Finite Group Databasebeta

← Group #98162

Character table — Group #98162

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444444448888888888888888888888888881616161616161616161616161616
order12222222444444444444224444444422444444444444444448888888844444488888888
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
χ311111111111111111111111111111111-1-1111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111-1-1111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-11111-1-1111-1-111-1-111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111-1-1-1-11111-1-1111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-111111111
χ71111111111111111111111-1-1-1-11111-1-1-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-111-1-1-1-11111
χ81111111111111111111111-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111-1111111-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i111-1-1-1ii−i−iii−i−i
χ10111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii111-1-1-1−i−iii−i−iii
χ11111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111-1-1iiii−i−i−i−i−i−i−i−iiiii-1-1-1111ii−i−i−i−iii
χ12111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-1-1111−i−iiiii−i−i
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i1-1-1-111−i−iii−i−iii
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii1-1-1-111ii−i−iii−i−i
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11-1-11111iiii−i−i−i−i−i−i−i−iiiii-1111-1-1−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1111-1-1ii−i−i−i−iii
χ1722222222222222-2-222-2-2222222-2-2-2-22200-2-2-200-2-2000000000000000000000000000000
χ1822222222222222-2-222-2-222-2-2-2-2-2-2-2-2-2-200-2220022000000000000000000000000000000
χ19222222222222-2-222-2-222-2-22222-2-222-2-200-2-2-20022000000000000000000000000000000
χ20222222222222-2-222-2-222-2-2-2-2-2-2-2-2222200-22200-2-2000000000000000000000000000000
χ2122222222-2-2-2-222222222-2-2000022-2-20022-20022000000000000000000-200-20000000000
χ2222222222-2-2-2-222222222-2-2000022-2-200-2-2-200-2-200000000000000000020020000000000
χ2322222222-2-2-2-222-2-222-2-2-2-20000-2-22200002000000000000000000000002-202-200000000
χ2422222222-2-2-2-222-2-222-2-2-2-20000-2-2220000200000000000000000000000-220-2200000000
χ2522222222-2-2-2-2-2-222-2-222220000-2-2-2-200002000000000000000000000002-20-2200000000
χ2622222222-2-2-2-2-2-222-2-222220000-2-2-2-20000200000000000000000000000-2202-200000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-222000022220022-200-2-2000000000000000000-20020000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2220000222200-2-2-20022000000000000000000200-20000000000
χ29222-22-2-2-222-2-22200-2-2002-222-2-200002-20000000000000000022−2−222−2−200000000002−22−2
χ30222-22-2-2-222-2-22200-2-2002-222-2-200002-200000000000000000−2−222−2−2220000000000−22−22
χ31222-22-2-2-222-2-22200-2-2002-2-2-2220000-220000000000000000022−2−222−2−20000000000−22−22
χ32222-22-2-2-222-2-22200-2-2002-2-2-2220000-2200000000000000000−2−222−2−22200000000002−22−2
χ33222-22-2-2-222-2-2-2-2002200-2222-2-20000-2200000000000000000i2i2−i2−i2−i2−i2i2i20000000000i2−i2−i2i2
χ34222-22-2-2-222-2-2-2-2002200-2222-2-20000-2200000000000000000−i2−i2i2i2i2i2−i2−i20000000000−i2i2i2−i2
χ35222-22-2-2-222-2-2-2-2002200-22-2-22200002-200000000000000000i2i2−i2−i2−i2−i2i2i20000000000−i2i2i2−i2
χ36222-22-2-2-222-2-2-2-2002200-22-2-22200002-200000000000000000−i2−i2i2i2i2i2−i2−i20000000000i2−i2−i2i2
χ3722-22-2-2-2200002i−2i2i−2i2i−2i2i−2i0000002-200002-20002i−2i001+i1+i−1−i−1−i1−i1−i−1+i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000
χ3822-22-2-2-2200002i−2i2i−2i2i−2i2i−2i0000002-200002-20002i−2i00−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000
χ3922-22-2-2-2200002i−2i2i−2i2i−2i2i−2i0000002-20000-22000−2i2i001+i1+i−1−i−1−i1−i1−i−1+i−1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000
χ4022-22-2-2-2200002i−2i2i−2i2i−2i2i−2i0000002-20000-22000−2i2i00−1−i−1−i1+i1+i−1+i−1+i1−i1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000
χ4122-22-2-2-220000−2i2i−2i2i−2i2i−2i2i0000002-200002-2000−2i2i001−i1−i−1+i−1+i1+i1+i−1−i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000
χ4222-22-2-2-220000−2i2i−2i2i−2i2i−2i2i0000002-200002-2000−2i2i00−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000
χ4322-22-2-2-220000−2i2i−2i2i−2i2i−2i2i0000002-20000-220002i−2i001−i1−i−1+i−1+i1+i1+i−1−i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000
χ4422-22-2-2-220000−2i2i−2i2i−2i2i−2i2i0000002-20000-220002i−2i00−1+i−1+i1−i1−i−1−i−1−i1+i1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000
χ452-2-2222-2-22-22-2002i−2i00−2i2i002-22-2002i−2i0000000002i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000001+i−1−i1−i−1+i0000
χ462-2-2222-2-22-22-2002i−2i00−2i2i002-22-2002i−2i0000000002i−2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000−1−i1+i−1+i1−i0000
χ472-2-2222-2-22-22-2002i−2i00−2i2i00-22-22002i−2i000000000−2i2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000−1−i1+i−1+i1−i0000
χ482-2-2222-2-22-22-2002i−2i00−2i2i00-22-22002i−2i000000000−2i2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000001+i−1−i1−i−1+i0000
χ492-2-2222-2-22-22-200−2i2i002i−2i002-22-200−2i2i000000000−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000001−i−1+i1+i−1−i0000
χ502-2-2222-2-22-22-200−2i2i002i−2i002-22-200−2i2i000000000−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000−1+i1−i−1−i1+i0000
χ512-2-2222-2-22-22-200−2i2i002i−2i00-22-2200−2i2i0000000002i−2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000−1+i1−i−1−i1+i0000
χ522-2-2222-2-22-22-200−2i2i002i−2i00-22-2200−2i2i0000000002i−2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000001−i−1+i1+i−1−i0000
χ53444-44-4-4-4-4-4444400-4-400-440000000000000000000000000000000000000000000000000
χ54444-44-4-4-4-4-444-4-40044004-40000000000000000000000000000000000000000000000000
χ5544-44-4-4-4400004i−4i−4i4i4i−4i−4i4i000000-440000000000000000000000000000000000000000000
χ5644-44-4-4-440000−4i4i4i−4i−4i4i4i−4i000000-440000000000000000000000000000000000000000000
χ5744-4-4-444-400004i−4i00−4i4i00000000000000000000000000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ300000000000000
χ5844-4-4-444-400004i−4i00−4i4i0000000000000000000000000000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ300000000000000
χ5944-4-4-444-40000−4i4i004i−4i00000000000000000000000000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ00000000000000
χ6044-4-4-444-40000−4i4i004i−4i0000000000000000000000000000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ00000000000000
χ614-444-4-44-40000004400-4-40000000000000000000002-2-222-2-220000000000000000000000
χ624-444-4-44-40000004400-4-4000000000000000000000-222-2-222-20000000000000000000000
χ634-444-4-44-4000000-4-400440000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000
χ644-444-4-44-4000000-4-40044000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000
χ654-4-4444-4-4-44-44004i−4i00−4i4i00000000−4i4i00000000000000000000000000000000000000000
χ664-4-4444-4-4-44-4400−4i4i004i−4i000000004i−4i00000000000000000000000000000000000000000
χ674-4-4-44-4444-4-4400000000004-4-44000000000000000000000000000000000000000000000
χ684-4-4-44-4444-4-440000000000-444-4000000000000000000000000000000000000000000000
χ694-4-4-44-444-444-4000000000000000000000004-40000000000000000000000000000000000
χ704-4-4-44-444-444-400000000000000000000000-440000000000000000000000000000000000
χ718-88-8-88-88000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.