Finite Group Databasebeta

← Group #350171

Character table — Group #350171

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444448888888888888888888888888888816161616161616163232
order12222222444444442244444444444444444444444444444444444888888888888888824
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111-1-1-1-1-1-1-1-111-1-11-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-1-1-1-1-111-1-11-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1
χ91111111111111111-1-1-1-1-1-11111-1-1-1-11111-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11-1
χ101111111111111111-1-1-1-1-1-11111-1-1-1-11111-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-11
χ111111111111111111-1-1-1-1-1-11111-1-1-1-111-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-111-11
χ121111111111111111-1-1-1-1-1-11111-1-1-1-111-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-11111-1-11-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-11
χ141111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1111-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-1111-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-11
χ172222222222-2-222-2-222-2-22200000000-2-222-20000-2-222-2-200000000000000000000000000
χ182222222222-2-222-2-222-2-22200000000-2-2-2-2-2000022-2-22200000000000000000000000000
χ192222222222-2-222-2-2-2-222-2-200000000-2-22220000-2-2-2-22200000000000000000000000000
χ202222222222-2-222-2-2-2-222-2-200000000-2-2-2-2200002222-2-200000000000000000000000000
χ2122222222-2-222-2-22222-2-2-2-22222-2-2-2-2-2-2002-2-22200000000000000000000000000000000
χ2222222222-2-222-2-22222-2-2-2-2-2-2-2-22222-2-200222-2-200000000000000000000000000000000
χ2322222222-2-222-2-222-2-2222222222222-2-200-2-2-2-2-200000000000000000000000000000000
χ2422222222-2-222-2-222-2-22222-2-2-2-2-2-2-2-2-2-200-2222200000000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-2000000002200-2000000000022-2-222-2-2000000000000000000
χ2622222222-2-2-2-2-2-2-2-22222-2-2000000002200-20000000000-2-222-2-222000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2220000000022002000000000022-2-2-2-222000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22200000000220020000000000-2-22222-2-2000000000000000000
χ2922-222-2-2-2002-2002-2002i−2i2i−2i22-2-22i2i−2i−2i0000000000000000000000022−2−2i2i2−i2−i22−2i2−i2000000
χ3022-222-2-2-2002-2002-2002i−2i2i−2i22-2-22i2i−2i−2i00000000000000000000000−2−222−i2−i2i2i2−22−i2i2000000
χ3122-222-2-2-2002-2002-2002i−2i2i−2i-2-222−2i−2i2i2i0000000000000000000000022−2−2i2i2−i2−i2−22−i2i2000000
χ3222-222-2-2-2002-2002-2002i−2i2i−2i-2-222−2i−2i2i2i00000000000000000000000−2−222−i2−i2i2i22−2i2−i2000000
χ3322-222-2-2-2002-2002-200−2i2i−2i2i22-2-2−2i−2i2i2i0000000000000000000000022−2−2−i2−i2i2i22−2−i2i2000000
χ3422-222-2-2-2002-2002-200−2i2i−2i2i22-2-2−2i−2i2i2i00000000000000000000000−2−222i2i2−i2−i2−22i2−i2000000
χ3522-222-2-2-2002-2002-200−2i2i−2i2i-2-2222i2i−2i−2i0000000000000000000000022−2−2−i2−i2i2i2−22i2−i2000000
χ3622-222-2-2-2002-2002-200−2i2i−2i2i-2-2222i2i−2i−2i00000000000000000000000−2−222i2i2−i2−i22−2−i2i2000000
χ372-222-22-2-22-22-22-2-220000002i−2i2i−2i00002-20002i−2i00002i−2i2i−2i00002-22-2000000000000000000
χ382-222-22-2-22-22-22-2-220000002i−2i2i−2i00002-20002i−2i0000−2i2i−2i2i0000-22-22000000000000000000
χ392-222-22-2-22-22-22-2-22000000−2i2i−2i2i00002-2000−2i2i00002i−2i2i−2i0000-22-22000000000000000000
χ402-222-22-2-22-22-22-2-22000000−2i2i−2i2i00002-2000−2i2i0000−2i2i−2i2i00002-22-2000000000000000000
χ412-222-22-2-22-2-222-22-200000000002i−2i2i−2i-22000002i−2i002i−2i−2i2i2-22-20000000000000000000000
χ422-222-22-2-22-2-222-22-200000000002i−2i2i−2i-22000002i−2i00−2i2i2i−2i-22-220000000000000000000000
χ432-222-22-2-22-2-222-22-20000000000−2i2i−2i2i-2200000−2i2i002i−2i−2i2i-22-220000000000000000000000
χ442-222-22-2-22-2-222-22-20000000000−2i2i−2i2i-2200000−2i2i00−2i2i2i−2i2-22-20000000000000000000000
χ452-222-22-2-2-222-2-22-220000002i−2i2i−2i0000-222i−2i0−2i2i002i−2i00002-2-220000000000000000000000
χ462-222-22-2-2-222-2-22-220000002i−2i2i−2i0000-22−2i2i0−2i2i00−2i2i0000-222-20000000000000000000000
χ472-222-22-2-2-222-2-22-22000000−2i2i−2i2i0000-222i−2i02i−2i002i−2i0000-222-20000000000000000000000
χ482-222-22-2-2-222-2-22-22000000−2i2i−2i2i0000-22−2i2i02i−2i00−2i2i00002-2-220000000000000000000000
χ492-222-22-2-2-22-22-222-200000000002i−2i2i−2i2-22i−2i000−2i2i−2i2i00000000-222-2000000000000000000
χ502-222-22-2-2-22-22-222-200000000002i−2i2i−2i2-2−2i2i000−2i2i2i−2i000000002-2-22000000000000000000
χ512-222-22-2-2-22-22-222-20000000000−2i2i−2i2i2-22i−2i0002i−2i−2i2i000000002-2-22000000000000000000
χ522-222-22-2-2-22-22-222-20000000000−2i2i−2i2i2-2−2i2i0002i−2i2i−2i00000000-222-2000000000000000000
χ5344-444-4-4-400-4400-44004i−4i−4i4i0000000000000000000000000000000000000000000000000
χ5444-444-4-4-400-4400-4400−4i4i4i−4i0000000000000000000000000000000000000000000000000
χ5544-4-4-444-44-400-44000000000000000000000000000000000000000000000000000002i2−2i200
χ5644-4-4-444-44-400-4400000000000000000000000000000000000000000000000000000−2i22i200
χ5744-4-4-444-4-44004-40000000000000000000000000000000000000000000000000002i2−2i20000
χ5844-4-4-444-4-44004-4000000000000000000000000000000000000000000000000000−2i22i20000
χ594-44-44-44-4000000004-4000000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i0000000000
χ604-44-44-44-4000000004-400000000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000
χ614-44-44-44-400000000-44000000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i0000000000
χ624-44-44-44-400000000-4400000000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000
χ634-4-44-4-444004400-4-40000004i−4i−4i4i000000000000000000000000000000000000000000000
χ644-4-44-4-444004400-4-4000000−4i4i4i−4i000000000000000000000000000000000000000000000
χ654-4-44-4-44400-4-4004400000000004-4-4400000000000000000000000000000000000000000
χ664-4-44-4-44400-4-400440000000000-444-400000000000000000000000000000000000000000
χ674-4-4-444-444400-4-40000000000000000000000000000000000000002i2−2i2−2i22i200000000000000
χ684-4-4-444-444400-4-4000000000000000000000000000000000000000−2i22i22i2−2i200000000000000
χ694-4-4-444-44-4-40044000000000000000000000000000000000000000000022−22−22220000000000
χ704-4-4-444-44-4-400440000000000000000000000000000000000000000000−222222−220000000000
χ71888-8-8-8-88000000000000000000000000000000000000000000000000000000000000000

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