−2i002-200000000
χ572-22-22-22-22-22-22i2i−2i−2i00002i2i−2i−2i2-200002-22-2-222i−2i0000002i−2i00000000002-22i−2i00002i−2i2-2000000000000000000000000
χ582-22-22-22-22-22-22i2i−2i−2i00002i2i−2i−2i2-200002-22-2-222i−2i0000002i−2i0000000000-22−2i2i0000−2i2i-22000000000000000000000000
χ592-22-22-22-22-22-22i2i−2i−2i0000−2i−2i2i2i-220000-22-222-22i−2i000000−2i2i00000000002i−2i-2200002-2−2i2i000000000000000000000000
χ602-22-22-22-22-22-22i2i−2i−2i0000−2i−2i2i2i-220000-22-222-22i−2i000000−2i2i0000000000−2i2i2-20000-222i−2i000000000000000000000000
χ612-22-22-22-22-22-2−2i−2i2i2i00002i2i−2i−2i-220000-22-222-2−2i2i0000002i−2i00000000002i−2i2-20000-22−2i2i000000000000000000000000
χ622-22-22-22-22-22-2−2i−2i2i2i00002i2i−2i−2i-220000-22-222-2−2i2i0000002i−2i0000000000−2i2i-2200002-22i−2i000000000000000000000000
χ632-22-22-22-22-22-2−2i−2i2i2i0000−2i−2i2i2i2-200002-22-2-22−2i2i000000−2i2i00000000002-2−2i2i0000−2i2i2-2000000000000000000000000
χ642-22-22-22-22-22-2−2i−2i2i2i0000−2i−2i2i2i2-200002-22-2-22−2i2i000000−2i2i0000000000-222i−2i00002i−2i-22000000000000000000000000
χ652-22-22-22-2-22-222i2i−2i−2i00002i2i−2i−2i2-20000-22-22-22−2i2i000000−2i2i0000002i−2i2-200002-22i−2i0000000000000000000000000000
χ662-22-22-22-2-22-222i2i−2i−2i00002i2i−2i−2i2-20000-22-22-22−2i2i000000−2i2i000000−2i2i-220000-22−2i2i0000000000000000000000000000
χ672-22-22-22-2-22-222i2i−2i−2i0000−2i−2i2i2i-2200002-22-22-2−2i2i0000002i−2i0000002-2−2i2i00002i−2i-220000000000000000000000000000
χ682-22-22-22-2-22-222i2i−2i−2i0000−2i−2i2i2i-2200002-22-22-2−2i2i0000002i−2i000000-222i−2i0000−2i2i2-20000000000000000000000000000
χ692-22-22-22-2-22-22−2i−2i2i2i00002i2i−2i−2i-2200002-22-22-22i−2i000000−2i2i0000002-22i−2i0000−2i2i-220000000000000000000000000000
χ702-22-22-22-2-22-22−2i−2i2i2i00002i2i−2i−2i-2200002-22-22-22i−2i000000−2i2i000000-22−2i2i00002i−2i2-20000000000000000000000000000
χ712-22-22-22-2-22-22−2i−2i2i2i0000−2i−2i2i2i2-20000-22-22-222i−2i0000002i−2i0000002i−2i-220000-222i−2i0000000000000000000000000000
χ722-22-22-22-2-22-22−2i−2i2i2i0000−2i−2i2i2i2-20000-22-22-222i−2i0000002i−2i000000−2i2i2-200002-2−2i2i0000000000000000000000000000
χ734444-4-4-4-400004-44-44-44-4000000000000000000004-400000000000000000000000000000000000000000000000000
χ744444-4-4-4-400004-44-4-44-4400000000000000000000-4400000000000000000000000000000000000000000000000000
χ754444-4-4-4-40000-44-444-44-400000000000000000000-4400000000000000000000000000000000000000000000000000
χ764444-4-4-4-40000-44-44-44-44000000000000000000004-400000000000000000000000000000000000000000000000000
χ7744-4-4-4-444000000004i−4i−4i4i4-44-400000000000000000000004i−4i00000000000000000000000000000000000000000000
χ7844-4-4-4-444000000004i−4i−4i4i-44-440000000000000000000000−4i4i00000000000000000000000000000000000000000000
χ7944-4-4-4-44400000000−4i4i4i−4i4-44-40000000000000000000000−4i4i00000000000000000000000000000000000000000000
χ8044-4-4-4-44400000000−4i4i4i−4i-44-4400000000000000000000004i−4i00000000000000000000000000000000000000000000
χ814-44-4-44-4400004i−4i−4i4i00000000004i−4i4i−4i0000000000000000004-4000000000000000000000000000000000000000000
χ824-44-4-44-4400004i−4i−4i4i0000000000−4i4i−4i4i000000000000000000-44000000000000000000000000000000000000000000
χ834-44-4-44-440000−4i4i4i−4i00000000004i−4i4i−4i000000000000000000-44000000000000000000000000000000000000000000
χ844-44-4-44-440000−4i4i4i−4i0000000000−4i4i−4i4i0000000000000000004-4000000000000000000000000000000000000000000
χ854-4-444-4-444-4-440000000000004400004-4-44-4-400000000000000000000000000000000000000000000000000000000
χ864-4-444-4-444-4-44000000000000-4-40000-444-44400000000000000000000000000000000000000000000000000000000
χ874-4-444-4-44-444-4000000000000440000-444-4-4-400000000000000000000000000000000000000000000000000000000
χ884-4-444-4-44-444-4000000000000-4-400004-4-444400000000000000000000000000000000000000000000000000000000
χ894-4-44-444-40000000000004i−4i−4i4i004-4-440000000000004i−4i000000000000000000000000000000000000000000000000
χ904-4-44-444-40000000000004i−4i−4i4i00-444-4000000000000−4i4i000000000000000000000000000000000000000000000000
χ914-4-44-444-4000000000000−4i4i4i−4i004-4-44000000000000−4i4i000000000000000000000000000000000000000000000000
χ924-4-44-444-4000000000000−4i4i4i−4i00-444-40000000000004i−4i000000000000000000000000000000000000000000000000

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