Finite Group Databasebeta

← Group #98191

Character table — Group #98191

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444444448888888888888888888888888881616161616161616161616161616
order12222222222244444444444444444444444444444888888888888888822244444448888
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
χ311111111111111111111111111111111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1
χ511111111111111111111111-1-1-1-11111-1-1-1-111-1-11111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-111111111
χ711111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1111111-1-1-1-1
χ811111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111-111-1-1-1-11111
χ911111111-1-1-1-1-1-11111-1-111-11111-1-1-1111-1-111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-1-1-111ii−i−iii−i−i
χ1011111111-1-1-1-1-1-11111-1-111-11111-1-1-1111-1-111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-1-1-111−i−iii−i−iii
χ1111111111-1-1-1-1-1-11111-1-111-11111-1-1-1111-1-1-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii-1111-1-1−i−iiiii−i−i
χ1211111111-1-1-1-1-1-11111-1-111-11111-1-1-1111-1-1-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i-1111-1-1ii−i−i−i−iii
χ1311111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-11-1-1111111-1-1iiii−i−i−i−iiiii−i−i−i−i111-1-1-1−i−iii−i−iii
χ1411111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-11-1-1111111-1-1−i−i−i−iiiii−i−i−i−iiiii111-1-1-1ii−i−iii−i−i
χ1511111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-11-1-111-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-1-1111ii−i−i−i−iii
χ1611111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-11-1-111-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1111−i−iiiii−i−i
χ1722222222222222-2-2-2-22222-20000-2-2-2-200002200220000000000000000-200-20000000000
χ1822222222222222-2-2-2-22222-20000-2-2-2-20000-2-200-2-2000000000000000020020000000000
χ19222222222222-2-22222-2-2-2-222222-2-22-2-2-2-2-2002200000000000000000000000000000000
χ20222222222222-2-22222-2-2-2-22-2-2-2-2-2-22-2222200-2-200000000000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2000022-220000000000000000000000000002-202-200000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2000022-22000000000000000000000000000-220-2200000000
χ2322222222-2-2-2-222222222-2-2-2222222-2-2-2-22200-2-200000000000000000000000000000000
χ2422222222-2-2-2-222222222-2-2-2-2-2-2-222-2-222-2-2002200000000000000000000000000000000
χ2522222222-2-2-2-222-2-2-2-222-2-220000-2-2220000000000000000000000000002-20-2200000000
χ2622222222-2-2-2-222-2-2-2-222-2-220000-2-222000000000000000000000000000-2202-200000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22220000222-200002200-2-20000000000000000-20020000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22220000222-20000-2-200220000000000000000200-20000000000
χ29222-2-2-22-222-2-2-2-20000222-200000000000002i−2i002i−2ii2i2−i2−i2i2i2−i2−i222−2−222−2−200000000000000
χ30222-2-2-22-222-2-2-2-20000222-200000000000002i−2i002i−2i−i2−i2i2i2−i2−i2i2i2−2−222−2−22200000000000000
χ31222-2-2-22-222-2-2-2-20000222-20000000000000−2i2i00−2i2ii2i2−i2−i2i2i2−i2−i2−2−222−2−22200000000000000
χ32222-2-2-22-222-2-2-2-20000222-20000000000000−2i2i00−2i2i−i2−i2i2i2−i2−i2i2i222−2−222−2−200000000000000
χ33222-2-2-22-2-2-222220000-2-22-200000000000002i−2i00−2i2i22−2−2−2−222−i2−i2i2i2i2i2−i2−i200000000000000
χ34222-2-2-22-2-2-222220000-2-22-200000000000002i−2i00−2i2i−2−22222−2−2i2i2−i2−i2−i2−i2i2i200000000000000
χ35222-2-2-22-2-2-222220000-2-22-20000000000000−2i2i002i−2i22−2−2−2−222i2i2−i2−i2−i2−i2i2i200000000000000
χ36222-2-2-22-2-2-222220000-2-22-20000000000000−2i2i002i−2i−2−22222−2−2−i2−i2i2i2i2i2−i2−i200000000000000
χ3722-2-222-2-200002i−2i22-2-22i−2i0002i2i−2i−2i2i−2i00002-2000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000001−i−1+i1+i−1−i0000
χ3822-2-222-2-200002i−2i22-2-22i−2i0002i2i−2i−2i2i−2i00002-200000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000−1+i1−i−1−i1+i0000
χ3922-2-222-2-200002i−2i22-2-22i−2i000−2i−2i2i2i2i−2i0000-22000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000−1+i1−i−1−i1+i0000
χ4022-2-222-2-200002i−2i22-2-22i−2i000−2i−2i2i2i2i−2i0000-2200000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000001−i−1+i1+i−1−i0000
χ4122-2-222-2-20000−2i2i22-2-2−2i2i0002i2i−2i−2i−2i2i0000-22000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000−1−i1+i−1+i1−i0000
χ4222-2-222-2-20000−2i2i22-2-2−2i2i0002i2i−2i−2i−2i2i0000-2200000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000001+i−1−i1−i−1+i0000
χ4322-2-222-2-20000−2i2i22-2-2−2i2i000−2i−2i2i2i−2i2i00002-2000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000001+i−1−i1−i−1+i0000
χ4422-2-222-2-20000−2i2i22-2-2−2i2i000−2i−2i2i2i−2i2i00002-200000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000−1−i1+i−1+i1−i0000
χ452-2-2-22-2222-22-2002-22-2000022-22-200-200000002-200i2−i2i2−i2i2−i2i2−i2000000000000000000i2−i2i2−i2
χ462-2-2-22-2222-22-2002-22-2000022-22-200-200000002-200−i2i2−i2i2−i2i2−i2i2000000000000000000−i2i2−i2i2
χ472-2-2-22-2222-22-2002-22-200002-22-2200-20000000-2200i2−i2i2−i2i2−i2i2−i2000000000000000000−i2i2−i2i2
χ482-2-2-22-2222-22-2002-22-200002-22-2200-20000000-2200−i2i2−i2i2−i2i2−i2i2000000000000000000i2−i2i2−i2
χ492-2-2-22-222-22-22002-22-20000-22-22-20020000000-22002−22−2−22−220000000000000000002−2−22
χ502-2-2-22-222-22-22002-22-20000-22-22-20020000000-2200−22−222−22−2000000000000000000−222−2
χ512-2-2-22-222-22-22002-22-20000-2-22-2200200000002-2002−22−2−22−22000000000000000000−222−2
χ522-2-2-22-222-22-22002-22-20000-2-22-2200200000002-200−22−222−22−20000000000000000002−2−22
χ53444-4-4-44-444-4-4440000-4-4-440000000000000000000000000000000000000000000000000
χ54444-4-4-44-4-4-444-4-4000044-440000000000000000000000000000000000000000000000000
χ5544-44-4-4-4400004i−4i0000−4i4i000000000000000000000000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ00000000000000
χ5644-44-4-4-4400004i−4i0000−4i4i00000000000000000000000000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ00000000000000
χ5744-44-4-4-440000−4i4i00004i−4i000000000000000000000000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ300000000000000
χ5844-44-4-4-440000−4i4i00004i−4i00000000000000000000000000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ300000000000000
χ5944-4-444-4-400004i−4i-4-4444i−4i0000000−4i4i000000000000000000000000000000000000000000
χ6044-4-444-4-40000−4i4i-4-444−4i4i00000004i−4i000000000000000000000000000000000000000000
χ614-4444-4-4-40000004-4-44000004i−4i−4i4i00000000000000000000000000000000000000000000
χ624-4444-4-4-40000004-4-4400000−4i4i4i−4i00000000000000000000000000000000000000000000
χ634-4444-4-4-4000000-444-400000000000004i−4i00000000000000000000000000000000000000
χ644-4444-4-4-4000000-444-40000000000000−4i4i00000000000000000000000000000000000000
χ654-4-44-444-44-4-44000000000000000000000000000002-2-222-2-220000000000000000000000
χ664-4-44-444-44-4-4400000000000000000000000000000-222-2-222-20000000000000000000000
χ674-4-44-444-4-444-4000000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000
χ684-4-44-444-4-444-400000000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000
χ694-4-4-44-4444-44-400-44-440000-4000000400000000000000000000000000000000000000000
χ704-4-4-44-444-44-4400-44-4400004000000-400000000000000000000000000000000000000000
χ718-88-8-88-88000000000000000000000000000000000000000000000000000000000000000

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