Finite Group Databasebeta

← Group #140495

Character table — Group #140495

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222222222222222222222444444444444444444448888888888888888161616161616161632323232
order1222444444444488888888888824888888888888888888888888888888888816161616161616168888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ611111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ711111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ811111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ911111111-1-1-1-1-1-11111-1-1-1-11111-1111-1-1-1-111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1i−ii−i
χ1011111111-1-1-1-1-1-11111-1-1-1-11111-1111-1-1-1-111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−ii−ii
χ1111111111-1-1-1-1-1-11111-1-1-1-11111-1111-1-1-1-111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−ii−ii
χ1211111111-1-1-1-1-1-11111-1-1-1-11111-1111-1-1-1-111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111i−ii−i
χ1311111111-1-1-1-1-1-1-1-1-1-111111111-1111-1-1-1-1-1-111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111i−i−ii
χ1411111111-1-1-1-1-1-1-1-1-1-111111111-1111-1-1-1-1-1-111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−iii−i
χ1511111111-1-1-1-1-1-1-1-1-1-111111111-1111-1-1-1-1-1-111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111−iii−i
χ1611111111-1-1-1-1-1-1-1-1-1-111111111-1111-1-1-1-1-1-111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1i−i−ii
χ172222222222222222222222-2-2-2-222-2-2-2-2-2-22222-2-2-2-2-2-2-2-20000000000000000000000000000
χ1822222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000000000
χ1922222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-22-2-2222222-2-2-2-2-2-222220000000000000000000000000000
χ2022222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-22-2-22222-2-2222222-2-2-2-20000000000000000000000000000
χ21222222-2-22222-2-2222222220000-2-2000000-2-2-2-2000000000000000000000000i2−i2i2−i2i2−i2i2−i20000
χ22222222-2-22222-2-2222222220000-2-2000000-2-2-2-2000000000000000000000000−i2i2−i2i2−i2i2−i2i20000
χ23222222-2-22222-2-2-2-2-2-2-2-2-2-20000-2-20000002222000000000000000000000000i2−i2i2−i2−i2i2−i2i20000
χ24222222-2-22222-2-2-2-2-2-2-2-2-2-20000-2-20000002222000000000000000000000000−i2i2−i2i2i2−i2i2−i20000
χ25222222-2-2-2-2-2-2222222-2-2-2-200002-2000000-2-222000000000000000000000000i2−i2−i2i2i2−i2−i2i20000
χ26222222-2-2-2-2-2-2222222-2-2-2-200002-2000000-2-222000000000000000000000000−i2i2i2−i2−i2i2i2−i20000
χ27222222-2-2-2-2-2-222-2-2-2-2222200002-200000022-2-2000000000000000000000000i2−i2−i2i2−i2i2i2−i20000
χ28222222-2-2-2-2-2-222-2-2-2-2222200002-200000022-2-2000000000000000000000000−i2i2i2−i2i2−i2−i2i20000
χ292222-2-22222-2-222000000002222-2-2-2-222-2-20000000000000000000022-2-222-2-2000000000000
χ302222-2-22222-2-222000000002222-2-2-2-222-2-200000000000000000000-2-222-2-222000000000000
χ312222-2-22222-2-22200000000-2-2-2-2-2-222-2-2220000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000
χ322222-2-22222-2-22200000000-2-2-2-2-2-222-2-222000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ332222-2-222-2-222-2-20000000022222-2-2-2-2-222000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ342222-2-222-2-222-2-20000000022222-2-2-2-2-22200000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ352222-2-222-2-222-2-200000000-2-2-2-22-22222-2-200000000000022-2-2-2-22200000000000000000000
χ362222-2-222-2-222-2-200000000-2-2-2-22-22222-2-2000000000000-2-22222-2-200000000000000000000
χ3722-2-2002-22i−2i002i−2ii2i2−i2−i222−2−222-2-200002i−2i00i2−i22−2i2i2−i2−i222−2−21+i−1−i1+i−1−i1−i−1+i1−i−1+i002ζ3−2ζ3002ζ−2ζ000000000000
χ3822-2-2002-22i−2i002i−2ii2i2−i2−i222−2−222-2-200002i−2i00i2−i22−2i2i2−i2−i222−2−2−1−i1+i−1−i1+i−1+i1−i−1+i1−i00−2ζ32ζ300−2ζ2ζ000000000000
χ3922-2-2002-22i−2i002i−2ii2i2−i2−i222−2−2-2-2220000−2i2i00i2−i22−2−i2−i2i2i2−2−2221−i−1+i−1+i1−i−1−i1+i1+i−1−i2ζ−2ζ002ζ3−2ζ300000000000000
χ4022-2-2002-22i−2i002i−2ii2i2−i2−i222−2−2-2-2220000−2i2i00i2−i22−2−i2−i2i2i2−2−222−1+i1−i1−i−1+i1+i−1−i−1−i1+i−2ζ2ζ00−2ζ32ζ300000000000000
χ4122-2-2002-22i−2i002i−2i−i2−i2i2i2−2−22222-2-200002i−2i00−i2i2−22−i2−i2i2i2−2−2221+i−1−i1+i−1−i1−i−1+i1−i−1+i00−2ζ32ζ300−2ζ2ζ000000000000
χ4222-2-2002-22i−2i002i−2i−i2−i2i2i2−2−22222-2-200002i−2i00−i2i2−22−i2−i2i2i2−2−222−1−i1+i−1−i1+i−1+i1−i−1+i1−i002ζ3−2ζ3002ζ−2ζ000000000000
χ4322-2-2002-22i−2i002i−2i−i2−i2i2i2−2−222-2-2220000−2i2i00−i2i2−22i2i2−i2−i222−2−21−i−1+i−1+i1−i−1−i1+i1+i−1−i−2ζ2ζ00−2ζ32ζ300000000000000
χ4422-2-2002-22i−2i002i−2i−i2−i2i2i2−2−222-2-2220000−2i2i00−i2i2−22i2i2−i2−i222−2−2−1+i1−i1−i−1+i1+i−1−i−1−i1+i2ζ−2ζ002ζ3−2ζ300000000000000
χ4522-2-2002-2−2i2i00−2i2ii2i2−i2−i2−2−22222-2-20000−2i2i00i2−i2−22i2i2−i2−i2−2−2221−i−1+i1−i−1+i1+i−1−i1+i−1−i002ζ−2ζ002ζ3−2ζ3000000000000
χ4622-2-2002-2−2i2i00−2i2ii2i2−i2−i2−2−22222-2-20000−2i2i00i2−i2−22i2i2−i2−i2−2−222−1+i1−i−1+i1−i−1−i1+i−1−i1+i00−2ζ2ζ00−2ζ32ζ3000000000000
χ4722-2-2002-2−2i2i00−2i2ii2i2−i2−i2−2−222-2-22200002i−2i00i2−i2−22−i2−i2i2i222−2−21+i−1−i−1−i1+i−1+i1−i1−i−1+i2ζ3−2ζ3002ζ−2ζ00000000000000
χ4822-2-2002-2−2i2i00−2i2ii2i2−i2−i2−2−222-2-22200002i−2i00i2−i2−22−i2−i2i2i222−2−2−1−i1+i1+i−1−i1−i−1+i−1+i1−i−2ζ32ζ300−2ζ2ζ00000000000000
χ4922-2-2002-2−2i2i00−2i2i−i2−i2i2i222−2−222-2-20000−2i2i00−i2i22−2−i2−i2i2i222−2−21−i−1+i1−i−1+i1+i−1−i1+i−1−i00−2ζ2ζ00−2ζ32ζ3000000000000
χ5022-2-2002-2−2i2i00−2i2i−i2−i2i2i222−2−222-2-20000−2i2i00−i2i22−2−i2−i2i2i222−2−2−1+i1−i−1+i1−i−1−i1+i−1−i1+i002ζ−2ζ002ζ3−2ζ3000000000000
χ5122-2-2002-2−2i2i00−2i2i−i2−i2i2i222−2−2-2-22200002i−2i00−i2i22−2i2i2−i2−i2−2−2221+i−1−i−1−i1+i−1+i1−i1−i−1+i−2ζ32ζ300−2ζ2ζ00000000000000
χ5222-2-2002-2−2i2i00−2i2i−i2−i2i2i222−2−2-2-22200002i−2i00−i2i22−2i2i2−i2−i2−2−222−1−i1+i1+i−1−i1−i−1+i−1+i1−i2ζ3−2ζ3002ζ−2ζ00000000000000
χ534444-4-4-4-444-4-4-4-4000000000000440000000000000000000000000000000000000000000000
χ544444-4-4-4-4-4-44444000000000000-440000000000000000000000000000000000000000000000
χ5544-4-400-444i−4i00−4i4i2i22i2−2i2−2i22222−22−22000000000000−2i22i2−2222000000000000000000000000000000000000
χ5644-4-400-444i−4i00−4i4i−2i2−2i22i22i2−22−2222220000000000002i2−2i222−22000000000000000000000000000000000000
χ5744-4-400-44−4i4i004i−4i2i22i2−2i2−2i2−22−222222000000000000−2i22i222−22000000000000000000000000000000000000
χ5844-4-400-44−4i4i004i−4i−2i2−2i22i22i22222−22−220000000000002i2−2i2−2222000000000000000000000000000000000000
χ594-44-40000004i−4i0022−2222−222i2−2i22i2−2i22i2−2i22i2−2i200000022−2200002i−2i2i−2i2-22-20000000000000000000000000000
χ604-44-40000004i−4i0022−2222−222i2−2i22i2−2i2−2i22i2−2i22i2000000−22220000−2i2i−2i2i-22-220000000000000000000000000000
χ614-44-40000004i−4i00−2222−2222−2i22i2−2i22i22i2−2i22i2−2i200000022−220000−2i2i−2i2i-22-220000000000000000000000000000
χ624-44-40000004i−4i00−2222−2222−2i22i2−2i22i2−2i22i2−2i22i2000000−222200002i−2i2i−2i2-22-20000000000000000000000000000
χ634-44-4000000−4i4i0022−2222−22−2i22i2−2i22i22i2−2i22i2−2i2000000−222200002i−2i2i−2i-22-220000000000000000000000000000
χ644-44-4000000−4i4i0022−2222−22−2i22i2−2i22i2−2i22i2−2i22i200000022−220000−2i2i−2i2i2-22-20000000000000000000000000000
χ654-44-4000000−4i4i00−2222−22222i2−2i22i2−2i22i2−2i22i2−2i2000000−22220000−2i2i−2i2i2-22-20000000000000000000000000000
χ664-44-4000000−4i4i00−2222−22222i2−2i22i2−2i2−2i22i2−2i22i200000022−2200002i−2i2i−2i-22-220000000000000000000000000000
χ674-4-444-40000000000004i−4i−4i4i2i2−2i2−2i22i2002i2−2i200000000000022−22−22220000000000000000000000000000
χ684-4-444-40000000000004i−4i−4i4i−2i22i22i2−2i200−2i22i2000000000000−222222−220000000000000000000000000000
χ694-4-444-4000000000000−4i4i4i−4i2i2−2i2−2i22i2002i2−2i2000000000000−222222−220000000000000000000000000000
χ704-4-444-4000000000000−4i4i4i−4i−2i22i22i2−2i200−2i22i200000000000022−22−22220000000000000000000000000000
χ714-4-44-44000000004i−4i−4i4i00002i2−2i2−2i22i200−2i22i200000000−222222−2200000000000000000000000000000000
χ724-4-44-44000000004i−4i−4i4i0000−2i22i22i2−2i2002i2−2i20000000022−22−222200000000000000000000000000000000
χ734-4-44-4400000000−4i4i4i−4i00002i2−2i2−2i22i200−2i22i20000000022−22−222200000000000000000000000000000000
χ744-4-44-4400000000−4i4i4i−4i0000−2i22i22i2−2i2002i2−2i200000000−222222−2200000000000000000000000000000000

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