Finite Group Databasebeta

← Group #425252

Character table — Group #425252

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222444444444444444444444444888888888888161616161616161616161616161616161616
order12224444222222444444444444448888888888888888224488888888244444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ311111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1-1-1
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-11111-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111-1-111
χ911111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-111
χ1011111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-111
χ1111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-11111-1-1
χ1211111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111111111
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1-1-11111
χ17222222222-2-2-2-222-2-2-22-200000000000000002222-2-2-2-20000000022-2-2000000002-200000000
χ18222222222-2-2-2-222-2-2-22-200000000000000002222-2-2-2-200000000-2-22200000000-2200000000
χ19222222222-2-2-2-222-2-2-22-20000000000000000-2-2-2-222220000000022-2-200000000-2200000000
χ20222222222-2-2-2-222-2-2-22-20000000000000000-2-2-2-2222200000000-2-222000000002-200000000
χ212222-2-2-2-2222222-2-2-2-2-2-2000000002i2i2i2i−2i−2i−2i−2i00000000000000002i−2i2i−2i0000002-20000000000
χ222222-2-2-2-2222222-2-2-2-2-2-2000000002i2i2i2i−2i−2i−2i−2i0000000000000000−2i2i−2i2i000000-220000000000
χ232222-2-2-2-2222222-2-2-2-2-2-200000000−2i−2i−2i−2i2i2i2i2i00000000000000002i−2i2i−2i000000-220000000000
χ242222-2-2-2-2222222-2-2-2-2-2-200000000−2i−2i−2i−2i2i2i2i2i0000000000000000−2i2i−2i2i0000002-20000000000
χ252222-2-2-2-22-2-2-2-22-2222-222222-2-2-2-20000000000000000000000002i−2i−2i2i0000000000002i−2i0000
χ262222-2-2-2-22-2-2-2-22-2222-222222-2-2-2-2000000000000000000000000−2i2i2i−2i000000000000−2i2i0000
χ272222-2-2-2-22-2-2-2-22-2222-22-2-2-2-222220000000000000000000000002i−2i−2i2i000000000000−2i2i0000
χ282222-2-2-2-22-2-2-2-22-2222-22-2-2-2-22222000000000000000000000000−2i2i2i−2i0000000000002i−2i0000
χ292222-2-2-2-2-222-2-2-2222-22-2000000000000000022-2-222-2-222-2-2000000002-20000000000000000
χ302222-2-2-2-2-222-2-2-2222-22-2000000000000000022-2-222-2-2-2-22200000000-220000000000000000
χ312222-2-2-2-2-222-2-2-2222-22-20000000000000000-2-222-2-22222-2-200000000-220000000000000000
χ322222-2-2-2-2-222-2-2-2222-22-20000000000000000-2-222-2-222-2-222000000002-20000000000000000
χ332222-2-2-2-2-2-2-222-22-2-2222000000000000000022-2-2-2-22200002i2i−2i−2i000000000000002i−2i000000
χ342222-2-2-2-2-2-2-222-22-2-2222000000000000000022-2-2-2-2220000−2i−2i2i2i00000000000000−2i2i000000
χ352222-2-2-2-2-2-2-222-22-2-22220000000000000000-2-22222-2-200002i2i−2i−2i00000000000000−2i2i000000
χ362222-2-2-2-2-2-2-222-22-2-22220000000000000000-2-22222-2-20000−2i−2i2i2i000000000000002i−2i000000
χ372-2-2222-2-222-22-2-222-2-2-220000000022-2-222-2-20000000000002i−2i2i−2i000000002i−2i000000000000
χ382-2-2222-2-222-22-2-222-2-2-220000000022-2-222-2-2000000000000−2i2i−2i2i00000000−2i2i000000000000
χ392-2-2222-2-222-22-2-222-2-2-2200000000-2-222-2-2220000000000002i−2i2i−2i00000000−2i2i000000000000
χ402-2-2222-2-222-22-2-222-2-2-2200000000-2-222-2-222000000000000−2i2i−2i2i000000002i−2i000000000000
χ412-2-2222-2-2-22-2-222-2-22-22222-2-222-2-200000000000000002-22-200000000000000000000002-200
χ422-2-2222-2-2-22-2-222-2-22-22222-2-222-2-20000000000000000-22-220000000000000000000000-2200
χ432-2-2222-2-2-22-2-222-2-22-222-2-222-2-22200000000000000002-22-20000000000000000000000-2200
χ442-2-2222-2-2-22-2-222-2-22-222-2-222-2-2220000000000000000-22-2200000000000000000000002-200
χ452-2-22-2-22222-22-2-2-2-2222-2000000002i2i−2i−2i−2i−2i2i2i000000002-2-220000000000000000000000002i−2i
χ462-2-22-2-22222-22-2-2-2-2222-2000000002i2i−2i−2i−2i−2i2i2i00000000-222-2000000000000000000000000−2i2i
χ472-2-22-2-22222-22-2-2-2-2222-200000000−2i−2i2i2i2i2i−2i−2i000000002-2-22000000000000000000000000−2i2i
χ482-2-22-2-22222-22-2-2-2-2222-200000000−2i−2i2i2i2i2i−2i−2i00000000-222-20000000000000000000000002i−2i
χ492-2-22-2-222-2-222-222-22-2-2222-2-2-2-222000000000000000000002-2-220000002-200000000000000
χ502-2-22-2-222-2-222-222-22-2-2222-2-2-2-22200000000000000000000-222-2000000-2200000000000000
χ512-2-22-2-222-2-222-222-22-2-22-2-22222-2-2000000000000000000002-2-22000000-2200000000000000
χ522-2-22-2-222-2-222-222-22-2-22-2-22222-2-200000000000000000000-222-20000002-200000000000000
χ5344444444-444-4-4-4-4-4-44-44000000000000000000000000000000000000000000000000000000
χ5444444444-4-4-444-4-444-4-4-4000000000000000000000000000000000000000000000000000000
χ5544-4-44i−4i4i−4i0000000000002-22-22i−2i2i−2i2ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000022−222i2−2i2000000000000000000000000000000
χ5644-4-44i−4i4i−4i0000000000002-22-22i−2i2i−2i−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ30000−2222−2i22i2000000000000000000000000000000
χ5744-4-44i−4i4i−4i000000000000-22-22−2i2i−2i2i2ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30000−2222−2i22i2000000000000000000000000000000
χ5844-4-44i−4i4i−4i000000000000-22-22−2i2i−2i2i−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000022−222i2−2i2000000000000000000000000000000
χ5944-4-4−4i4i−4i4i0000000000002-22-2−2i2i−2i2i2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ0000−22222i2−2i2000000000000000000000000000000
χ6044-4-4−4i4i−4i4i0000000000002-22-2−2i2i−2i2i−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000022−22−2i22i2000000000000000000000000000000
χ6144-4-4−4i4i−4i4i000000000000-22-222i−2i2i−2i2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000022−22−2i22i2000000000000000000000000000000
χ6244-4-4−4i4i−4i4i000000000000-22-222i−2i2i−2i−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ0000−22222i2−2i2000000000000000000000000000000
χ634-44-44i−4i−4i4i0000000000002-2-222i−2i−2i2i2ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ322−222i2−2i20000000000000000000000000000000000
χ644-44-44i−4i−4i4i0000000000002-2-222i−2i−2i2i−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ3−2222−2i22i20000000000000000000000000000000000
χ654-44-44i−4i−4i4i000000000000-222-2−2i2i2i−2i2ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ3−2222−2i22i20000000000000000000000000000000000
χ664-44-44i−4i−4i4i000000000000-222-2−2i2i2i−2i−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ322−222i2−2i20000000000000000000000000000000000
χ674-44-4−4i4i4i−4i0000000000002-2-22−2i2i2i−2i2ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ−22222i2−2i20000000000000000000000000000000000
χ684-44-4−4i4i4i−4i0000000000002-2-22−2i2i2i−2i−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ22−22−2i22i20000000000000000000000000000000000
χ694-44-4−4i4i4i−4i000000000000-222-22i−2i−2i2i2ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ22−22−2i22i20000000000000000000000000000000000
χ704-44-4−4i4i4i−4i000000000000-222-22i−2i−2i2i−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ−22222i2−2i20000000000000000000000000000000000
χ714-4-4444-4-44-44-44-44-444-4-4000000000000000000000000000000000000000000000000000000
χ724-4-4444-4-4-4-444-44-44-444-4000000000000000000000000000000000000000000000000000000
χ734-4-44-4-4444-44-44-4-44-4-444000000000000000000000000000000000000000000000000000000
χ744-4-44-4-444-44-4-44444-44-4-4000000000000000000000000000000000000000000000000000000

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