Finite Group Databasebeta

← Group #380552

Character table — Group #380552

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111111111111222222222222222244444444444444444444888888888888888888888888888888881616161616161616
order12222222444444442222222244444444224444444444444444444444444444444444888888888888888822444444
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
χ51111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-111-1-11-1
χ61111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1-111-11
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-11-1-111-11
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111-111-1-11-1
χ9111111111111111111-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111
χ10111111111111111111-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1
χ11111111111111111111-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-11111-1-1
χ12111111111111111111-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-111
χ13111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-1-1111-1
χ14111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1111-1-1-11
χ15111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1111-1-1-11
χ16111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-1111-1
χ1711111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111ii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−i111-11-1-1-1
χ1811111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111ii−i−iii−i−iii−i−iii−i−i−i−iii−i−iii−i−iii−i−iii-1-1-11-1111
χ1911111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111−i−iii−i−iii−i−iii−i−iiiii−i−iii−i−iii−i−iii−i−i-1-1-11-1111
χ2011111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii111-11-1-1-1
χ2111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111ii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iii1-11-1-11-11
χ2211111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111ii−i−iii−i−i−i−iii−i−iii−i−iii−i−iiiii−i−iii−i−i-11-111-11-1
χ2311111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111−i−iii−i−iiiii−i−iii−i−iii−i−iii−i−i−i−iii−i−iii-11-111-11-1
χ2411111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i1-11-1-11-11
χ2511111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1ii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iii11-11-11-1-1
χ2611111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1ii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−i-1-11-11-111
χ2711111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iii-1-11-11-111
χ2811111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i11-11-11-1-1
χ2911111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1ii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−i1-1-111-1-11
χ3011111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iii-111-1-111-1
χ3111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i-111-1-111-1
χ3211111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii1-1-111-1-11
χ332222222222222222-2-22222-2-2-2-2-2-22222-2-222-2-222-2-222-2-222-2-2-2-20000000000000000000000000000000000000000
χ342222222222222222-2-22222-2-2-2-2-2-22222-2-2-2-222-2-222-2-222-2-222-2-20000000000000000000000000000000000000000
χ352222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-222-2-2-2-222-2-222220000000000000000000000000000000000000000
χ362222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-222-2-22222-2-222-2-2220000000000000000000000000000000000000000
χ3722222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-222-2-20000000000000000000000000000000000000000
χ3822222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-222-2-22222-2-2-2-22222-2-2-2-20000000000000000000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-222-2-2-2-222-2-2-2-22222-2-222-2-2-2-222-2-22222-2-2220000000000000000000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-222-2-2-2-222-2-2-2-22222-2-2-2-22222-2-222-2-2-2-222220000000000000000000000000000000000000000
χ4122-222-2-2-22i2i−2i−2i2i2i−2i−2i0022-2-20000002i2i−2i−2i00002-2002i−2i002-2002i−2i001+i−1−i1−i−1+i1+i−1−i1−i−1+i1+i−1−i1−i−1+i1+i−1−i1−i−1+i000000000000000000000000
χ4222-222-2-2-22i2i−2i−2i2i2i−2i−2i0022-2-20000002i2i−2i−2i00002-2002i−2i002-2002i−2i00−1−i1+i−1+i1−i−1−i1+i−1+i1−i−1−i1+i−1+i1−i−1−i1+i−1+i1−i000000000000000000000000
χ4322-222-2-2-22i2i−2i−2i2i2i−2i−2i0022-2-20000002i2i−2i−2i0000-2200−2i2i00-2200−2i2i001+i−1−i1−i−1+i1+i−1−i1−i−1+i−1−i1+i−1+i1−i−1−i1+i−1+i1−i000000000000000000000000
χ4422-222-2-2-22i2i−2i−2i2i2i−2i−2i0022-2-20000002i2i−2i−2i0000-2200−2i2i00-2200−2i2i00−1−i1+i−1+i1−i−1−i1+i−1+i1−i1+i−1−i1−i−1+i1+i−1−i1−i−1+i000000000000000000000000
χ4522-222-2-2-22i2i−2i−2i2i2i−2i−2i00-2-222000000−2i−2i2i2i00002-2002i−2i00-2200−2i2i001+i−1−i1−i−1+i−1−i1+i−1+i1−i1+i−1−i1−i−1+i−1−i1+i−1+i1−i000000000000000000000000
χ4622-222-2-2-22i2i−2i−2i2i2i−2i−2i00-2-222000000−2i−2i2i2i00002-2002i−2i00-2200−2i2i00−1−i1+i−1+i1−i1+i−1−i1−i−1+i−1−i1+i−1+i1−i1+i−1−i1−i−1+i000000000000000000000000
χ4722-222-2-2-22i2i−2i−2i2i2i−2i−2i00-2-222000000−2i−2i2i2i0000-2200−2i2i002-2002i−2i001+i−1−i1−i−1+i−1−i1+i−1+i1−i−1−i1+i−1+i1−i1+i−1−i1−i−1+i000000000000000000000000
χ4822-222-2-2-22i2i−2i−2i2i2i−2i−2i00-2-222000000−2i−2i2i2i0000-2200−2i2i002-2002i−2i00−1−i1+i−1+i1−i1+i−1−i1−i−1+i1+i−1−i1−i−1+i−1−i1+i−1+i1−i000000000000000000000000
χ4922-222-2-2-2−2i−2i2i2i−2i−2i2i2i0022-2-2000000−2i−2i2i2i00002-200−2i2i002-200−2i2i001−i−1+i1+i−1−i1−i−1+i1+i−1−i1−i−1+i1+i−1−i1−i−1+i1+i−1−i000000000000000000000000
χ5022-222-2-2-2−2i−2i2i2i−2i−2i2i2i0022-2-2000000−2i−2i2i2i00002-200−2i2i002-200−2i2i00−1+i1−i−1−i1+i−1+i1−i−1−i1+i−1+i1−i−1−i1+i−1+i1−i−1−i1+i000000000000000000000000
χ5122-222-2-2-2−2i−2i2i2i−2i−2i2i2i0022-2-2000000−2i−2i2i2i0000-22002i−2i00-22002i−2i001−i−1+i1+i−1−i1−i−1+i1+i−1−i−1+i1−i−1−i1+i−1+i1−i−1−i1+i000000000000000000000000
χ5222-222-2-2-2−2i−2i2i2i−2i−2i2i2i0022-2-2000000−2i−2i2i2i0000-22002i−2i00-22002i−2i00−1+i1−i−1−i1+i−1+i1−i−1−i1+i1−i−1+i1+i−1−i1−i−1+i1+i−1−i000000000000000000000000
χ5322-222-2-2-2−2i−2i2i2i−2i−2i2i2i00-2-2220000002i2i−2i−2i00002-200−2i2i00-22002i−2i001−i−1+i1+i−1−i−1+i1−i−1−i1+i1−i−1+i1+i−1−i−1+i1−i−1−i1+i000000000000000000000000
χ5422-222-2-2-2−2i−2i2i2i−2i−2i2i2i00-2-2220000002i2i−2i−2i00002-200−2i2i00-22002i−2i00−1+i1−i−1−i1+i1−i−1+i1+i−1−i−1+i1−i−1−i1+i1−i−1+i1+i−1−i000000000000000000000000
χ5522-222-2-2-2−2i−2i2i2i−2i−2i2i2i00-2-2220000002i2i−2i−2i0000-22002i−2i002-200−2i2i001−i−1+i1+i−1−i−1+i1−i−1−i1+i−1+i1−i−1−i1+i1−i−1+i1+i−1−i000000000000000000000000
χ5622-222-2-2-2−2i−2i2i2i−2i−2i2i2i00-2-2220000002i2i−2i−2i0000-22002i−2i002-200−2i2i00−1+i1−i−1−i1+i1−i−1+i1+i−1−i1−i−1+i1+i−1−i−1+i1−i−1−i1+i000000000000000000000000
χ572-2-22-22-222-22-22-22-2222-22-2-2-222-2-22-22-22-200000000000000002-20000000000000000000000002i−2i2i−2i2i−2i2i−2i00000000
χ582-2-22-22-222-22-22-22-2222-22-2-2-222-2-22-22-22-200000000000000002-2000000000000000000000000−2i2i−2i2i−2i2i−2i2i00000000
χ592-2-22-22-222-22-22-22-222-22-22-2-222-2-2-22-22-220000000000000000-220000000000000000000000002i−2i2i−2i−2i2i−2i2i00000000
χ602-2-22-22-222-22-22-22-222-22-22-2-222-2-2-22-22-220000000000000000-22000000000000000000000000−2i2i−2i2i2i−2i2i−2i00000000
χ612-2-22-22-222-22-22-22-2-2-22-22-222-2-2222-22-2-220000000000000000-2200000000000000002-22-22-22-20000000000000000
χ622-2-22-22-222-22-22-22-2-2-22-22-222-2-2222-22-2-220000000000000000-220000000000000000-22-22-22-220000000000000000
χ632-2-22-22-222-22-22-22-2-2-2-22-2222-2-222-22-222-200000000000000002-200000000000000002-22-2-22-220000000000000000
χ642-2-22-22-222-22-22-22-2-2-2-22-2222-2-222-22-222-200000000000000002-20000000000000000-22-222-22-20000000000000000
χ652-2-22-22-22-22-22-22-22222-22-2-2-2-2-222-22-222-20000000000000000-2200000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ662-2-22-22-22-22-22-22-22222-22-2-2-2-2-222-22-222-20000000000000000-220000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ672-2-22-22-22-22-22-22-2222-22-22-2-2-2-2222-22-2-2200000000000000002-200000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ682-2-22-22-22-22-22-22-2222-22-22-2-2-2-2222-22-2-2200000000000000002-20000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ692-2-22-22-22-22-22-22-22-2-22-22-22222-2-2-22-22-2200000000000000002-20000000000000000000000002-2-222-2-2200000000
χ702-2-22-22-22-22-22-22-22-2-22-22-22222-2-2-22-22-2200000000000000002-2000000000000000000000000-222-2-222-200000000
χ712-2-22-22-22-22-22-22-22-2-2-22-222222-2-22-22-22-20000000000000000-220000000000000000000000002-2-22-222-200000000
χ722-2-22-22-22-22-22-22-22-2-2-22-222222-2-22-22-22-20000000000000000-22000000000000000000000000-222-22-2-2200000000
χ73444-4-4-4-444444-4-4-4-44-400004-44-44-40000000000000000000000000000000000000000000000000000000000000000
χ74444-4-4-4-444444-4-4-4-4-440000-44-44-440000000000000000000000000000000000000000000000000000000000000000
χ75444-4-4-4-44-4-4-4-444444-400004-4-44-440000000000000000000000000000000000000000000000000000000000000000
χ76444-4-4-4-44-4-4-4-44444-440000-444-44-40000000000000000000000000000000000000000000000000000000000000000
χ7744-4-4-444-44i4i−4i−4i−4i−4i4i4i0000000000000000004-4004i−4i0000000000000000000000000000000000000000000000000000
χ7844-4-4-444-44i4i−4i−4i−4i−4i4i4i000000000000000000-4400−4i4i0000000000000000000000000000000000000000000000000000
χ7944-4-4-444-4−4i−4i4i4i4i4i−4i−4i0000000000000000004-400−4i4i0000000000000000000000000000000000000000000000000000
χ8044-4-4-444-4−4i−4i4i4i4i4i−4i−4i000000000000000000-44004i−4i0000000000000000000000000000000000000000000000000000
χ814-444-4-44-44i−4i−4i4i4i−4i−4i4i004-4-440000004i−4i−4i4i000000000000000000000000000000000000000000000000000000000000
χ824-444-4-44-44i−4i−4i4i4i−4i−4i4i00-444-4000000−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000
χ834-444-4-44-4−4i4i4i−4i−4i4i4i−4i004-4-44000000−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000
χ844-444-4-44-4−4i4i4i−4i−4i4i4i−4i00-444-40000004i−4i−4i4i000000000000000000000000000000000000000000000000000000000000
χ854-44-444-4-44i−4i−4i4i−4i4i4i−4i000000000000000000000000004i−4i004-400000000000000000000000000000000000000000000
χ864-44-444-4-44i−4i−4i4i−4i4i4i−4i00000000000000000000000000−4i4i00-4400000000000000000000000000000000000000000000
χ874-44-444-4-4−4i4i4i−4i4i−4i−4i4i000000000000000000000000004i−4i00-4400000000000000000000000000000000000000000000
χ884-44-444-4-4−4i4i4i−4i4i−4i−4i4i00000000000000000000000000−4i4i004-400000000000000000000000000000000000000000000
χ894-4-4-44-4444-44-4-44-444-40000-444-4-440000000000000000000000000000000000000000000000000000000000000000
χ904-4-4-44-4444-44-4-44-44-4400004-4-444-40000000000000000000000000000000000000000000000000000000000000000
χ914-4-4-44-444-44-444-44-44-40000-44-444-40000000000000000000000000000000000000000000000000000000000000000
χ924-4-4-44-444-44-444-44-4-4400004-44-4-440000000000000000000000000000000000000000000000000000000000000000

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