Finite Group Databasebeta

← Group #263609

Character table — Group #263609

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111222222222222444444444444488888888888888888888881616161616161616161616163232
order12222244444488884444444888888244444888888888888888822444444444488
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ4111111111111111111111111111111-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111-1-11-1-11111111-111-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111
χ611111111111111111-1-11-1-11111111-111-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1
χ711111111111111111-1-11-1-11111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ811111111111111111-1-11-1-11111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111
χ9111111111111-1-1-1-11111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-111-1-11-1
χ10111111111111-1-1-1-11111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-111-11
χ11111111111111-1-1-1-11111111-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-1-1-1111111111-11-111-1-1-1-111-11
χ12111111111111-1-1-1-11111111-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-1-1-111111111-11-11-1-11111-1-11-1
χ13111111111111-1-1-1-11-1-11-1-11-1-1-1-1-1-1-111-111-1-1-1-11111-1-1-1-111111-11-1-1-111-1-1111-1
χ14111111111111-1-1-1-11-1-11-1-11-1-1-1-1-1-1-111-111-1-1-1-11111-1-1-1-11111-11-1111-1-111-1-1-11
χ15111111111111-1-1-1-11-1-11-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11-11-1-1-11111-1-1-11
χ16111111111111-1-1-1-11-1-11-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-11-1111-1-1-1-1111-1
χ17222222222-22-20000-222-222-2000000-222-2-2-222-2-200000000000000000000000000
χ18222222222-22-20000-222-222-2000000-2-2-2-222-2-22200000000000000000000000000
χ19222222222-22-20000-2-2-2-2-2-2-20000002222-2-2-2-22200000000000000000000000000
χ20222222222-22-20000-2-2-2-2-2-2-20000002-2-222222-2-200000000000000000000000000
χ21222222-2-2-22-222222-200200-222-2-2-2-2000000000000000000000000002-22-2000000
χ22222222-2-2-22-222222-200200-222-2-2-2-200000000000000000000000000-22-22000000
χ23222222-2-2-22-22-2-2-2-2-200200-2-2-22222000000000000000000000000002-2-22000000
χ24222222-2-2-22-22-2-2-2-2-200200-2-2-2222200000000000000000000000000-222-2000000
χ252222-2-22-2-22222222200-200-2-2-222-2-2000000000000000000000022-2-20000000000
χ262222-2-22-2-22222222200-200-2-2-222-2-20000000000000000000000-2-2220000000000
χ272222-2-22-2-2222-2-2-2-2200-200-222-2-22200000000000000000000002-2-220000000000
χ282222-2-22-2-2222-2-2-2-2200-200-222-2-2220000000000000000000000-222-20000000000
χ292222-2-2-2222-222222-222-2-2-22-2-2-2-222-2002000000-2-2220000000000000000000000
χ302222-2-2-2222-222222-2-2-2-2222-2-2-2-222200-200000022-2-20000000000000000000000
χ312222-2-2-2222-22-2-2-2-2-222-2-2-222222-2-2-200200000022-2-20000000000000000000000
χ322222-2-2-2222-22-2-2-2-2-2-2-2-22222222-2-2200-2000000-2-2220000000000000000000000
χ332222-2-2-222-2-2-200002222-2-2-2000000200-200000000002i2i−2i−2i2i2i−2i−2i00000000000000
χ342222-2-2-222-2-2-200002222-2-2-2000000200-20000000000−2i−2i2i2i−2i−2i2i2i00000000000000
χ352222-2-2-222-2-2-200002-2-2222-2000000-200200000000002i2i−2i−2i−2i−2i2i2i00000000000000
χ362222-2-2-222-2-2-200002-2-2222-2000000-20020000000000−2i−2i2i2i2i2i−2i−2i00000000000000
χ372-22-22-2-22-202022−2−202i−2i02i−2i02−22−22−200002-2002i−2ii2−i2i2−i22−22−2i2−i2i2−i200000000000000
χ382-22-22-2-22-202022−2−202i−2i02i−2i02−22−22−20000-2200−2i2ii2−i2i2−i2−22−22−i2i2−i2i200000000000000
χ392-22-22-2-22-202022−2−20−2i2i0−2i2i02−22−22−200002-200−2i2i−i2i2−i2i22−22−2−i2i2−i2i200000000000000
χ402-22-22-2-22-202022−2−20−2i2i0−2i2i02−22−22−20000-22002i−2i−i2i2−i2i2−22−22i2−i2i2−i200000000000000
χ412-22-22-2-22-2020−2−22202i−2i02i−2i0−22−22−2200002-2002i−2i−i2i2−i2i2−22−22−i2i2−i2i200000000000000
χ422-22-22-2-22-2020−2−22202i−2i02i−2i0−22−22−220000-2200−2i2i−i2i2−i2i22−22−2i2−i2i2−i200000000000000
χ432-22-22-2-22-2020−2−2220−2i2i0−2i2i0−22−22−2200002-200−2i2ii2−i2i2−i2−22−22i2−i2i2−i200000000000000
χ442-22-22-2-22-2020−2−2220−2i2i0−2i2i0−22−22−220000-22002i−2ii2−i2i2−i22−22−2−i2i2−i2i200000000000000
χ452-22-2-2222-20-2022−2−202i−2i0−2i2i0−22−222−202i−2i0002-200−i2i2i2−i2i2−i2−i2i2−222−200000000000000
χ462-22-2-2222-20-2022−2−202i−2i0−2i2i0−22−222−20−2i2i000-2200−i2i2i2−i2−i2i2i2−i22−2−2200000000000000
χ472-22-2-2222-20-2022−2−20−2i2i02i−2i0−22−222−202i−2i000-2200i2−i2−i2i2i2−i2−i2i22−2−2200000000000000
χ482-22-2-2222-20-2022−2−20−2i2i02i−2i0−22−222−20−2i2i0002-200i2−i2−i2i2−i2i2i2−i2−222−200000000000000
χ492-22-2-2222-20-20−2−22202i−2i0−2i2i02−22−2−2202i−2i0002-200i2−i2−i2i2−i2i2i2−i22−2−2200000000000000
χ502-22-2-2222-20-20−2−22202i−2i0−2i2i02−22−2−220−2i2i000-2200i2−i2−i2i2i2−i2−i2i2−222−200000000000000
χ512-22-2-2222-20-20−2−2220−2i2i02i−2i02−22−2−2202i−2i000-2200−i2i2i2−i2−i2i2i2−i2−222−200000000000000
χ522-22-2-2222-20-20−2−2220−2i2i02i−2i02−22−2−220−2i2i0002-200−i2i2i2−i2i2−i2−i2i22−2−2200000000000000
χ53444444-4-4-4-4-4-40000400-4004000000000000000000000000000000000000000000
χ544444-4-44-4-4-44-40000-4004004000000000000000000000000000000000000000000
χ554-44-44-44-440-402222−22−22000000022−22−2222−2222000000000000000000000000000000000000
χ564-44-44-44-440-40−22−2222220000000−222222−2222−22000000000000000000000000000000000000
χ574-44-4-44-4-440402222−22−220000000−222222−22−2222000000000000000000000000000000000000
χ584-44-4-44-4-44040−22−222222000000022−22−222222−22000000000000000000000000000000000000
χ594-4-440000040-44-44-400000000000000000000000000000000000000000002i−2i2i−2i00
χ604-4-440000040-44-44-40000000000000000000000000000000000000000000−2i2i−2i2i00
χ614-4-440000040-4-44-4400000000000000000000000000000000000000000002i−2i−2i2i00
χ624-4-440000040-4-44-440000000000000000000000000000000000000000000−2i2i2i−2i00
χ6388-8-80000000042−42−42420000000000000000000000000000000000000000000000000
χ6488-8-800000000−424242−420000000000000000000000000000000000000000000000000
χ658-8-8800000-80800000000000000000000000000000000000000000000000000000

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