Finite Group Databasebeta

← Group #99501

Character table — Group #99501

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size111111111111111144444444444488888888888888888888888888888888888816161616161616161616
order12222222444444444444444444444444888888888888888888888888888888884488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ311111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1
χ51111111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1
χ61111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1
χ71111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111
χ911111111-1-1-1-1-1-1-1-11-1-111-1-1-1111-111-1-1ii−i−iii−i−i1111-1-1-1-11111-1-1-1-1iiii−i−i−i−i1-1ii−i−ii−ii−i
χ1011111111-1-1-1-1-1-1-1-11-1-111-1-1-1111-111-1-1ii−i−iii−i−i-1-1-1-11111-1-1-1-11111−i−i−i−iiiii1-1−i−iiii−ii−i
χ1111111111-1-1-1-1-1-1-1-11-1-111-1-1-1111-111-1-1−i−iii−i−iii1111-1-1-1-11111-1-1-1-1−i−i−i−iiiii1-1−i−iii−ii−ii
χ1211111111-1-1-1-1-1-1-1-11-1-111-1-1-1111-111-1-1−i−iii−i−iii-1-1-1-11111-1-1-1-11111iiii−i−i−i−i1-1ii−i−i−ii−ii
χ1311111111-1-1-1-1-1-1-1-11-1-111-1-1-1111-1-1-111ii−i−i−i−iii1111-1-1-1-1-1-1-1-11111iiii−i−i−i−i-11−i−iiii−i−ii
χ1411111111-1-1-1-1-1-1-1-11-1-111-1-1-1111-1-1-111ii−i−i−i−iii-1-1-1-111111111-1-1-1-1−i−i−i−iiiii-11ii−i−ii−i−ii
χ1511111111-1-1-1-1-1-1-1-11-1-111-1-1-1111-1-1-111−i−iiiii−i−i1111-1-1-1-1-1-1-1-11111−i−i−i−iiiii-11ii−i−i−iii−i
χ1611111111-1-1-1-1-1-1-1-11-1-111-1-1-1111-1-1-111−i−iiiii−i−i-1-1-1-111111111-1-1-1-1iiii−i−i−i−i-11−i−iii−iii−i
χ172222222222222222222-2-2-2-2-2-2-22-2000022220000000000000000000000000000000000-2-200
χ182222222222222222222-2-2-2-2-2-2-22-20000-2-2-2-200000000000000000000000000000000002200
χ192222222222222222-2-2-2222-2-2-2-2-22222200000000000000000000000000000000-2-200000000
χ202222222222222222-2-2-2222-2-2-2-2-22-2-2-2-2000000000000000000000000000000002200000000
χ212222222222222222-2-2-2-2-2-22222-2-200000000222200000000000000000000000000000000-2-2
χ222222222222222222-2-2-2-2-2-22222-2-200000000-2-2-2-20000000000000000000000000000000022
χ2322222222-2-2-2-2-2-2-2-22-2-2-2-2222-2-22200002i2i−2i−2i0000000000000000000000000000000000−2i2i00
χ2422222222-2-2-2-2-2-2-2-22-2-2-2-2222-2-2220000−2i−2i2i2i00000000000000000000000000000000002i−2i00
χ2522222222-2-2-2-2-2-2-2-2-22222-222-2-2-2-222-2-200000000000000000000000000000000-2200000000
χ2622222222-2-2-2-2-2-2-2-2-22222-222-2-2-2-2-2-222000000000000000000000000000000002-200000000
χ2722222222-2-2-2-2-2-2-2-2-222-2-22-2-222-22000000002i2i−2i−2i00000000000000000000000000000000−2i2i
χ2822222222-2-2-2-2-2-2-2-2-222-2-22-2-222-2200000000−2i−2i2i2i000000000000000000000000000000002i−2i
χ292222-2-2-2-22222-2-2-2-222-20000000-2000002-22-2000022−2−222−2−20000000022−2−222−2−20000000000
χ302222-2-2-2-22222-2-2-2-222-20000000-2000002-22-20000−2−222−2−22200000000−2−222−2−2220000000000
χ312222-2-2-2-22222-2-2-2-222-20000000-200000-22-22000022−2−222−2−200000000−2−222−2−2220000000000
χ322222-2-2-2-22222-2-2-2-222-20000000-200000-22-220000−2−222−2−2220000000022−2−222−2−20000000000
χ332222-2-2-2-2-2-2-2-222222-220000000-2000002i−2i−2i2i000022−2−2−2−22200000000i2i2−i2−i2−i2−i2i2i20000000000
χ342222-2-2-2-2-2-2-2-222222-220000000-2000002i−2i−2i2i0000−2−22222−2−200000000−i2−i2i2i2i2i2−i2−i20000000000
χ352222-2-2-2-2-2-2-2-222222-220000000-200000−2i2i2i−2i000022−2−2−2−22200000000−i2−i2i2i2i2i2−i2−i20000000000
χ362222-2-2-2-2-2-2-2-222222-220000000-200000−2i2i2i−2i0000−2−22222−2−200000000i2i2−i2−i2−i2−i2i2i20000000000
χ3722-2-222-2-222-2-222-2-20002-2-20000022-22-200000000i2−i2i2−i2i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2000000000000000000
χ3822-2-222-2-222-2-222-2-20002-2-20000022-22-200000000−i2i2−i2i2−i2i2−i2i2−i2−i2i2i2−i2−i2i2i2000000000000000000
χ3922-2-222-2-222-2-222-2-20002-2-2000002-22-2200000000i2−i2i2−i2i2−i2i2−i2−i2−i2i2i2−i2−i2i2i2000000000000000000
χ4022-2-222-2-222-2-222-2-20002-2-2000002-22-2200000000−i2i2−i2i2−i2i2−i2i2i2i2−i2−i2i2i2−i2−i2000000000000000000
χ4122-2-222-2-2-2-222-2-2220002-2200000-22-2-2200000000i2−i2i2−i2−i2i2−i2i2i2i2−i2−i2−i2−i2i2i2000000000000000000
χ4222-2-222-2-2-2-222-2-2220002-2200000-22-2-2200000000−i2i2−i2i2i2−i2i2−i2−i2−i2i2i2i2i2−i2−i2000000000000000000
χ4322-2-222-2-2-2-222-2-2220002-2200000-2-222-200000000i2−i2i2−i2−i2i2−i2i2−i2−i2i2i2i2i2−i2−i2000000000000000000
χ4422-2-222-2-2-2-222-2-2220002-2200000-2-222-200000000−i2i2−i2i2i2−i2i2−i2i2i2−i2−i2−i2−i2i2i2000000000000000000
χ452-22-22-22-22i−2i2i−2i2i−2i2i−2i0000002i−2i2-200000000002ζ−2ζ2ζ3−2ζ3000000002−22−2i2−i2i2−i21+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000
χ462-22-22-22-22i−2i2i−2i2i−2i2i−2i0000002i−2i2-200000000002ζ−2ζ2ζ3−2ζ300000000−22−22−i2i2−i2i2−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000
χ472-22-22-22-22i−2i2i−2i2i−2i2i−2i0000002i−2i2-20000000000−2ζ2ζ−2ζ32ζ3000000002−22−2i2−i2i2−i2−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000
χ482-22-22-22-22i−2i2i−2i2i−2i2i−2i0000002i−2i2-20000000000−2ζ2ζ−2ζ32ζ300000000−22−22−i2i2−i2i21+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000
χ492-22-22-22-2−2i2i−2i2i−2i2i−2i2i000000−2i2i2-200000000002ζ3−2ζ32ζ−2ζ000000002−22−2−i2i2−i2i2−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000
χ502-22-22-22-2−2i2i−2i2i−2i2i−2i2i000000−2i2i2-200000000002ζ3−2ζ32ζ−2ζ00000000−22−22i2−i2i2−i21−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000
χ512-22-22-22-2−2i2i−2i2i−2i2i−2i2i000000−2i2i2-20000000000−2ζ32ζ3−2ζ2ζ000000002−22−2−i2i2−i2i21−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000
χ522-22-22-22-2−2i2i−2i2i−2i2i−2i2i000000−2i2i2-20000000000−2ζ32ζ3−2ζ2ζ00000000−22−22i2−i2i2−i2−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000
χ534444-4-4-4-44444-4-4-4-4-4-440000000400000000000000000000000000000000000000000000000
χ544444-4-4-4-4-4-4-4-44444-44-40000000400000000000000000000000000000000000000000000000
χ5544-4-444-4-444-4-444-4-4000-44400000-40000000000000000000000000000000000000000000000
χ5644-4-444-4-4-4-444-4-444000-44-40000040000000000000000000000000000000000000000000000
χ5744-4-4-4-44444-4-4-4-4440000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000000000000000
χ5844-4-4-4-44444-4-4-4-444000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000
χ5944-4-4-4-444-4-44444-4-40000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ6044-4-4-4-444-4-44444-4-4000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ614-44-44-44-44i−4i4i−4i4i−4i4i−4i000000−4i4i-44000000000000000000000000000000000000000000000000
χ624-44-44-44-4−4i4i−4i4i−4i4i−4i4i0000004i−4i-44000000000000000000000000000000000000000000000000
χ634-44-4-44-444i−4i4i−4i−4i4i−4i4i00000000000000000000000000000000000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ30000000000
χ644-44-4-44-444i−4i4i−4i−4i4i−4i4i0000000000000000000000000000000000000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ30000000000
χ654-44-4-44-44−4i4i−4i4i4i−4i4i−4i00000000000000000000000000000000000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ0000000000
χ664-44-4-44-44−4i4i−4i4i4i−4i4i−4i0000000000000000000000000000000000000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ0000000000
χ674-4-444-4-444i−4i−4i4i4i−4i−4i4i000000000000000000000000000000002i−2i−2i2i-222-2000000000000000000
χ684-4-444-4-444i−4i−4i4i4i−4i−4i4i00000000000000000000000000000000−2i2i2i−2i2-2-22000000000000000000
χ694-4-444-4-44−4i4i4i−4i−4i4i4i−4i000000000000000000000000000000002i−2i−2i2i2-2-22000000000000000000
χ704-4-444-4-44−4i4i4i−4i−4i4i4i−4i00000000000000000000000000000000−2i2i2i−2i-222-2000000000000000000
χ714-4-44-444-44i−4i−4i4i−4i4i4i−4i000000000000000000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ724-4-44-444-44i−4i−4i4i−4i4i4i−4i00000000000000000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ734-4-44-444-4−4i4i4i−4i4i−4i−4i4i000000000000000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ744-4-44-444-4−4i4i4i−4i4i−4i−4i4i00000000000000000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ30000

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