Finite Group Databasebeta

← Group #98285

Character table — Group #98285

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444444448888888888888888888888888881616161616161616161616161616
order12222222444444444444444444444422444444444888888888888888822444488888888
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
χ31111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-111-1-11-1-1-1-111111111111111111111-1-11-1-11-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-111-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111111111
χ7111111111111111111111111-1-1-1-111-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-111-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-111-11111-1-1-1-1
χ911111111-1-11111-1-1-1-1-1-1-111-11111-1-1-1-1111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1111ii−i−iii−i−i
χ1011111111-1-11111-1-1-1-1-1-1-111-11111-1-1-1-1111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1111−i−iii−i−iii
χ1111111111-1-11111-1-1-1-1-1-1-111-11111-1-1-1-1111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii111-1-1-1ii−i−i−i−iii
χ1211111111-1-11111-1-1-1-1-1-1-111-11111-1-1-1-1111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i111-1-1-1−i−iiiii−i−i
χ1311111111-1-11111-1-1-1-1-1-1-111-1-1-1-1-1-1-1111-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1-11−i−iii−i−iii
χ1411111111-1-11111-1-1-1-1-1-1-111-1-1-1-1-1-1-1111-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1-11ii−i−iii−i−i
χ1511111111-1-11111-1-1-1-1-1-1-111-1-1-1-1-1-1-1111-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii-1-1111-1−i−iiiii−i−i
χ1611111111-1-11111-1-1-1-1-1-1-111-1-1-1-1-1-1-1111-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-1111-1ii−i−i−i−iii
χ1722222222222222-2-222-2-22-2-2-222222-2-2-2-2-2-2220000000000000000000000000000000000
χ1822222222222222-2-222-2-22-2-2-2-2-2-2-22-222-222-2-20000000000000000000000000000000000
χ192222222222-2-2-2-2222222-222-20000-2-200-200002222000000000000000000-200-200000000
χ202222222222-2-2-2-2222222-222-20000-2-200-20000-2-2-2-2000000000000000000200200000000
χ212222222222-2-2-2-2-2-222-2-2-2-2-220000-220020000000000000000000000002-202-2000000000
χ222222222222-2-2-2-2-2-222-2-2-2-2-220000-22002000000000000000000000000-220-22000000000
χ2322222222-2-2222222-2-222-2-2-222222-2222-2-2-2-2-20000000000000000000000000000000000
χ2422222222-2-2222222-2-222-2-2-22-2-2-2-2-22-2-2-222220000000000000000000000000000000000
χ2522222222-2-2-2-2-2-222-2-2222-2-2-200002-20020000000000000000000000002-20-22000000000
χ2622222222-2-2-2-2-2-222-2-2222-2-2-200002-2002000000000000000000000000-2202-2000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222200002200-2000022-2-2000000000000000000200-200000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222200002200-20000-2-222000000000000000000-200200000000
χ2922-22-22-2-22222-2-200-2-200-20002i2i−2i−2i20000002i−2i000000000000i2i2−i2−i2i2i2−i2−i200000000002−22−2
χ3022-22-22-2-22222-2-200-2-200-20002i2i−2i−2i20000002i−2i000000000000−i2−i2i2i2−i2−i2i2i20000000000−22−22
χ3122-22-22-2-22222-2-200-2-200-2000−2i−2i2i2i2000000−2i2i000000000000i2i2−i2−i2i2i2−i2−i20000000000−22−22
χ3222-22-22-2-22222-2-200-2-200-2000−2i−2i2i2i2000000−2i2i000000000000−i2−i2i2i2−i2−i2i2i200000000002−22−2
χ3322-22-22-2-2-2-222-2-200220020002i2i−2i−2i-2000000−2i2i00000000000022−2−2−2−2220000000000−i2i2i2−i2
χ3422-22-22-2-2-2-222-2-200220020002i2i−2i−2i-2000000−2i2i000000000000−2−22222−2−20000000000i2−i2−i2i2
χ3522-22-22-2-2-2-222-2-20022002000−2i−2i2i2i-20000002i−2i00000000000022−2−2−2−2220000000000i2−i2−i2i2
χ3622-22-22-2-2-2-222-2-20022002000−2i−2i2i2i-20000002i−2i000000000000−2−22222−2−20000000000−i2i2i2−i2
χ3722-2-22-22-22i−2i00002i−2i2i−2i2i−2i02-2000000000000002-22i−2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000
χ3822-2-22-22-22i−2i00002i−2i2i−2i2i−2i02-2000000000000002-22i−2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000
χ3922-2-22-22-22i−2i00002i−2i2i−2i2i−2i02-200000000000000-22−2i2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000
χ4022-2-22-22-22i−2i00002i−2i2i−2i2i−2i02-200000000000000-22−2i2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000
χ4122-2-22-22-2−2i2i0000−2i2i−2i2i−2i2i02-2000000000000002-2−2i2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000
χ4222-2-22-22-2−2i2i0000−2i2i−2i2i−2i2i02-2000000000000002-2−2i2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000
χ4322-2-22-22-2−2i2i0000−2i2i−2i2i−2i2i02-200000000000000-222i−2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000
χ4422-2-22-22-2−2i2i0000−2i2i−2i2i−2i2i02-200000000000000-222i−2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000
χ452-2-2-2-2222002-22-22200-2-200022-22-20-22-2000000000i2−i2i2−i2i2−i2i2−i200000000000000i2−i2i2−i20000
χ462-2-2-2-2222002-22-22200-2-200022-22-20-22-2000000000−i2i2−i2i2−i2i2−i2i200000000000000−i2i2−i2i20000
χ472-2-2-2-2222002-22-22200-2-20002-22-220-2-22000000000i2−i2i2−i2i2−i2i2−i200000000000000−i2i2−i2i20000
χ482-2-2-2-2222002-22-22200-2-20002-22-220-2-22000000000−i2i2−i2i2−i2i2−i2i200000000000000i2−i2i2−i20000
χ492-2-2-2-2222002-22-2-2-20022000-22-22-202-220000000002−22−2−22−22000000000000002−2−220000
χ502-2-2-2-2222002-22-2-2-20022000-22-22-202-22000000000−22−222−22−200000000000000−222−20000
χ512-2-2-2-2222002-22-2-2-20022000-2-22-22022-20000000002−22−2−22−2200000000000000−222−20000
χ522-2-2-2-2222002-22-2-2-20022000-2-22-22022-2000000000−22−222−22−2000000000000002−2−220000
χ53444-4-4-4-444i−4i000000−4i4i00000000000000000000000000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ00000000000000
χ54444-4-4-4-444i−4i000000−4i4i0000000000000000000000000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ00000000000000
χ55444-4-4-4-44−4i4i0000004i−4i00000000000000000000000000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ300000000000000
χ56444-4-4-4-44−4i4i0000004i−4i0000000000000000000000000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ300000000000000
χ5744-44-44-4-444-4-44400-4-40040000000-4000000000000000000000000000000000000000000
χ5844-44-44-4-4-4-4-4-444004400-400000004000000000000000000000000000000000000000000
χ5944-4-44-44-44i−4i0000−4i4i4i−4i−4i4i0-44000000000000000000000000000000000000000000000000
χ6044-4-44-44-4−4i4i00004i−4i−4i4i4i−4i0-44000000000000000000000000000000000000000000000000
χ614-444-4-44-40000004i−4i00−4i4i0000000000000000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ0000000000000000000000
χ624-444-4-44-40000004i−4i00−4i4i000000000000000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ0000000000000000000000
χ634-444-4-44-4000000−4i4i004i−4i0000000000000000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ30000000000000000000000
χ644-444-4-44-4000000−4i4i004i−4i000000000000000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ30000000000000000000000
χ654-44-444-4-4004-4-4400000000004i−4i−4i4i0000000000000000000000000000000000000000000
χ664-44-444-4-4004-4-440000000000−4i4i4i−4i0000000000000000000000000000000000000000000
χ674-44-444-4-400-444-400000000000000000004i−4i000000000000000000000000000000000000
χ684-44-444-4-400-444-40000000000000000000−4i4i000000000000000000000000000000000000
χ694-4-4-4-444400-44-444400-4-4000-400000400000000000000000000000000000000000000000
χ704-4-4-4-444400-44-44-4-40044000400000-400000000000000000000000000000000000000000
χ718-8-888-8-88000000000000000000000000000000000000000000000000000000000000000

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