Finite Group Databasebeta

← Group #98136

Character table — Group #98136

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444444448888888888888888888888888881616161616161616161616161616
order12222222444444444444224444444422444444444444444448888888822444488888888
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
χ311111111111111111111111111111111-1-111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111-1-111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-111-1-111-1-11-1-1111111111111111111-1-11-1-11-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-111-1-111-1-11-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111111111
χ7111111111111111111111111-1-1-1-111-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-111-111-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111111111-111-11111-1-1-1-1
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−i-1-1111-1ii−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−iiiii-1-1111-1−i−iii−i−iii
χ11111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111-1-111iiii−i−i−i−i−i−i−i−iiiii11-1-1-11ii−i−i−i−iii
χ12111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111-1-111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-11−i−iiiii−i−i
χ13111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1111-1-1iiii−i−i−i−iiiii−i−i−i−i111-1-1-1−i−iii−i−iii
χ14111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1111-1-1−i−i−i−iiiii−i−i−i−iiiii111-1-1-1ii−i−iii−i−i
χ15111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-111111iiii−i−i−i−i−i−i−i−iiiii-1-1-1111−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-111111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1111ii−i−i−i−iii
χ1722222222222222-2-222-2-222-2-22222-2-2-2-200-2-2-22200000000000000000000000000000000
χ1822222222222222-2-222-2-222-2-2-2-2-2-2-2-2220022-2-2-200000000000000000000000000000000
χ19222222222222-2-222-2-222-2-2-2-22222222200-2-2-2-2-200000000000000000000000000000000
χ20222222222222-2-222-2-222-2-2-2-2-2-2-2-222-2-20022-22200000000000000000000000000000000
χ2122222222-2-2-2-222222222-2-2220000-2-2002200-20022000000000000000000-200-200000000
χ2222222222-2-2-2-222222222-2-2220000-2-200-2-200-200-2-2000000000000000000200200000000
χ2322222222-2-2-2-222-2-222-2-2-2-2-2-20000220000002000000000000000000002-202-2000000000
χ2422222222-2-2-2-222-2-222-2-2-2-2-2-2000022000000200000000000000000000-220-22000000000
χ2522222222-2-2-2-2-2-222-2-22222-2-20000-2-20000002000000000000000000002-20-22000000000
χ2622222222-2-2-2-2-2-222-2-22222-2-20000-2-2000000200000000000000000000-2202-2000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22222000022002200-200-2-2000000000000000000-200200000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222200002200-2-200-20022000000000000000000200-200000000
χ29222-2-2-22-200002i−2i2i−2i2i−2i2i−2i002-2000000002-2000002i−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−2i002-2000000002-2000002i−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−2i002-200000000-2200000−2i2i1+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−2i002-200000000-2200000−2i2i−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−2i2i002-2000000002-200000−2i2i1−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−2i2i002-2000000002-200000−2i2i−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−2i2i002-200000000-22000002i−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−2i2i002-200000000-22000002i−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
χ3722-2-222-2-222-2-22200-2-200-22002i2i−2i−2i0000000002i−2i0000000000i2−i2i2−i2i2−i2i2−i200000000002−22−2
χ3822-2-222-2-222-2-22200-2-200-22002i2i−2i−2i0000000002i−2i0000000000−i2i2−i2i2−i2i2−i2i20000000000−22−22
χ3922-2-222-2-222-2-22200-2-200-2200−2i−2i2i2i000000000−2i2i0000000000i2−i2i2−i2i2−i2i2−i20000000000−22−22
χ4022-2-222-2-222-2-22200-2-200-2200−2i−2i2i2i000000000−2i2i0000000000−i2i2−i2i2−i2i2−i2i200000000002−22−2
χ4122-2-222-2-222-2-2-2-20022002-2002i2i−2i−2i000000000−2i2i00000000002−22−2−22−220000000000−i2i2i2−i2
χ4222-2-222-2-222-2-2-2-20022002-2002i2i−2i−2i000000000−2i2i0000000000−22−222−22−20000000000i2−i2−i2i2
χ4322-2-222-2-222-2-2-2-20022002-200−2i−2i2i2i0000000002i−2i00000000002−22−2−22−220000000000i2−i2−i2i2
χ4422-2-222-2-222-2-2-2-20022002-200−2i−2i2i2i0000000002i−2i0000000000−22−222−22−20000000000−i2i2i2−i2
χ452-2222-2-2-22-22-2002i−2i00−2i2i00002i−2i2i−2i2i−2i2-20000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000001+i−1−i1−i−1+i0000
χ462-2222-2-2-22-22-2002i−2i00−2i2i00002i−2i2i−2i2i−2i2-2000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000−1−i1+i−1+i1−i0000
χ472-2222-2-2-22-22-2002i−2i00−2i2i0000−2i2i−2i2i2i−2i-220000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000−1−i1+i−1+i1−i0000
χ482-2222-2-2-22-22-2002i−2i00−2i2i0000−2i2i−2i2i2i−2i-22000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000001+i−1−i1−i−1+i0000
χ492-2222-2-2-22-22-200−2i2i002i−2i00002i−2i2i−2i−2i2i-220000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000−1+i1−i−1−i1+i0000
χ502-2222-2-2-22-22-200−2i2i002i−2i00002i−2i2i−2i−2i2i-22000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000001−i−1+i1+i−1−i0000
χ512-2222-2-2-22-22-200−2i2i002i−2i0000−2i2i−2i2i−2i2i2-20000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000001−i−1+i1+i−1−i0000
χ522-2222-2-2-22-22-200−2i2i002i−2i0000−2i2i−2i2i−2i2i2-2000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000−1+i1−i−1−i1+i0000
χ53444-4-4-44-400004i−4i−4i4i4i−4i−4i4i00-4400000000000000000000000000000000000000000000000
χ54444-4-4-44-40000−4i4i4i−4i−4i4i4i−4i00-4400000000000000000000000000000000000000000000000
χ5544-44-4-4-4400004i−4i00−4i4i00000000000000000000000000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ00000000000000
χ5644-44-4-4-4400004i−4i00−4i4i0000000000000000000000000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ00000000000000
χ5744-44-4-4-440000−4i4i004i−4i00000000000000000000000000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ300000000000000
χ5844-44-4-4-440000−4i4i004i−4i0000000000000000000000000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ300000000000000
χ5944-4-444-4-4-4-4444400-4-4004-40000000000000000000000000000000000000000000000000
χ6044-4-444-4-4-4-444-4-4004400-440000000000000000000000000000000000000000000000000
χ614-4444-4-4-4-44-44004i−4i00−4i4i00000000−4i4i00000000000000000000000000000000000000000
χ624-4444-4-4-4-44-4400−4i4i004i−4i000000004i−4i00000000000000000000000000000000000000000
χ634-44-4-44-440000004400-4-40000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000
χ644-44-4-44-440000004400-4-4000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000
χ654-44-4-44-44000000-4-400440000000000000000000002-2-222-2-220000000000000000000000
χ664-44-4-44-44000000-4-40044000000000000000000000-222-2-222-20000000000000000000000
χ674-4-4-44-4444-4-440000000000004-4-440000000000000000000000000000000000000000000
χ684-4-4-44-4444-4-44000000000000-444-40000000000000000000000000000000000000000000
χ694-4-4-44-444-444-400000000000000000000004-400000000000000000000000000000000000
χ704-4-4-44-444-444-40000000000000000000000-4400000000000000000000000000000000000
χ718-8-88-888-8000000000000000000000000000000000000000000000000000000000000000

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