Finite Group Databasebeta

← Group #102429

Character table — Group #102429

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222222222222444488888888888888888888888888161616161616161632323232
order12222222222244444444444422224444448888888888888888888888882244
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-11-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-11
χ5111111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ6111111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-11-11
χ8111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111-11-1
χ922222222222222222222-2-2-2-20000-2-200002222-2-2-2-200000000000000000000
χ1022222222222222222222-2-2-2-20000-2-20000-2-2-2-2222200000000000000000000
χ11222222222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-20000000000000000000000000000
χ12222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-222220000000000000000000000000000
χ13222222222222-2-2-2-2-2-2-2-2-2-2-2-20000220000000000002i2i2i2i−2i−2i−2i−2i000000000000
χ14222222222222-2-2-2-2-2-2-2-2-2-2-2-2000022000000000000−2i−2i−2i−2i2i2i2i2i000000000000
χ1522222222-2-2-2-222-2-222-2-22-22-200002-2000000000000000000000000000020-20
χ1622222222-2-2-2-222-2-222-2-22-22-200002-20000000000000000000000000000-2020
χ1722222222-2-2-2-222-2-222-2-2-22-220000-220000000000000000000000000000020-2
χ1822222222-2-2-2-222-2-222-2-2-22-220000-2200000000000000000000000000000-202
χ1922222222-2-2-2-2-2-222-2-2222-22-20000-220000000000000000000022-2-200000000
χ2022222222-2-2-2-2-2-222-2-2222-22-20000-2200000000000000000000-2-22200000000
χ2122222222-2-2-2-2-2-222-2-222-22-2200002-200000000000000000000000022-2-20000
χ2222222222-2-2-2-2-2-222-2-222-22-2200002-2000000000000000000000000-2-2220000
χ2322-2-22-2-2222-2-20000000022-2-20000002i2i−2i−2i22−2−222−2−2i2i2−i2−i2i2i2−i2−i2000000000000
χ2422-2-22-2-2222-2-20000000022-2-20000002i2i−2i−2i−2−222−2−222−i2−i2i2i2−i2−i2i2i2000000000000
χ2522-2-22-2-2222-2-20000000022-2-2000000−2i−2i2i2i22−2−222−2−2−i2−i2i2i2−i2−i2i2i2000000000000
χ2622-2-22-2-2222-2-20000000022-2-2000000−2i−2i2i2i−2−222−2−222i2i2−i2−i2i2i2−i2−i2000000000000
χ2722-2-22-2-2222-2-200000000-2-22222-2-200000022−2−2−2−22222−2−2−2−222000000000000
χ2822-2-22-2-2222-2-200000000-2-22222-2-2000000−2−22222−2−2−2−22222−2−2000000000000
χ2922-2-22-2-2222-2-200000000-2-222-2-22200000022−2−2−2−222−2−22222−2−2000000000000
χ3022-2-22-2-2222-2-200000000-2-222-2-222000000−2−22222−2−222−2−2−2−222000000000000
χ312-22-2-2-2222-22-22-2-2-22-2220000000000000000002-22-2000000002−22−22−22−20000
χ322-22-2-2-2222-22-22-2-2-22-2220000000000000000002-22-200000000−22−22−22−220000
χ332-22-2-2-2222-22-22-2-2-22-222000000000000000000-22-22000000002−22−2−22−220000
χ342-22-2-2-2222-22-22-2-2-22-222000000000000000000-22-2200000000−22−222−22−20000
χ352-22-2-2-222-22-22-22-2-2-2222000000000000002-22-20000000000002−2−222−2−220000
χ362-22-2-2-222-22-22-22-2-2-2222000000000000002-22-2000000000000−222−2−222−20000
χ372-22-2-2-222-22-22-22-2-2-222200000000000000-22-220000000000002−2−22−222−20000
χ382-22-2-2-222-22-22-22-2-2-222200000000000000-22-22000000000000−222−22−2−220000
χ39444-4-44-4-40000004i−4i004i−4i00000000000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000000000000
χ40444-4-44-4-40000004i−4i004i−4i0000000000000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000000000000
χ41444-4-44-4-4000000−4i4i00−4i4i00000000000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000000000000
χ42444-4-44-4-4000000−4i4i00−4i4i0000000000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000000000000
χ4344-44-4-44-400004400-4-40000000000000000000000002i−2i−2i2i−2i2i2i−2i000000000000
χ4444-44-4-44-400004400-4-4000000000000000000000000−2i2i2i−2i2i−2i−2i2i000000000000
χ4544-44-4-44-40000-4-400440000000000000000000000002-2-222-2-22000000000000
χ4644-44-4-44-40000-4-40044000000000000000000000000-222-2-222-2000000000000
χ4744-4-44-4-44-4-444000000004-4-4400000000000000000000000000000000000000
χ4844-4-44-4-44-4-44400000000-444-400000000000000000000000000000000000000
χ494-4444-4-4-40000004i−4i00−4i4i00002-22-2002i−2i2i−2i0000000000000000000000000000
χ504-4444-4-4-40000004i−4i00−4i4i0000-22-2200−2i2i−2i2i0000000000000000000000000000
χ514-4444-4-4-4000000−4i4i004i−4i00002-22-200−2i2i−2i2i0000000000000000000000000000
χ524-4444-4-4-4000000−4i4i004i−4i0000-22-22002i−2i2i−2i0000000000000000000000000000
χ534-44-4-4-4444-44-4-4444-44-4-4000000000000000000000000000000000000000000
χ544-44-4-4-444-44-444-4444-4-4-4000000000000000000000000000000000000000000
χ554-4-44-44-444-4-440000000000000000000000000022−22−222200000000000000000000
χ564-4-44-44-444-4-4400000000000000000000000000−222222−2200000000000000000000
χ574-4-44-44-44-444-4000000000000000000000022−22−2222000000000000000000000000
χ584-4-44-44-44-444-40000000000000000000000−222222−22000000000000000000000000
χ594-4-4-4444-400004-400-440000002-2-2200-222-20000000000000000000000000000
χ604-4-4-4444-400004-400-44000000-222-2002-2-220000000000000000000000000000
χ614-4-4-4444-40000-44004-40000002-2-22002-2-220000000000000000000000000000
χ624-4-4-4444-40000-44004-4000000-222-200-222-20000000000000000000000000000

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