Finite Group Databasebeta

← Group #97490

Character table — Group #97490

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222444444444444444444444444888888888888161616161616161616161616161616161616
order12222222222244444444444444448888888888888888224444444444244444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-11-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-111-1-111-1-1-11-1-11-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-111-1-111-1-11-1-11-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-111111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-11-1-11-11111-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11-1-1111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-11111-1-1-1-1-1-1-1111ii−i−iii−i−iii−i−i
χ1011111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1-1-1-1-11111-1111-1-1ii−i−i−i−iii−i−iii
χ1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-11111-1-1-1-1111-11-11-1−i−iiiii−i−i−i−iii
χ1211111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111-1-11111-1-111-1-1-11−i−iii−i−iiiii−i−i
χ1311111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-11111-1-1-1-1-1-1-1111−i−iii−i−iii−i−iii
χ1411111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1-1-1-1-11111-1111-1-1−i−iiiii−i−iii−i−i
χ1511111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-11111-1-1-1-1111-11-11-1ii−i−i−i−iiiii−i−i
χ1611111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-11111-1-111-1-1-11ii−i−iii−i−i−i−iii
χ1722222222222222-2-222-2-222-2-2-2-2-2-2000000000000000000000022002200-200-2000000000000
χ1822222222222222-2-222-2-222-2-2-2-2-2-20000000000000000000000-2-200-2-2002002000000000000
χ19222222222222-2-222-2-222-2-222-2-2-2-200000000000000000000220022000-200-20000000000000
χ20222222222222-2-222-2-222-2-222-2-2-2-200000000000000000000-2-200-2-200020020000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000022-2-200000000200-200000000000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000-2-22200000000-200200000000000000
χ2322222222-2-2-2-222222222-2-2-2-222-2-20000000000000000222200000000-200-200000000000000
χ2422222222-2-2-2-222222222-2-2-2-222-2-20000000000000000-2-2-2-200000000200200000000000000
χ2522222222-2-2-2-222-2-222-2-2-2-222-2-222000000000000000000002200-2-2000200-20000000000000
χ2622222222-2-2-2-222-2-222-2-2-2-222-2-22200000000000000000000-2-20022000-20020000000000000
χ2722222222-2-2-2-2-2-222-2-22222-2-2-2-22200000000000000000000002200-2-200200-2000000000000
χ2822222222-2-2-2-2-2-222-2-22222-2-2-2-2220000000000000000000000-2-2002200-2002000000000000
χ29222-2-2-2-2200002i−2i2i−2i2i−2i2i−2i00002-2001+i1+i1+i1+i−1−i−1−i−1−i−1−i1−i1−i1−i1−i−1+i−1+i−1+i−1+i2-22i−2i000000000000001+i−1−i1−i−1+i00000000
χ30222-2-2-2-2200002i−2i2i−2i2i−2i2i−2i00002-2001+i1+i1+i1+i−1−i−1−i−1−i−1−i1−i1−i1−i1−i−1+i−1+i−1+i−1+i-22−2i2i00000000000000−1−i1+i−1+i1−i00000000
χ31222-2-2-2-2200002i−2i2i−2i2i−2i2i−2i00002-200−1−i−1−i−1−i−1−i1+i1+i1+i1+i−1+i−1+i−1+i−1+i1−i1−i1−i1−i2-22i−2i00000000000000−1−i1+i−1+i1−i00000000
χ32222-2-2-2-2200002i−2i2i−2i2i−2i2i−2i00002-200−1−i−1−i−1−i−1−i1+i1+i1+i1+i−1+i−1+i−1+i−1+i1−i1−i1−i1−i-22−2i2i000000000000001+i−1−i1−i−1+i00000000
χ33222-2-2-2-220000−2i2i−2i2i−2i2i−2i2i00002-2001−i1−i1−i1−i−1+i−1+i−1+i−1+i1+i1+i1+i1+i−1−i−1−i−1−i−1−i2-2−2i2i000000000000001−i−1+i1+i−1−i00000000
χ34222-2-2-2-220000−2i2i−2i2i−2i2i−2i2i00002-2001−i1−i1−i1−i−1+i−1+i−1+i−1+i1+i1+i1+i1+i−1−i−1−i−1−i−1−i-222i−2i00000000000000−1+i1−i−1−i1+i00000000
χ35222-2-2-2-220000−2i2i−2i2i−2i2i−2i2i00002-200−1+i−1+i−1+i−1+i1−i1−i1−i1−i−1−i−1−i−1−i−1−i1+i1+i1+i1+i2-2−2i2i00000000000000−1+i1−i−1−i1+i00000000
χ36222-2-2-2-220000−2i2i−2i2i−2i2i−2i2i00002-200−1+i−1+i−1+i−1+i1−i1−i1−i1−i−1−i−1−i−1−i−1−i1+i1+i1+i1+i-222i−2i000000000000001−i−1+i1+i−1−i00000000
χ3722-222-2-2-222-2-200-2-20022002-20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200002i−2i002i−2i0000000000002−22−20000
χ3822-222-2-2-222-2-200-2-20022002-20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000−2i2i00−2i2i000000000000−22−220000
χ3922-222-2-2-222-2-200-2-20022002-20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200002i−2i002i−2i000000000000−22−220000
χ4022-222-2-2-222-2-200-2-20022002-20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000−2i2i00−2i2i0000000000002−22−20000
χ4122-222-2-2-2-2-222002200-2-2002-2000022−2−222−2−2−2−222−2−22200002i−2i00−2i2i000000000000−i2i2i2−i20000
χ4222-222-2-2-2-2-222002200-2-2002-2000022−2−222−2−2−2−222−2−2220000−2i2i002i−2i000000000000i2−i2−i2i20000
χ4322-222-2-2-2-2-222002200-2-2002-20000−2−222−2−22222−2−222−2−200002i−2i00−2i2i000000000000i2−i2−i2i20000
χ4422-222-2-2-2-2-222002200-2-2002-20000−2−222−2−22222−2−222−2−20000−2i2i002i−2i000000000000−i2i2i2−i20000
χ452-222-22-2-22-22-2-2-20022002-2000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000002i−2i002i−2i000000000000002−22−2
χ462-222-22-2-22-22-2-2-20022002-2000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000−2i2i00−2i2i00000000000000−22−22
χ472-222-22-2-22-22-2-2-20022002-2000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000002i−2i002i−2i00000000000000−22−22
χ482-222-22-2-22-22-2-2-20022002-2000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000−2i2i00−2i2i000000000000002−22−2
χ492-222-22-2-2-22-222200-2-2002-20000002−22−22−22−2−22−22−22−220000002i−2i00−2i2i00000000000000−i2i2i2−i2
χ502-222-22-2-2-22-222200-2-2002-20000002−22−22−22−2−22−22−22−22000000−2i2i002i−2i00000000000000i2−i2−i2i2
χ512-222-22-2-2-22-222200-2-2002-2000000−22−22−22−222−22−22−22−20000002i−2i00−2i2i00000000000000i2−i2−i2i2
χ522-222-22-2-2-22-222200-2-2002-2000000−22−22−22−222−22−22−22−2000000−2i2i002i−2i00000000000000−i2i2i2−i2
χ53444-4-4-4-4400004i−4i−4i4i4i−4i−4i4i0000-44000000000000000000000000000000000000000000000000
χ54444-4-4-4-440000−4i4i4i−4i−4i4i4i−4i0000-44000000000000000000000000000000000000000000000000
χ5544-444-4-4-444-4-4004400-4-400-4400000000000000000000000000000000000000000000000000
χ5644-444-4-4-4-4-44400-4-4004400-4400000000000000000000000000000000000000000000000000
χ5744-4-4-444-40000004i−4i00−4i4i000000002ζ2ζ−2ζ−2ζ−2ζ−2ζ2ζ2ζ2ζ32ζ3−2ζ3−2ζ3−2ζ3−2ζ32ζ32ζ3000000000000000000000000000000
χ5844-4-4-444-40000004i−4i00−4i4i00000000−2ζ−2ζ2ζ2ζ2ζ2ζ−2ζ−2ζ−2ζ3−2ζ32ζ32ζ32ζ32ζ3−2ζ3−2ζ3000000000000000000000000000000
χ5944-4-4-444-4000000−4i4i004i−4i000000002ζ32ζ3−2ζ3−2ζ3−2ζ3−2ζ32ζ32ζ32ζ2ζ−2ζ−2ζ−2ζ−2ζ2ζ2ζ000000000000000000000000000000
χ6044-4-4-444-4000000−4i4i004i−4i00000000−2ζ3−2ζ32ζ32ζ32ζ32ζ3−2ζ3−2ζ3−2ζ−2ζ2ζ2ζ2ζ2ζ−2ζ−2ζ000000000000000000000000000000
χ614-444-44-4-44-44-44400-4-400-440000000000000000000000000000000000000000000000000000
χ624-444-44-4-4-44-44-4-4004400-440000000000000000000000000000000000000000000000000000
χ634-44-44-44-400004i−4i00−4i4i00000000002ζ−2ζ2ζ−2ζ−2ζ2ζ−2ζ2ζ2ζ3−2ζ32ζ3−2ζ3−2ζ32ζ3−2ζ32ζ3000000000000000000000000000000
χ644-44-44-44-400004i−4i00−4i4i0000000000−2ζ2ζ−2ζ2ζ2ζ−2ζ2ζ−2ζ−2ζ32ζ3−2ζ32ζ32ζ3−2ζ32ζ3−2ζ3000000000000000000000000000000
χ654-44-44-44-40000−4i4i004i−4i00000000002ζ3−2ζ32ζ3−2ζ3−2ζ32ζ3−2ζ32ζ32ζ−2ζ2ζ−2ζ−2ζ2ζ−2ζ2ζ000000000000000000000000000000
χ664-44-44-44-40000−4i4i004i−4i0000000000−2ζ32ζ3−2ζ32ζ32ζ3−2ζ32ζ3−2ζ3−2ζ2ζ−2ζ2ζ2ζ−2ζ2ζ−2ζ000000000000000000000000000000
χ674-4-44-4-4444-4-4400000000000000002-2-222-2-222-2-222-2-22000000000000000000000000000000
χ684-4-44-4-4444-4-440000000000000000-222-2-222-2-222-2-222-2000000000000000000000000000000
χ694-4-44-4-444-444-400000000000000002i−2i−2i2i2i−2i−2i2i−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000
χ704-4-44-4-444-444-40000000000000000−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i000000000000000000000000000000
χ714-4-4-444-440000000000000000004-42i−2i−2i2i−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000
χ724-4-4-444-440000000000000000004-4−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i−2i2i2i−2i000000000000000000000000000000
χ734-4-4-444-44000000000000000000-442-2-22-222-22-2-22-222-2000000000000000000000000000000
χ744-4-4-444-44000000000000000000-44-222-22-2-22-222-22-2-22000000000000000000000000000000

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