Finite Group Databasebeta

← Group #267709

Character table — Group #267709

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222222244442222444444444422444488888888888888884444444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111
χ51111111111111111-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-11111-1-111-1-1-1-1
χ61111111111111111-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-1-1-111-1-11111
χ71111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-1-1-111-1-1-1-11111
χ81111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1111-1-11111-1-1-1-1
χ9111111111111-1-1-1-11111-1-1-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111-1-1
χ10111111111111-1-1-1-11111-1-1-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-111
χ11111111111111-1-1-1-11111-1-1-1-111-1-111-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-111
χ12111111111111-1-1-1-11111-1-1-1-111-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1111111-1-1-1-1-1-1-1-111111-11-111-1-111-1-1-1-111
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1111111-1-1-1-1-1-1-1-11111-11-11-1-111-1-11111-1-1
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-1-111111111-1-1-1-11-11-1-1-1-1-1111111-1-1
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-1-111111111-1-1-1-1-11-111111-1-1-1-1-1-111
χ1722222222222222222222-2-2-2-2-2-222-2-2-2-2-2-22200000000000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-2-2-222-2-22222-2-200000000000000000000000000000000
χ19222222222222-2-2-2-222222222-2-2-2-2-2-222-2-2-2-200000000000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ2122222222-2-2-2-22222000022-2-22-2-2-22-2000000000000000000000020-20002-200000000
χ2222222222-2-2-2-22222000022-2-22-2-2-22-20000000000000000000000-202000-2200000000
χ2322222222-2-2-2-222220000-2-222-22-2-2-220000000000000000000000020-200002-2000000
χ2422222222-2-2-2-222220000-2-222-22-2-2-2200000000000000000000000-2020000-22000000
χ2522222222-2-2-2-2-2-2-2-2000022-2-2-2222-220000000000000000000000020-20000-22000000
χ2622222222-2-2-2-2-2-2-2-2000022-2-2-2222-2200000000000000000000000-20200002-2000000
χ2722222222-2-2-2-2-2-2-2-20000-2-2222-2222-2000000000000000000000020-2000-2200000000
χ2822222222-2-2-2-2-2-2-2-20000-2-2222-2222-20000000000000000000000-2020002-200000000
χ292222-2-2-2-222-2-2000022-2-22-22-20000002-2000022−2−222−2−222−2−222−2−20000000000000000
χ302222-2-2-2-222-2-2000022-2-22-22-20000002-20000−2−222−2−222−2−222−2−2220000000000000000
χ312222-2-2-2-222-2-2000022-2-2-22-22000000-22000022−2−2−2−22222−2−2−2−2220000000000000000
χ322222-2-2-2-222-2-2000022-2-2-22-22000000-220000−2−22222−2−2−2−22222−2−20000000000000000
χ332222-2-2-2-222-2-20000-2-2222-22-2000000-22000022−2−222−2−2−2−222−2−2220000000000000000
χ342222-2-2-2-222-2-20000-2-2222-22-2000000-220000−2−222−2−22222−2−222−2−20000000000000000
χ352222-2-2-2-222-2-20000-2-222-22-220000002-2000022−2−2−2−222−2−22222−2−20000000000000000
χ362222-2-2-2-222-2-20000-2-222-22-220000002-20000−2−22222−2−222−2−2−2−2220000000000000000
χ372-2-2222-2-22-22-22i2i−2i−2i2-22-20000002i−2i0000002i−2i2−22−2i2−i2i2−i22−22−2i2−i2i2−i20000000000000000
χ382-2-2222-2-22-22-22i2i−2i−2i2-22-20000002i−2i0000002i−2i−22−22−i2i2−i2i2−22−22−i2i2−i2i20000000000000000
χ392-2-2222-2-22-22-22i2i−2i−2i-22-220000002i−2i000000−2i2i2−22−2i2−i2i2−i2−22−22−i2i2−i2i20000000000000000
χ402-2-2222-2-22-22-22i2i−2i−2i-22-220000002i−2i000000−2i2i−22−22−i2i2−i2i22−22−2i2−i2i2−i20000000000000000
χ412-2-2222-2-22-22-2−2i−2i2i2i2-22-2000000−2i2i000000−2i2i2−22−2−i2i2−i2i22−22−2−i2i2−i2i20000000000000000
χ422-2-2222-2-22-22-2−2i−2i2i2i2-22-2000000−2i2i000000−2i2i−22−22i2−i2i2−i2−22−22i2−i2i2−i20000000000000000
χ432-2-2222-2-22-22-2−2i−2i2i2i-22-22000000−2i2i0000002i−2i2−22−2−i2i2−i2i2−22−22i2−i2i2−i20000000000000000
χ442-2-2222-2-22-22-2−2i−2i2i2i-22-22000000−2i2i0000002i−2i−22−22i2−i2i2−i22−22−2−i2i2−i2i20000000000000000
χ452-2-22-2-2222-2-2200002-2-2200002200-2-2002-20000002i−2i−2i2i00002i−2i−2i2i0000000000000000
χ462-2-22-2-2222-2-2200002-2-2200002200-2-2002-2000000−2i2i2i−2i0000−2i2i2i−2i0000000000000000
χ472-2-22-2-2222-2-2200002-2-220000-2-2002200-22002-2-2200002-2-2200000000000000000000
χ482-2-22-2-2222-2-2200002-2-220000-2-2002200-2200-222-20000-222-200000000000000000000
χ492-2-22-2-2222-2-220000-222-200002200-2-200-220000002i−2i−2i2i0000−2i2i2i−2i0000000000000000
χ502-2-22-2-2222-2-220000-222-200002200-2-200-22000000−2i2i2i−2i00002i−2i−2i2i0000000000000000
χ512-2-22-2-2222-2-220000-222-20000-2-20022002-2002-2-220000-222-200000000000000000000
χ522-2-22-2-2222-2-220000-222-20000-2-20022002-200-222-200002-2-2200000000000000000000
χ534444-4-4-4-4-4-444000000004-4-4400000000000000000000000000000000000000000000
χ544444-4-4-4-4-4-44400000000-444-400000000000000000000000000000000000000000000
χ5544-4-44-44-400004-44-40000000000000000000000000000000000000000000000002i−2i2i−2i
χ5644-4-44-44-400004-44-4000000000000000000000000000000000000000000000000−2i2i−2i2i
χ5744-4-44-44-40000-44-440000000000000000000000000000000000000000000000002i−2i−2i2i
χ5844-4-44-44-40000-44-44000000000000000000000000000000000000000000000000−2i2i2i−2i
χ594-44-44-4-4400004i−4i−4i4i00000000000000000000000000000000000000002i−2i00002-20000
χ604-44-44-4-4400004i−4i−4i4i0000000000000000000000000000000000000000−2i2i0000-220000
χ614-44-44-4-440000−4i4i4i−4i00000000000000000000000000000000000000002i−2i0000-220000
χ624-44-44-4-440000−4i4i4i−4i0000000000000000000000000000000000000000−2i2i00002-20000
χ634-4-4444-4-4-44-444i4i−4i−4i0000000000−4i4i0000000000000000000000000000000000000000
χ644-4-4444-4-4-44-44−4i−4i4i4i00000000004i−4i0000000000000000000000000000000000000000
χ654-4-44-4-444-444-40000000000004-400-4400000000000000000000000000000000000000
χ664-4-44-4-444-444-4000000000000-44004-400000000000000000000000000000000000000
χ6788-8-8-88-88000000000000000000000000000000000000000000000000000000000000
χ688-88-8-888-8000000000000000000000000000000000000000000000000000000000000

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