Finite Group Databasebeta

← Group #98301

Character table — Group #98301

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444444448888888888888888888888888881616161616161616161616161616
order12222222444444444444444444444422224444444888888888888888824444488888888
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
χ5111111111111111111111111-1-1-1-111-1-111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-111-1-111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111
χ7111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ8111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-111111111-1-111111111-1-1-1-1
χ911111111-1-1-1-11111-1-1-1-1-1-1111111-1-11111-1-1-1-11-1-1iiii−i−i−i−iiiii−i−i−i−i-11-1-111ii−i−iii−i−i
χ1011111111-1-1-1-11111-1-1-1-1-1-1111111-1-11111-1-1-1-11-1-1−i−i−i−iiiii−i−i−i−iiiii-11-1-111−i−iii−i−iii
χ1111111111-1-1-1-11111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1111iiii−i−i−i−i−i−i−i−iiiii1-111-1-1ii−i−i−i−iii
χ1211111111-1-1-1-11111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1111−i−i−i−iiiiiiiii−i−i−i−i1-111-1-1−i−iiiii−i−i
χ1311111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111-1-1iiii−i−i−i−iiiii−i−i−i−i-1111-1-1−i−iii−i−iii
χ1411111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111-1-1−i−i−i−iiiii−i−i−i−iiiii-1111-1-1ii−i−iii−i−i
χ1511111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111iiii−i−i−i−i−i−i−i−iiiii1-1-1-111−i−iiiii−i−i
χ1611111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111−i−i−i−iiiiiiiii−i−i−i−i1-1-1-111ii−i−i−i−iii
χ17222222222222-2-2-2-22222-2-2220000-2-200220000-2220000000000000000-2-2000000000000
χ18222222222222-2-2-2-22222-2-2220000-2-200-2-20000-2-2-2000000000000000022000000000000
χ192222222222-2-2222222-2-22-2-2-222222-2-2-20022-2-2-200000000000000000000000000000000
χ202222222222-2-2222222-2-22-2-2-2-2-2-2-22-22200-2-222-200000000000000000000000000000000
χ212222222222-2-2-2-2-2-222-2-2-22-2-20000-22000000002000000000000000000002-22-200000000
χ222222222222-2-2-2-2-2-222-2-2-22-2-20000-2200000000200000000000000000000-22-2200000000
χ2322222222-2-2222222-2-222-22-2-22222-22-2-200-2-222-200000000000000000000000000000000
χ2422222222-2-2222222-2-222-22-2-2-2-2-2-2-22220022-2-2-200000000000000000000000000000000
χ2522222222-2-222-2-2-2-2-2-2222-2-2-200002-2000000002000000000000000000002-2-2200000000
χ2622222222-2-222-2-2-2-2-2-2222-2-2-200002-200000000200000000000000000000-222-200000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222200002200220000-2-2-200000000000000002-2000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222200002200-2-20000-2220000000000000000-22000000000000
χ29222-2-2-2-222i−2i2i−2i00002i−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
χ30222-2-2-2-222i−2i2i−2i00002i−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
χ31222-2-2-2-222i−2i2i−2i00002i−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
χ32222-2-2-2-222i−2i2i−2i00002i−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
χ33222-2-2-2-22−2i2i−2i2i0000−2i2i−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
χ34222-2-2-2-22−2i2i−2i2i0000−2i2i−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
χ35222-2-2-2-22−2i2i−2i2i0000−2i2i−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
χ36222-2-2-2-22−2i2i−2i2i0000−2i2i−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
χ3722-22-22-2-2002222-2-200-2-20-2002i2i−2i−2i020000002i−2i0002−22−22−22−200000000000000i2−i2i2−i20000
χ3822-22-22-2-2002222-2-200-2-20-2002i2i−2i−2i020000002i−2i000−22−22−22−2200000000000000−i2i2−i2i20000
χ3922-22-22-2-2002222-2-200-2-20-200−2i−2i2i2i02000000−2i2i0002−22−22−22−200000000000000−i2i2−i2i20000
χ4022-22-22-2-2002222-2-200-2-20-200−2i−2i2i2i02000000−2i2i000−22−22−22−2200000000000000i2−i2i2−i20000
χ4122-22-22-2-200-2-222-2-2002202002i2i−2i−2i0-2000000−2i2i000i2−i2i2−i2−i2i2−i2i200000000000000−222−20000
χ4222-22-22-2-200-2-222-2-2002202002i2i−2i−2i0-2000000−2i2i000−i2i2−i2i2i2−i2i2−i2000000000000002−2−220000
χ4322-22-22-2-200-2-222-2-200220200−2i−2i2i2i0-20000002i−2i000i2−i2i2−i2−i2i2−i2i2000000000000002−2−220000
χ4422-22-22-2-200-2-222-2-200220200−2i−2i2i2i0-20000002i−2i000−i2i2−i2i2i2−i2i2−i200000000000000−222−20000
χ452-22-222-2-222002-22-2-2-200-20002i−2i2i−2i2000002i−2i00000000000002−22−22−22−20000000000i2−i2i2−i2
χ462-22-222-2-222002-22-2-2-200-20002i−2i2i−2i2000002i−2i0000000000000−22−22−22−220000000000−i2i2−i2i2
χ472-22-222-2-222002-22-2-2-200-2000−2i2i−2i2i200000−2i2i00000000000002−22−22−22−20000000000−i2i2−i2i2
χ482-22-222-2-222002-22-2-2-200-2000−2i2i−2i2i200000−2i2i0000000000000−22−22−22−220000000000i2−i2i2−i2
χ492-22-222-2-2-2-2002-22-2220020002i−2i2i−2i-200000−2i2i0000000000000i2−i2i2−i2−i2i2−i2i20000000000−222−2
χ502-22-222-2-2-2-2002-22-2220020002i−2i2i−2i-200000−2i2i0000000000000−i2i2−i2i2i2−i2i2−i200000000002−2−22
χ512-22-222-2-2-2-2002-22-222002000−2i2i−2i2i-2000002i−2i0000000000000i2−i2i2−i2−i2i2−i2i200000000002−2−22
χ522-22-222-2-2-2-2002-22-222002000−2i2i−2i2i-2000002i−2i0000000000000−i2i2−i2i2i2−i2i2−i20000000000−222−2
χ53444-4-4-4-444i−4i−4i4i00004i−4i−4i4i00-4400000000000000000000000000000000000000000000000
χ54444-4-4-4-44−4i4i4i−4i0000−4i4i4i−4i00-4400000000000000000000000000000000000000000000000
χ5544-44-44-4-40044-4-44400-4-4040000000-400000000000000000000000000000000000000000
χ5644-44-44-4-400-4-4-4-44400440-40000000400000000000000000000000000000000000000000
χ5744-4-44-44-4004i−4i000000−4i4i0000000000000000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ30000000000000000000000
χ5844-4-44-44-4004i−4i000000−4i4i000000000000000000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ30000000000000000000000
χ5944-4-44-44-400−4i4i0000004i−4i0000000000000000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ0000000000000000000000
χ6044-4-44-44-400−4i4i0000004i−4i000000000000000000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ0000000000000000000000
χ614-444-4-44-44i−4i000000−4i4i00000000000000000000000000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ300000000000000
χ624-444-4-44-44i−4i000000−4i4i0000000000000000000000000000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ300000000000000
χ634-444-4-44-4−4i4i0000004i−4i00000000000000000000000000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ00000000000000
χ644-444-4-44-4−4i4i0000004i−4i0000000000000000000000000000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ00000000000000
χ654-44-444-4-44400-44-44-4-40040000000-4000000000000000000000000000000000000000000
χ664-44-444-4-4-4-400-44-444400-400000004000000000000000000000000000000000000000000
χ674-4-4-4-444400004-4-44000000004-4-440000000000000000000000000000000000000000000
χ684-4-4-4-444400004-4-4400000000-444-40000000000000000000000000000000000000000000
χ694-4-4-4-44440000-444-4000000000000004-4000000000000000000000000000000000000000
χ704-4-4-4-44440000-444-400000000000000-44000000000000000000000000000000000000000
χ718-8-888-8-88000000000000000000000000000000000000000000000000000000000000000

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