Finite Group Databasebeta

← Group #98296

Character table — Group #98296

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444444448888888888888888888888888881616161616161616161616161616
order12222222444444444444222244444444444444444888888888888888844444488888888
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
χ311111111111111111111111111111111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-1111111-1-1-1-1111-1-11111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111-1-1-1-1111111-1-1-1-1111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-111111111
χ711111111111111111111-1-1-1-1111111-1-1-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-111-1-1-1-11111
χ811111111111111111111-1-1-1-1111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111-1111111-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111111-1-1iiii−i−i−i−iiiii−i−i−i−i-1111-1-1ii−i−iii−i−i
χ10111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111111-1-1−i−i−i−iiiii−i−i−i−iiiii-1111-1-1−i−iii−i−iii
χ11111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-11-1-11111iiii−i−i−i−i−i−i−i−iiiii1-1-1-111ii−i−i−i−iii
χ12111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-11-1-11111−i−i−i−iiiiiiiii−i−i−i−i1-1-1-111−i−iiiii−i−i
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1111−i−iii−i−iii
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1111ii−i−iii−i−i
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii111-1-1-1−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i111-1-1-1ii−i−i−i−iii
χ1722222222222222-2-222-2-222222-2-2-22-222-2-2-200-2-200000000000000000000000000000000
χ1822222222222222-2-222-2-2-2-2-2-22-2-2-22-2-2-222-2002200000000000000000000000000000000
χ19222222222222-2-222-2-2222222-22-2-2-22-2-222-200-2-200000000000000000000000000000000
χ20222222222222-2-222-2-222-2-2-2-2-22-2-2-2222-2-2-2002200000000000000000000000000000000
χ2122222222-2-2-2-2222222220000-2-222-2-20000-22200220000000000000000-200-20000000000
χ2222222222-2-2-2-2222222220000-2-222-2-20000-2-2-200-2-2000000000000000020020000000000
χ2322222222-2-2-2-222-2-222-2-20000-22-2-2-2200002000000000000000000000002-202-200000000
χ2422222222-2-2-2-222-2-222-2-20000-22-2-2-220000200000000000000000000000-220-2200000000
χ2522222222-2-2-2-2-2-222-2-22200002-2-2-22-200002000000000000000000000002-20-2200000000
χ2622222222-2-2-2-2-2-222-2-22200002-2-2-22-20000200000000000000000000000-2202-200000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-200002222220000-22200-2-20000000000000000200-20000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-200002222220000-2-2-200220000000000000000-20020000000000
χ29222-22-2-2-222-2-2002200-2-222-2-202000-2002-2000000022−2−222−2−2000000000000002−22−20000
χ30222-22-2-2-222-2-2002200-2-222-2-202000-2002-20000000−2−222−2−22200000000000000−22−220000
χ31222-22-2-2-222-2-2002200-2-2-2-22202000-200-22000000022−2−222−2−200000000000000−22−220000
χ32222-22-2-2-222-2-2002200-2-2-2-22202000-200-220000000−2−222−2−222000000000000002−22−20000
χ33222-22-2-2-222-2-200-2-2002222-2-20-2000200-220000000i2i2−i2−i2−i2−i2i2i200000000000000i2−i2−i2i20000
χ34222-22-2-2-222-2-200-2-2002222-2-20-2000200-220000000−i2−i2i2i2i2i2−i2−i200000000000000−i2i2i2−i20000
χ35222-22-2-2-222-2-200-2-20022-2-2220-20002002-20000000i2i2−i2−i2−i2−i2i2i200000000000000−i2i2i2−i20000
χ36222-22-2-2-222-2-200-2-20022-2-2220-20002002-20000000−i2−i2i2i2i2i2−i2−i200000000000000i2−i2−i2i20000
χ3722-22-22-2-22-22-22200-2-2002-22-22000-202-20000000000000000022−2−222−2−200000000002−22−2
χ3822-22-22-2-22-22-22200-2-2002-22-22000-202-200000000000000000−2−222−2−2220000000000−22−22
χ3922-22-22-2-22-22-22200-2-200-22-222000-20-220000000000000000022−2−222−2−20000000000−22−22
χ4022-22-22-2-22-22-22200-2-200-22-222000-20-2200000000000000000−2−222−2−22200000000002−22−2
χ4122-22-22-2-22-22-2-2-20022002-22-2-200020-2200000000000000000i2i2−i2−i2−i2−i2i2i20000000000i2−i2−i2i2
χ4222-22-22-2-22-22-2-2-20022002-22-2-200020-2200000000000000000−i2−i2i2i2i2i2−i2−i20000000000−i2i2i2−i2
χ4322-22-22-2-22-22-2-2-2002200-22-22-2000202-200000000000000000i2i2−i2−i2−i2−i2i2i20000000000−i2i2i2−i2
χ4422-22-22-2-22-22-2-2-2002200-22-22-2000202-200000000000000000−i2−i2i2i2i2i2−i2−i20000000000i2−i2−i2i2
χ452-222-2-2-2200002i−2i2i−2i2i−2i2i−2i0000002-200000002i−2i002-21+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000
χ462-222-2-2-2200002i−2i2i−2i2i−2i2i−2i0000002-200000002i−2i002-2−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000
χ472-222-2-2-2200002i−2i2i−2i2i−2i2i−2i0000002-20000000−2i2i00-221+i−1−i1+i−1−i1−i−1+i1−i−1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000
χ482-222-2-2-2200002i−2i2i−2i2i−2i2i−2i0000002-20000000−2i2i00-22−1−i1+i−1−i1+i−1+i1−i−1+i1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000
χ492-222-2-2-220000−2i2i−2i2i−2i2i−2i2i0000002-200000002i−2i00-221−i−1+i1−i−1+i1+i−1−i1+i−1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000
χ502-222-2-2-220000−2i2i−2i2i−2i2i−2i2i0000002-200000002i−2i00-22−1+i1−i−1+i1−i−1−i1+i−1−i1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000
χ512-222-2-2-220000−2i2i−2i2i−2i2i−2i2i0000002-20000000−2i2i002-21−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000
χ522-222-2-2-220000−2i2i−2i2i−2i2i−2i2i0000002-20000000−2i2i002-2−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000
χ53444-44-4-4-4-4-444004400-4-400000-4000400000000000000000000000000000000000000000
χ54444-44-4-4-4-4-44400-4-40044000004000-400000000000000000000000000000000000000000
χ5544-44-44-4-4-44-444400-4-4000000-40004000000000000000000000000000000000000000000
χ5644-44-44-4-4-44-44-4-400440000004000-4000000000000000000000000000000000000000000
χ5744-4-4-4-4444-4-44000000004-4-4400000000000000000000000000000000000000000000000
χ5844-4-4-4-4444-4-4400000000-444-400000000000000000000000000000000000000000000000
χ5944-4-4-4-444-444-400000000000000000000000004-400000000000000000000000000000000
χ6044-4-4-4-444-444-40000000000000000000000000-4400000000000000000000000000000000
χ614-444-4-4-4400004i−4i−4i4i4i−4i−4i4i000000-440000000000000000000000000000000000000000000
χ624-444-4-4-440000−4i4i4i−4i−4i4i4i−4i000000-440000000000000000000000000000000000000000000
χ634-44-4-444-40000004i−4i00−4i4i0000000000000000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ30000000000000000000000
χ644-44-4-444-40000004i−4i00−4i4i000000000000000000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ30000000000000000000000
χ654-44-4-444-4000000−4i4i004i−4i0000000000000000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ0000000000000000000000
χ664-44-4-444-4000000−4i4i004i−4i000000000000000000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ0000000000000000000000
χ674-4-444-44-400004i−4i00−4i4i00000000000000000000000000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ00000000000000
χ684-4-444-44-400004i−4i00−4i4i0000000000000000000000000000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ00000000000000
χ694-4-444-44-40000−4i4i004i−4i00000000000000000000000000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ300000000000000
χ704-4-444-44-40000−4i4i004i−4i0000000000000000000000000000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ300000000000000
χ718-8-8-888-88000000000000000000000000000000000000000000000000000000000000000

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