Finite Group Databasebeta

← Group #375630

Character table — Group #375630

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111111111111222222222222222244444444444444444444888888888888888888888888888888881616161616161616
order12222222222222224444444444444444444444444444444444444444444444444444888888888888888844444444
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
χ91111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1
χ101111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111
χ111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-111
χ121111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ131111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ141111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ151111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ161111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111
χ171-1-1-1-1111-1-1-1-111111111-1-11111-1-1-1-1-1-111-1-111-1-111-1-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−i1-11-11-11-1
χ181-1-1-1-1111-1-1-1-111111111-1-11111-1-1-1-1-1-111-1-111-1-111-1-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i−i−iii−i−iii−i−iii−i−iii-11-11-11-11
χ191-1-1-1-1111-1-1-1-111111111-1-11111-1-1-1-1-1-111-1-111-1-111-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−iiiii−i−iii−i−iii−i−iii−i−i-11-11-11-11
χ201-1-1-1-1111-1-1-1-111111111-1-11111-1-1-1-1-1-111-1-111-1-111-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii1-11-11-11-1
χ211-1-1-1-1111-1-1-1-111111111-1-11111-1-1-1-1-1-111-1-1-1-111-1-111-1-111-1-111ii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iii1-11-1-11-11
χ221-1-1-1-1111-1-1-1-111111111-1-11111-1-1-1-1-1-111-1-1-1-111-1-111-1-111-1-111ii−i−iii−i−i−i−iii−i−iii−i−iii−i−iiiii−i−iii−i−i-11-111-11-1
χ231-1-1-1-1111-1-1-1-111111111-1-11111-1-1-1-1-1-111-1-1-1-111-1-111-1-111-1-111−i−iii−i−iiiii−i−iii−i−iii−i−iii−i−i−i−iii−i−iii-11-111-11-1
χ241-1-1-1-1111-1-1-1-111111111-1-11111-1-1-1-1-1-111-1-1-1-111-1-111-1-111-1-111−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i1-11-1-11-11
χ251-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iii1-1-111-1-11
χ261-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−i-111-1-111-1
χ271-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iii-111-1-111-1
χ281-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i1-1-111-1-11
χ291-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−i1-1-11-111-1
χ301-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iii-111-11-1-11
χ311-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i-111-11-1-11
χ321-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii1-1-11-111-1
χ332222222222222222-2-2-2-2-2-222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-222220000000000000000000000000000000000000000
χ342222222222222222-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-222222222-2-2-2-20000000000000000000000000000000000000000
χ352222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-20000000000000000000000000000000000000000
χ362222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2222222220000000000000000000000000000000000000000
χ37222-2-22-2-222-2-222-2-222-2-22-2000000002-2000000002i−2i2i−2i00002i−2i2i−2i00002-22-22i−2i2i−2i0000000000000000000000000000
χ38222-2-22-2-222-2-222-2-222-2-22-2000000002-2000000002i−2i2i−2i00002i−2i2i−2i0000-22-22−2i2i−2i2i0000000000000000000000000000
χ39222-2-22-2-222-2-222-2-222-2-22-2000000002-200000000−2i2i−2i2i0000−2i2i−2i2i00002-22-2−2i2i−2i2i0000000000000000000000000000
χ40222-2-22-2-222-2-222-2-222-2-22-2000000002-200000000−2i2i−2i2i0000−2i2i−2i2i0000-22-222i−2i2i−2i0000000000000000000000000000
χ41222-2-22-2-222-2-222-2-2-2-222-2200000000-22000000002i−2i2i−2i0000−2i2i−2i2i2-22-2000000002i−2i2i−2i000000000000000000000000
χ42222-2-22-2-222-2-222-2-2-2-222-2200000000-22000000002i−2i2i−2i0000−2i2i−2i2i-22-2200000000−2i2i−2i2i000000000000000000000000
χ43222-2-22-2-222-2-222-2-2-2-222-2200000000-2200000000−2i2i−2i2i00002i−2i2i−2i2-22-200000000−2i2i−2i2i000000000000000000000000
χ44222-2-22-2-222-2-222-2-2-2-222-2200000000-2200000000−2i2i−2i2i00002i−2i2i−2i-22-22000000002i−2i2i−2i000000000000000000000000
χ4522-22-2-22-22-22-22-22-22-22-22-22i2i−2i−2i2i2i−2i−2i-222i−2i2i−2i00000000000000000000000000000000000000002i−2i2i−2i2-22-200000000
χ4622-22-2-22-22-22-22-22-22-22-22-22i2i−2i−2i2i2i−2i−2i-222i−2i2i−2i0000000000000000000000000000000000000000−2i2i−2i2i-22-2200000000
χ4722-22-2-22-22-22-22-22-22-22-22-2−2i−2i2i2i−2i−2i2i2i-22−2i2i−2i2i00000000000000000000000000000000000000002i−2i2i−2i-22-2200000000
χ4822-22-2-22-22-22-22-22-22-22-22-2−2i−2i2i2i−2i−2i2i2i-22−2i2i−2i2i0000000000000000000000000000000000000000−2i2i−2i2i2-22-200000000
χ4922-22-2-22-22-22-22-22-2-22-22-222i2i−2i−2i2i2i−2i−2i2-2−2i2i−2i2i000000000000000000000000000000002-22-22i−2i2i−2i0000000000000000
χ5022-22-2-22-22-22-22-22-2-22-22-222i2i−2i−2i2i2i−2i−2i2-2−2i2i−2i2i00000000000000000000000000000000-22-22−2i2i−2i2i0000000000000000
χ5122-22-2-22-22-22-22-22-2-22-22-22−2i−2i2i2i−2i−2i2i2i2-22i−2i2i−2i000000000000000000000000000000002-22-2−2i2i−2i2i0000000000000000
χ5222-22-2-22-22-22-22-22-2-22-22-22−2i−2i2i2i−2i−2i2i2i2-22i−2i2i−2i00000000000000000000000000000000-22-222i−2i2i−2i0000000000000000
χ532-22-22-22-2-22-222-22-22-22-2-222i2i−2i−2i−2i−2i2i2i2-22i−2i−2i2i00000000000000000000000000000000000000002-2-22−2i2i2i−2i00000000
χ542-22-22-22-2-22-222-22-22-22-2-222i2i−2i−2i−2i−2i2i2i2-22i−2i−2i2i0000000000000000000000000000000000000000-222-22i−2i−2i2i00000000
χ552-22-22-22-2-22-222-22-22-22-2-22−2i−2i2i2i2i2i−2i−2i2-2−2i2i2i−2i00000000000000000000000000000000000000002-2-222i−2i−2i2i00000000
χ562-22-22-22-2-22-222-22-22-22-2-22−2i−2i2i2i2i2i−2i−2i2-2−2i2i2i−2i0000000000000000000000000000000000000000-222-2−2i2i2i−2i00000000
χ572-22-22-22-2-22-222-22-2-22-222-22i2i−2i−2i−2i−2i2i2i-22−2i2i2i−2i000000000000000000000000000000002i−2i−2i2i-222-20000000000000000
χ582-22-22-22-2-22-222-22-2-22-222-22i2i−2i−2i−2i−2i2i2i-22−2i2i2i−2i00000000000000000000000000000000−2i2i2i−2i2-2-220000000000000000
χ592-22-22-22-2-22-222-22-2-22-222-2−2i−2i2i2i2i2i−2i−2i-222i−2i−2i2i000000000000000000000000000000002i−2i−2i2i2-2-220000000000000000
χ602-22-22-22-2-22-222-22-2-22-222-2−2i−2i2i2i2i2i−2i−2i-222i−2i−2i2i00000000000000000000000000000000−2i2i2i−2i-222-20000000000000000
χ612-2-2222-2-2-2-22222-2-222-2-2-2200000000-22000000002i−2i−2i2i00002i−2i−2i2i00002i−2i−2i2i-222-20000000000000000000000000000
χ622-2-2222-2-2-2-22222-2-222-2-2-2200000000-22000000002i−2i−2i2i00002i−2i−2i2i0000−2i2i2i−2i2-2-220000000000000000000000000000
χ632-2-2222-2-2-2-22222-2-222-2-2-2200000000-2200000000−2i2i2i−2i0000−2i2i2i−2i00002i−2i−2i2i2-2-220000000000000000000000000000
χ642-2-2222-2-2-2-22222-2-222-2-2-2200000000-2200000000−2i2i2i−2i0000−2i2i2i−2i0000−2i2i2i−2i-222-20000000000000000000000000000
χ652-2-2222-2-2-2-22222-2-2-2-2222-2000000002-2000000002i−2i−2i2i0000−2i2i2i−2i2i−2i−2i2i00000000-222-2000000000000000000000000
χ662-2-2222-2-2-2-22222-2-2-2-2222-2000000002-2000000002i−2i−2i2i0000−2i2i2i−2i−2i2i2i−2i000000002-2-22000000000000000000000000
χ672-2-2222-2-2-2-22222-2-2-2-2222-2000000002-200000000−2i2i2i−2i00002i−2i−2i2i2i−2i−2i2i000000002-2-22000000000000000000000000
χ682-2-2222-2-2-2-22222-2-2-2-2222-2000000002-200000000−2i2i2i−2i00002i−2i−2i2i−2i2i2i−2i00000000-222-2000000000000000000000000
χ692-2-2-2-2222-2-2-2-22222-2-2-2-2222222-2-2-2-222-2-22222-2-2-2-222-2-22222-2-20000000000000000000000000000000000000000
χ702-2-2-2-2222-2-2-2-22222-2-2-2-2222222-2-2-2-222-2-222-2-22222-2-222-2-2-2-2220000000000000000000000000000000000000000
χ712-2-2-2-2222-2-2-2-22222-2-2-2-222-2-2-2-222222222-2-222-2-222-2-2-2-222-2-2220000000000000000000000000000000000000000
χ722-2-2-2-2222-2-2-2-22222-2-2-2-222-2-2-2-222222222-2-2-2-222-2-22222-2-222-2-20000000000000000000000000000000000000000
χ7344444-4-44-4-4-4-4-444-40000004-44-44-44-400000000000000000000000000000000000000000000000000000000000000
χ7444444-4-44-4-4-4-4-444-4000000-44-44-44-4400000000000000000000000000000000000000000000000000000000000000
χ75444-4-4-44-4-4-444-44-4400000000000000000000000000004i−4i4i−4i00000000000000000000000000000000000000000000
χ76444-4-4-44-4-4-444-44-440000000000000000000000000000−4i4i−4i4i00000000000000000000000000000000000000000000
χ7744-44-44-4-4-44-44-4-4440000004i−4i−4i4i4i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000
χ7844-44-44-4-4-44-44-4-444000000−4i4i4i−4i−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000
χ7944-4-44444-444-4-4-4-4-4000000000000000000004-44-40000000000000000000000000000000000000000000000000000
χ8044-4-44444-444-4-4-4-4-400000000000000000000-44-440000000000000000000000000000000000000000000000000000
χ8144-4-44-4-444-4-444-4-444-4-444400000000-4-4000000000000000000000000000000000000000000000000000000000000
χ8244-4-44-4-444-4-444-4-44-444-4-4-40000000044000000000000000000000000000000000000000000000000000000000000
χ834-444-44444-4-44-4-4-4-4000000000000000000004-4-440000000000000000000000000000000000000000000000000000
χ844-444-44444-4-44-4-4-4-400000000000000000000-444-40000000000000000000000000000000000000000000000000000
χ854-444-4-4-44-444-44-4-444-4-44-4-40000000044000000000000000000000000000000000000000000000000000000000000
χ864-444-4-4-44-444-44-4-44-444-44400000000-4-4000000000000000000000000000000000000000000000000000000000000
χ874-44-444-4-44-44-4-4-4440000004i−4i−4i4i−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000
χ884-44-444-4-44-44-4-4-444000000−4i4i4i−4i4i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000
χ894-4-444-44-444-4-4-44-4400000000000000000000000000004i−4i−4i4i00000000000000000000000000000000000000000000
χ904-4-444-44-444-4-4-44-440000000000000000000000000000−4i4i4i−4i00000000000000000000000000000000000000000000
χ914-4-4-4-4-4-444444-444-40000004-44-4-44-4400000000000000000000000000000000000000000000000000000000000000
χ924-4-4-4-4-4-444444-444-4000000-44-444-44-400000000000000000000000000000000000000000000000000000000000000

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