Finite Group Databasebeta

← Group #98166

Character table — Group #98166

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444444448888888888888888888888888881616161616161616161616161616
order12222222444444444444222244444422444444444888888888888888822444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-11111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-111111111-1-1-1-1-1-11111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111-1-1-1-111111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111
χ711111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ811111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-11111111111-1-1111111-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1111-1-1iiii−i−i−i−iiiii−i−i−i−i111-1-1-1ii−i−iii−i−i
χ10111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1111-1-1−i−i−i−iiiii−i−i−i−iiiii111-1-1-1−i−iii−i−iii
χ11111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111iiii−i−i−i−i−i−i−i−iiiii-1-1-1111ii−i−i−i−iii
χ12111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1111−i−iiiii−i−i
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-11-1-1iiii−i−i−i−iiiii−i−i−i−i-1-11-111−i−iii−i−iii
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-11-1-1−i−i−i−iiiii−i−i−i−iiiii-1-11-111ii−i−iii−i−i
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1111iiii−i−i−i−i−i−i−i−iiiii11-11-1-1−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1111−i−i−i−iiiiiiiii−i−i−i−i11-11-1-1ii−i−i−i−iii
χ1722222222222222-2-222-2-22222-2-222-2-20022-2-2-2-2-200000000000000000000000000000000
χ1822222222222222-2-222-2-2-2-2-2-2-2-222-2-200-2-22222-200000000000000000000000000000000
χ19222222222222-2-222-2-2222222-2-2-2-22200-2-222-2-2-200000000000000000000000000000000
χ20222222222222-2-222-2-222-2-2-2-2-2-2-2-2220022-2-222-200000000000000000000000000000000
χ2122222222-2-2-2-222222222000022-2-2-2-222000000-222000000000000000000-2-20000000000
χ2222222222-2-2-2-222222222000022-2-2-2-2-2-2000000-2-2-2000000000000000000220000000000
χ2322222222-2-2-2-222-2-222-2-20000-2-2-2-2220000000020000000000000000002-2002-200000000
χ2422222222-2-2-2-222-2-222-2-20000-2-2-2-222000000002000000000000000000-2200-2200000000
χ2522222222-2-2-2-2-2-222-2-2220000-2-222-2-20000000020000000000000000002-200-2200000000
χ2622222222-2-2-2-2-2-222-2-2220000-2-222-2-2000000002000000000000000000-22002-200000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2000022222222000000-2-2-2000000000000000000-220000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-20000222222-2-2000000-2220000000000000000002-20000000000
χ29222-2-2-22-200002i−2i2i−2i2i−2i2i−2i00002-200002-200000002i−2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000000000
χ30222-2-2-22-200002i−2i2i−2i2i−2i2i−2i00002-200002-200000002i−2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000000000
χ31222-2-2-22-200002i−2i2i−2i2i−2i2i−2i00002-20000-220000000−2i2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000000000
χ32222-2-2-22-200002i−2i2i−2i2i−2i2i−2i00002-20000-220000000−2i2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000000000
χ33222-2-2-22-20000−2i2i−2i2i−2i2i−2i2i00002-200002-20000000−2i2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000000000
χ34222-2-2-22-20000−2i2i−2i2i−2i2i−2i2i00002-200002-20000000−2i2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000000000
χ35222-2-2-22-20000−2i2i−2i2i−2i2i−2i2i00002-20000-2200000002i−2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000000000
χ36222-2-2-22-20000−2i2i−2i2i−2i2i−2i2i00002-20000-2200000002i−2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000000000
χ3722-222-2-2-222-2-2002i−2i00−2i2i22-2-200002i−2i00002i−2i000001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000001−i−1+i1+i−1−i0000
χ3822-222-2-2-222-2-2002i−2i00−2i2i22-2-200002i−2i00002i−2i00000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000−1+i1−i−1−i1+i0000
χ3922-222-2-2-222-2-2002i−2i00−2i2i-2-22200002i−2i0000−2i2i000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000−1+i1−i−1−i1+i0000
χ4022-222-2-2-222-2-2002i−2i00−2i2i-2-22200002i−2i0000−2i2i00000−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000001−i−1+i1+i−1−i0000
χ4122-222-2-2-222-2-200−2i2i002i−2i22-2-20000−2i2i0000−2i2i000001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000001+i−1−i1−i−1+i0000
χ4222-222-2-2-222-2-200−2i2i002i−2i22-2-20000−2i2i0000−2i2i00000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000−1−i1+i−1+i1−i0000
χ4322-222-2-2-222-2-200−2i2i002i−2i-2-2220000−2i2i00002i−2i000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000−1−i1+i−1+i1−i0000
χ4422-222-2-2-222-2-200−2i2i002i−2i-2-2220000−2i2i00002i−2i00000−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000001+i−1−i1−i−1+i0000
χ452-222-22-2-22-22-22i−2i00−2i2i002-22-2002i−2i00002i−2i0000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000001−i−1+i1+i−1−i
χ462-222-22-2-22-22-22i−2i00−2i2i002-22-2002i−2i00002i−2i000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000−1+i1−i−1−i1+i
χ472-222-22-2-22-22-22i−2i00−2i2i00-22-22002i−2i0000−2i2i0000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000−1+i1−i−1−i1+i
χ482-222-22-2-22-22-22i−2i00−2i2i00-22-22002i−2i0000−2i2i000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000001−i−1+i1+i−1−i
χ492-222-22-2-22-22-2−2i2i002i−2i002-22-200−2i2i0000−2i2i0000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000001+i−1−i1−i−1+i
χ502-222-22-2-22-22-2−2i2i002i−2i002-22-200−2i2i0000−2i2i000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000−1−i1+i−1+i1−i
χ512-222-22-2-22-22-2−2i2i002i−2i00-22-2200−2i2i00002i−2i0000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000−1−i1+i−1+i1−i
χ522-222-22-2-22-22-2−2i2i002i−2i00-22-2200−2i2i00002i−2i000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000001+i−1−i1−i−1+i
χ53444-4-4-44-400004i−4i−4i4i4i−4i−4i4i0000-44000000000000000000000000000000000000000000000
χ54444-4-4-44-40000−4i4i4i−4i−4i4i4i−4i0000-44000000000000000000000000000000000000000000000
χ5544-444-4-4-4-4-444004i−4i00−4i4i00000000−4i4i00000000000000000000000000000000000000000
χ5644-444-4-4-4-4-44400−4i4i004i−4i000000004i−4i00000000000000000000000000000000000000000
χ5744-4-4-44-440000004400-4-40000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000
χ5844-4-4-44-440000004400-4-4000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000
χ5944-4-4-44-44000000-4-400440000000000000000000002-2-222-2-220000000000000000000000
χ6044-4-4-44-44000000-4-40044000000000000000000000-222-2-222-20000000000000000000000
χ614-444-44-4-4-44-444i−4i00−4i4i00000000−4i4i0000000000000000000000000000000000000000000
χ624-444-44-4-4-44-44−4i4i004i−4i000000004i−4i0000000000000000000000000000000000000000000
χ634-44-44-4-4400004400-4-400000000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000
χ644-44-44-4-4400004400-4-40000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000
χ654-44-44-4-440000-4-4004400000000000000000000000000000002-2-222-2-2200000000000000
χ664-44-44-4-440000-4-400440000000000000000000000000000000-222-2-222-200000000000000
χ674-4-44-4-4444-4-44000000004-4-4400000000000000000000000000000000000000000000000
χ684-4-44-4-4444-4-4400000000-444-400000000000000000000000000000000000000000000000
χ694-4-44-4-444-444-40000000000000000000000004-4000000000000000000000000000000000
χ704-4-44-4-444-444-4000000000000000000000000-44000000000000000000000000000000000
χ718-8-8-8888-8000000000000000000000000000000000000000000000000000000000000000

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