Finite Group Databasebeta

← Group #267697

Character table — Group #267697

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222222222222244444444444444444488888888888888884444444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111
χ5111111111111111111-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11-1111-111-1-1-1-1
χ6111111111111111111-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-11-1-1-11-1-11111
χ7111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11-1-1-11-1-1-11111
χ8111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1111-1111-1-1-1-1
χ91111111111-1-1-1-111-1-1111111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11-11-11111-1-1-1-111-1-1
χ101111111111-1-1-1-111-1-1111111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-11-11-1-1-1-11111-1-111
χ111111111111-1-1-1-111-1-1111111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-111111-11-111-1-1-1-111-1-111
χ121111111111-1-1-1-111-1-1111111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-11-11-1-11111-1-111-1-1
χ131111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-111111-1-111-111-11-1-1-1-111
χ141111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-11111-111-1-11-1-11-11111-1-1
χ151111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-11-1-111-1-1-1-111111-1-1
χ161111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1-111-1-11111-1-1-1-1-111
χ172222222222222222222222-2-2-2-2-2-2-2-222-2-2-2-200000000000000000000000000000000
χ18222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ192222222222-2-2-2-222-2-22222-2-22222-2-2-2-2-2-22200000000000000000000000000000000
χ202222222222-2-2-2-222-2-2-2-2-2-2-2-22222-2-22222-2-200000000000000000000000000000000
χ2122222222-2-22222-2-2-2-200002-222-2-22-200000000000000000000002200-2000-20000000
χ2222222222-2-22222-2-2-2-200002-222-2-22-20000000000000000000000-2-200200020000000
χ2322222222-2-22222-2-2-2-20000-22-2-222-22000000000000000000000000220-2000-2000000
χ2422222222-2-22222-2-2-2-20000-22-2-222-22000000000000000000000000-2-2020002000000
χ2522222222-2-2-2-2-2-2-2-22200002-2-2-2222-200000000000000000000002-200-200020000000
χ2622222222-2-2-2-2-2-2-2-22200002-2-2-2222-20000000000000000000000-22002000-20000000
χ2722222222-2-2-2-2-2-2-2-2220000-2222-2-2-220000000000000000000000002-20-20002000000
χ2822222222-2-2-2-2-2-2-2-2220000-2222-2-2-22000000000000000000000000-2202000-2000000
χ292222-2-2-2-22222-2-2-2-22-222-2-2000000002-2000022−2−222−2−222−2−222−2−20000000000000000
χ302222-2-2-2-22222-2-2-2-22-222-2-2000000002-20000−2−222−2−222−2−222−2−2220000000000000000
χ312222-2-2-2-22222-2-2-2-22-2-2-22200000000-22000022−2−222−2−2−2−222−2−2220000000000000000
χ322222-2-2-2-22222-2-2-2-22-2-2-22200000000-220000−2−222−2−22222−2−222−2−20000000000000000
χ332222-2-2-2-222-2-222-2-2-2222-2-200000000-22000022−2−2−2−22222−2−2−2−2220000000000000000
χ342222-2-2-2-222-2-222-2-2-2222-2-200000000-220000−2−22222−2−2−2−22222−2−20000000000000000
χ352222-2-2-2-222-2-222-2-2-22-2-222000000002-2000022−2−2−2−222−2−22222−2−20000000000000000
χ362222-2-2-2-222-2-222-2-2-22-2-222000000002-20000−2−22222−2−222−2−2−2−2220000000000000000
χ372-2-222-22-22-200002-2002-22-2002i−2i2i−2i0000002i−2i2−22−2i2−i2i2−i22−22−2i2−i2i2−i20000000000000000
χ382-2-222-22-22-200002-2002-22-2002i−2i2i−2i0000002i−2i−22−22−i2i2−i2i2−22−22−i2i2−i2i20000000000000000
χ392-2-222-22-22-200002-2002-22-200−2i2i−2i2i000000−2i2i2−22−2−i2i2−i2i22−22−2−i2i2−i2i20000000000000000
χ402-2-222-22-22-200002-2002-22-200−2i2i−2i2i000000−2i2i−22−22i2−i2i2−i2−22−22i2−i2i2−i20000000000000000
χ412-2-222-22-22-200002-200-22-22002i−2i2i−2i000000−2i2i2−22−2i2−i2i2−i2−22−22−i2i2−i2i20000000000000000
χ422-2-222-22-22-200002-200-22-22002i−2i2i−2i000000−2i2i−22−22−i2i2−i2i22−22−2i2−i2i2−i20000000000000000
χ432-2-222-22-22-200002-200-22-2200−2i2i−2i2i0000002i−2i2−22−2−i2i2−i2i2−22−22i2−i2i2−i20000000000000000
χ442-2-222-22-22-200002-200-22-2200−2i2i−2i2i0000002i−2i−22−22i2−i2i2−i22−22−2−i2i2−i2i20000000000000000
χ452-2-22-22-222-20000-22002-2-22220000-2-2002-20000002i−2i−2i2i00002i−2i−2i2i0000000000000000
χ462-2-22-22-222-20000-22002-2-22220000-2-2002-2000000−2i2i2i−2i0000−2i2i2i−2i0000000000000000
χ472-2-22-22-222-20000-22002-2-22-2-200002200-22002-2-2200002-2-2200000000000000000000
χ482-2-22-22-222-20000-22002-2-22-2-200002200-2200-222-20000-222-200000000000000000000
χ492-2-22-22-222-20000-2200-222-2220000-2-200-220000002i−2i−2i2i0000−2i2i2i−2i0000000000000000
χ502-2-22-22-222-20000-2200-222-2220000-2-200-22000000−2i2i2i−2i00002i−2i−2i2i0000000000000000
χ512-2-22-22-222-20000-2200-222-2-2-2000022002-2002-2-220000-222-200000000000000000000
χ522-2-22-22-222-20000-2200-222-2-2-2000022002-200-222-200002-2-2200000000000000000000
χ534444-4-4-4-4-4-444-4-444-4400000000000000000000000000000000000000000000000000
χ544444-4-4-4-4-4-4-4-444444-400000000000000000000000000000000000000000000000000
χ5544-4-444-4-4004-44-4000000000000000000000000000000000000000000000000002-22-2
χ5644-4-444-4-4004-44-400000000000000000000000000000000000000000000000000-22-22
χ5744-4-444-4-400-44-44000000000000000000000000000000000000000000000000002-2-22
χ5844-4-444-4-400-44-4400000000000000000000000000000000000000000000000000-222-2
χ5944-4-4-4-444004-4-44000000000000000000000000000000000000000000002-2002-20000
χ6044-4-4-4-444004-4-4400000000000000000000000000000000000000000000-2200-220000
χ6144-4-4-4-44400-444-4000000000000000000000000000000000000000000002-200-220000
χ6244-4-4-4-44400-444-400000000000000000000000000000000000000000000-22002-20000
χ634-4-444-44-4-440000-44000000004i−4i−4i4i0000000000000000000000000000000000000000
χ644-4-444-44-4-440000-4400000000−4i4i4i−4i0000000000000000000000000000000000000000
χ654-4-44-44-44-4400004-40000004-40000-4400000000000000000000000000000000000000
χ664-4-44-44-44-4400004-4000000-4400004-400000000000000000000000000000000000000
χ678-88-88-8-88000000000000000000000000000000000000000000000000000000000000
χ688-88-8-888-8000000000000000000000000000000000000000000000000000000000000

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