Finite Group Databasebeta

← Group #347671

Character table — Group #347671

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444444444444444444448888888888888888161616161616161632323232
order12222222444444448888888822444444448888888888882222444488888888888888882244
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
χ5111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-111
χ8111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1111111-1-1
χ91111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11-11-1
χ101111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-11-11
χ111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-11-11
χ121111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111-11-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1111111-1-1-1-1111-1-11
χ141111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111-1-11111-1-1-111-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-111-1-1-1-111-111-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1-1-11111-1-11-1-11
χ172222222222-2-2-222-20000000022-2-222-2-2-2-200000000000022-2-2-2-22200000000000000000000
χ182222222222-2-2-222-20000000022-2-222-2-2-2-2000000000000-2-22222-2-200000000000000000000
χ192222222222-2-2-222-200000000-2-2-2-2-2-222220000000000002222-2-2-2-200000000000000000000
χ202222222222-2-2-222-200000000-2-2-2-2-2-22222000000000000-2-2-2-2222200000000000000000000
χ2122222222-2-2222-2-222222222222-2-2-2-2-2-222-2-2-2-2-2-2-2-222220000000000000000000000000000
χ2222222222-2-2222-2-2222222222-2-2-2-22222-2-2-2-2-2-22222-2-2-2-20000000000000000000000000000
χ2322222222-2-2222-2-22-2-2-2-2-2-2-2-222-2-2-2-2-2-22222222222-2-2-2-20000000000000000000000000000
χ2422222222-2-2222-2-22-2-2-2-2-2-2-2-2-2-2-2-22222-2-22222-2-2-2-222220000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-2000000002222-2-222-2-2000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ2622222222-2-2-2-2-2-2-2-2000000002222-2-222-2-200000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ2722222222-2-2-2-2-2-2-2-200000000-2-22222-2-222000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ2822222222-2-2-2-2-2-2-2-200000000-2-22222-2-22200000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ2922-2-2-2-222002-2-20022222-2-2-2-22-20000002-20000000022-2-200000000000000002−22−22−22−20000
χ3022-2-2-2-222002-2-20022222-2-2-2-22-20000002-20000000022-2-20000000000000000−22−22−22−220000
χ3122-2-2-2-222002-2-20022222-2-2-2-2-22000000-2200000000-2-22200000000000000002−22−2−22−220000
χ3222-2-2-2-222002-2-20022222-2-2-2-2-22000000-2200000000-2-2220000000000000000−22−222−22−20000
χ3322-2-2-2-222002-2-2002-2-2-2-222222-20000002-200000000-2-22200000000000000002−2−222−2−220000
χ3422-2-2-2-222002-2-2002-2-2-2-222222-20000002-200000000-2-2220000000000000000−222−2−222−20000
χ3522-2-2-2-222002-2-2002-2-2-2-22222-22000000-220000000022-2-200000000000000002−2−22−222−20000
χ3622-2-2-2-222002-2-2002-2-2-2-22222-22000000-220000000022-2-20000000000000000−222−22−2−220000
χ372-2-2-2222-22-222-22-2-200000000002-200000000002i2i−2i−2i2i−2i2i−2i002-2002-22i−2i2i−2i0000000000000000
χ382-2-2-2222-22-222-22-2-200000000002-200000000002i2i−2i−2i2i−2i2i−2i00-2200-22−2i2i−2i2i0000000000000000
χ392-2-2-2222-22-222-22-2-200000000002-20000000000−2i−2i2i2i−2i2i−2i2i002-2002-2−2i2i−2i2i0000000000000000
χ402-2-2-2222-22-222-22-2-200000000002-20000000000−2i−2i2i2i−2i2i−2i2i00-2200-222i−2i2i−2i0000000000000000
χ412-2-2-2222-22-2-2-222-2222-2-222-2-200-2200000022-2-200000000002-200-2200002-22-2000000000000
χ422-2-2-2222-22-2-2-222-2222-2-222-2-200-2200000022-2-20000000000-22002-20000-22-22000000000000
χ432-2-2-2222-22-2-2-222-22-2-222-2-22200-22000000-2-22200000000002-200-220000-22-22000000000000
χ442-2-2-2222-22-2-2-222-22-2-222-2-22200-22000000-2-2220000000000-22002-200002-22-2000000000000
χ452-2-2-2222-2-2222-2-22-20000000000-2200000000002i2i−2i−2i−2i2i−2i2i2-2002-20000002i−2i−2i2i000000000000
χ462-2-2-2222-2-2222-2-22-20000000000-2200000000002i2i−2i−2i−2i2i−2i2i-2200-22000000−2i2i2i−2i000000000000
χ472-2-2-2222-2-2222-2-22-20000000000-220000000000−2i−2i2i2i2i−2i2i−2i2-2002-2000000−2i2i2i−2i000000000000
χ482-2-2-2222-2-2222-2-22-20000000000-220000000000−2i−2i2i2i2i−2i2i−2i-2200-220000002i−2i−2i2i000000000000
χ492-2-2-2222-2-22-2-22-22222-2-222-2-2002-2000000-2-222000000002-200-22002-2-220000000000000000
χ502-2-2-2222-2-22-2-22-22222-2-222-2-2002-2000000-2-22200000000-22002-200-222-20000000000000000
χ512-2-2-2222-2-22-2-22-222-2-222-2-222002-200000022-2-2000000002-200-2200-222-20000000000000000
χ522-2-2-2222-2-22-2-22-222-2-222-2-222002-200000022-2-200000000-22002-2002-2-220000000000000000
χ53444-44-4-4-40000000022−2222−2222−2222−2200004i−4i000000002i2−2i22i2−2i200000000000000000000000000000000
χ54444-44-4-4-40000000022−2222−2222−2222−220000−4i4i00000000−2i22i2−2i22i200000000000000000000000000000000
χ55444-44-4-4-400000000−2222−2222−2222−222200004i−4i00000000−2i22i2−2i22i200000000000000000000000000000000
χ56444-44-4-4-400000000−2222−2222−2222−22220000−4i4i000000002i2−2i22i2−2i200000000000000000000000000000000
χ5744-44-44-4-444000-4-4022−2222−22−2222−2222000000000022−2222−22000000000000000000000000000000000000
χ5844-44-44-4-444000-4-40−2222−222222−2222−220000000000−2222−2222000000000000000000000000000000000000
χ5944-44-44-4-4-4-400044022−2222−22−2222−22220000000000−2222−2222000000000000000000000000000000000000
χ6044-44-44-4-4-4-4000440−2222−222222−2222−22000000000022−2222−22000000000000000000000000000000000000
χ6144-4-4-4-44400-44400-4000000004-4000000-440000000000000000000000000000000000000000
χ6244-4-4-4-44400-44400-400000000-440000004-40000000000000000000000000000000000000000
χ634-444-4-44-4004-4400-4000000000000000000000000004i−4i−4i4i0000000000000000000000000000
χ644-444-4-44-4004-4400-400000000000000000000000000−4i4i4i−4i0000000000000000000000000000
χ654-444-4-44-400-44-400444-4-4-4-44400000000000000000000000000000000000000000000000000
χ664-444-4-44-400-44-4004-4-44444-4-400000000000000000000000000000000000000000000000000
χ674-44-4-44-444-4000-44022−22−2222−222222−22000000000022−22−2222000000000000000000000000000000000000
χ684-44-4-44-444-4000-440−222222−2222−22−22220000000000−222222−22000000000000000000000000000000000000
χ694-44-4-44-44-440004-4022−22−2222−222222−220000000000−222222−22000000000000000000000000000000000000
χ704-44-4-44-44-440004-40−222222−2222−22−2222000000000022−22−2222000000000000000000000000000000000000
χ714-4-444-4-440000000022−22−222222−22−22220000004-400000022−22−222200000000000000000000000000000000
χ724-4-444-4-440000000022−22−222222−22−2222000000-44000000−222222−2200000000000000000000000000000000
χ734-4-444-4-4400000000−222222−22−222222−220000004-4000000−222222−2200000000000000000000000000000000
χ744-4-444-4-4400000000−222222−22−222222−22000000-4400000022−22−222200000000000000000000000000000000

Here i is the imaginary unit (i² = −1).