Finite Group Databasebeta

← Group #311342

Character table — Group #311342

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444444444448888888844444444448888888888888888244444888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ3111111111111111111111111111111-1-111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111-1-11-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-111-1-111-11
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-11
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1111-1-111-1-11-1
χ91111111111111111-1-1-1-1111111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111
χ101111111111111111-1-1-1-1111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ111111111111111111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1
χ121111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111
χ131111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111111-111-1-1-1-1111-1
χ141111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-11-111-1-111-1-1-11
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111-11-1-11111-1-1-11
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-11-1-111-1-1111-1
χ17222222222-22-2-222-22222-2-20000000000-2-20022-2-222-2-2000000000000000000000000
χ18222222222-22-2-222-22222-2-20000000000-2-200-2-222-2-222000000000000000000000000
χ19222222222-22-2-222-2-2-2-2-2-2-20000000000220022-2-2-2-222000000000000000000000000
χ20222222222-22-2-222-2-2-2-2-2-2-200000000002200-2-22222-2-2000000000000000000000000
χ2122222222-22-222-2-220000-2-22222-2-2-2-222002200000000000000000000-2-20000000000
χ2222222222-22-222-2-220000-2-22222-2-2-2-2-2-200-2-200000000000000000000220000000000
χ2322222222-22-222-2-220000-2-2-2-2-2-222222200-2-200000000000000000000-220000000000
χ2422222222-22-222-2-220000-2-2-2-2-2-22222-2-20022000000000000000000002-20000000000
χ25222-2-2-2-2220-200-22022-2-200i2i2−i2−i2i2i2−i2−i20000002i−2i002i−2i00i2i2−i2−i222−2−222−2−2000000000000
χ26222-2-2-2-2220-200-22022-2-200i2i2−i2−i2i2i2−i2−i2000000−2i2i00−2i2i00i2i2−i2−i2−2−222−2−222000000000000
χ27222-2-2-2-2220-200-22022-2-200−i2−i2i2i2−i2−i2i2i20000002i−2i002i−2i00−i2−i2i2i2−2−222−2−222000000000000
χ28222-2-2-2-2220-200-22022-2-200−i2−i2i2i2−i2−i2i2i2000000−2i2i00−2i2i00−i2−i2i2i222−2−222−2−2000000000000
χ29222-2-2-2-2220-200-220-2-22200i2i2−i2−i2i2i2−i2−i20000002i−2i00−2i2i00−i2−i2i2i222−2−2−2−222000000000000
χ30222-2-2-2-2220-200-220-2-22200i2i2−i2−i2i2i2−i2−i2000000−2i2i002i−2i00−i2−i2i2i2−2−22222−2−2000000000000
χ31222-2-2-2-2220-200-220-2-22200−i2−i2i2i2−i2−i2i2i20000002i−2i00−2i2i00i2i2−i2−i2−2−22222−2−2000000000000
χ32222-2-2-2-2220-200-220-2-22200−i2−i2i2i2−i2−i2i2i2000000−2i2i002i−2i00i2i2−i2−i222−2−2−2−222000000000000
χ332-2222-2-2-2-20-2002202i−2i2i−2i002−22−22−22−2000000002i−2i002-2i2−i2i2−i2i2−i2i2−i22−22−2000000000000
χ342-2222-2-2-2-20-2002202i−2i2i−2i002−22−22−22−200000000−2i2i00-22i2−i2i2−i2−i2i2−i2i2−22−22000000000000
χ352-2222-2-2-2-20-2002202i−2i2i−2i00−22−22−22−22000000002i−2i002-2−i2i2−i2i2−i2i2−i2i2−22−22000000000000
χ362-2222-2-2-2-20-2002202i−2i2i−2i00−22−22−22−2200000000−2i2i00-22−i2i2−i2i2i2−i2i2−i22−22−2000000000000
χ372-2222-2-2-2-20-200220−2i2i−2i2i002−22−22−22−2000000002i−2i00-22−i2i2−i2i2i2−i2i2−i2−22−22000000000000
χ382-2222-2-2-2-20-200220−2i2i−2i2i002−22−22−22−200000000−2i2i002-2−i2i2−i2i2−i2i2−i2i22−22−2000000000000
χ392-2222-2-2-2-20-200220−2i2i−2i2i00−22−22−22−22000000002i−2i00-22i2−i2i2−i2−i2i2−i2i22−22−2000000000000
χ402-2222-2-2-2-20-200220−2i2i−2i2i00−22−22−22−2200000000−2i2i002-2i2−i2i2−i2i2−i2i2−i2−22−22000000000000
χ412-22-2-222-222-2-2-22-220000-222i−2i−2i2i−2i2i2i−2i00000000000000000000000000002-22i−2i000000
χ422-22-2-222-222-2-2-22-220000-222i−2i−2i2i−2i2i2i−2i0000000000000000000000000000-22−2i2i000000
χ432-22-2-222-222-2-2-22-220000-22−2i2i2i−2i2i−2i−2i2i00000000000000000000000000002-2−2i2i000000
χ442-22-2-222-222-2-2-22-220000-22−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000-222i−2i000000
χ452-22-2-222-2-222-2-2-2222i−2i−2i2i2-22i−2i−2i2i2i−2i−2i2i002i−2i0000000000-222-200000000000000000000
χ462-22-2-222-2-222-2-2-2222i−2i−2i2i2-2−2i2i2i−2i−2i2i2i−2i002i−2i00000000002-2-2200000000000000000000
χ472-22-2-222-2-222-2-2-222−2i2i2i−2i2-22i−2i−2i2i2i−2i−2i2i00−2i2i00000000002-2-2200000000000000000000
χ482-22-2-222-2-222-2-2-222−2i2i2i−2i2-2−2i2i2i−2i−2i2i2i−2i00−2i2i0000000000-222-200000000000000000000
χ492-22-2-222-2-2-2222-22-22i−2i−2i2i-220000000000−2i2i000000000000002i−2i−2i2i2-2-22000000000000
χ502-22-2-222-2-2-2222-22-22i−2i−2i2i-220000000000−2i2i00000000000000−2i2i2i−2i-222-2000000000000
χ512-22-2-222-2-2-2222-22-2−2i2i2i−2i-2200000000002i−2i000000000000002i−2i−2i2i-222-2000000000000
χ522-22-2-222-2-2-2222-22-2−2i2i2i−2i-2200000000002i−2i00000000000000−2i2i2i−2i2-2-22000000000000
χ5344444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000000
χ54444-4-4-4-44-404004-400000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000000000000000
χ55444-4-4-4-44-404004-40000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000000000000000
χ5644-44-44-4-40404-400-40000000000000000004-400000000000000000000000000000000
χ5744-44-44-4-40404-400-4000000000000000000-4400000000000000000000000000000000
χ5844-44-44-4-40-40-440040000000000000000000000000000000000000000000000002i2−2i200
χ5944-44-44-4-40-40-44004000000000000000000000000000000000000000000000000−2i22i200
χ604-4444-4-4-440400-4-4000000022−2222−22−2222−222200000000000000000000000000000000000000
χ614-4444-4-4-440400-4-40000000−2222−222222−2222−2200000000000000000000000000000000000000
χ624-44-4-444-44-4-4444-4-400004-40000000000000000000000000000000000000000000000
χ634-4-4-444-44040-4400-4000000000000004i−4i000000000000000000000000000000000000
χ644-4-4-444-44040-4400-400000000000000−4i4i000000000000000000000000000000000000
χ654-4-4-444-440-404-4004000000000000000000000000000000000000000000000022−220000
χ664-4-4-444-440-404-40040000000000000000000000000000000000000000000000−22220000
χ6788-8-88-88-8000000000000000000000000000000000000000000000000000000000000
χ688-8-88-8-888000000000000000000000000000000000000000000000000000000000000

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