Finite Group Databasebeta

← Group #311382

Character table — Group #311382

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444444444448888888844444444448888888888888888444444888844
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
χ51111111111111111111111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-111-111-1-11-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111-1-1-111-11
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-111-11
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-111-1-1111-1-11-1
χ91111111111111111-1-1-1-1111111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11-1-1-1-11-1-1-1-111
χ101111111111111111-1-1-1-1111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-1-1-111111-1-1
χ111111111111111111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-11111-11111-1-1
χ121111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-11111-1-1-1-1-111
χ131111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111111-1-1-1-1-1111-1
χ141111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1111-1-1-111-1-1-11
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-111111-1-1-11
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1111-1-1111-1
χ17222222222-22-2-222-22222-2-20000000000-2-20022-2-2-2-222000000000000000000000000
χ18222222222-22-2-222-22222-2-20000000000-2-200-2-22222-2-2000000000000000000000000
χ19222222222-22-2-222-2-2-2-2-2-2-20000000000220022-2-222-2-2000000000000000000000000
χ20222222222-22-2-222-2-2-2-2-2-2-200000000002200-2-222-2-222000000000000000000000000
χ2122222222-22-222-2-220000-2-22222-2-2-2-222002200000000000000000000-20000-2000000
χ2222222222-22-222-2-220000-2-22222-2-2-2-2-2-200-2-200000000000000000000200002000000
χ2322222222-22-222-2-220000-2-2-2-2-2-222222200-2-200000000000000000000-200002000000
χ2422222222-22-222-2-220000-2-2-2-2-2-22222-2-200220000000000000000000020000-2000000
χ2522-2-222-2-2-20-20022022-2-20022−2−222−2−2000000002i−2i2i−2i0022−2−2i2i2−i2−i2i2i2−i2−i2000000000000
χ2622-2-222-2-2-20-20022022-2-20022−2−222−2−200000000−2i2i−2i2i0022−2−2−i2−i2i2i2−i2−i2i2i2000000000000
χ2722-2-222-2-2-20-20022022-2-200−2−222−2−222000000002i−2i2i−2i00−2−222−i2−i2i2i2−i2−i2i2i2000000000000
χ2822-2-222-2-2-20-20022022-2-200−2−222−2−22200000000−2i2i−2i2i00−2−222i2i2−i2−i2i2i2−i2−i2000000000000
χ2922-2-222-2-2-20-200220-2-2220022−2−222−2−2000000002i−2i−2i2i00−2−222i2i2−i2−i2−i2−i2i2i2000000000000
χ3022-2-222-2-2-20-200220-2-2220022−2−222−2−200000000−2i2i2i−2i00−2−222−i2−i2i2i2i2i2−i2−i2000000000000
χ3122-2-222-2-2-20-200220-2-22200−2−222−2−222000000002i−2i−2i2i0022−2−2−i2−i2i2i2i2i2−i2−i2000000000000
χ3222-2-222-2-2-20-200220-2-22200−2−222−2−22200000000−2i2i2i−2i0022−2−2i2i2−i2−i2−i2−i2i2i2000000000000
χ332-22-22-22-222-2-2-22-220000-222i−2i2i−2i2i−2i2i−2i0000000000000000000000000002-22i−2i0000000
χ342-22-22-22-222-2-2-22-220000-222i−2i2i−2i2i−2i2i−2i000000000000000000000000000-22−2i2i0000000
χ352-22-22-22-222-2-2-22-220000-22−2i2i−2i2i−2i2i−2i2i0000000000000000000000000002-2−2i2i0000000
χ362-22-22-22-222-2-2-22-220000-22−2i2i−2i2i−2i2i−2i2i000000000000000000000000000-222i−2i0000000
χ372-22-22-22-2-222-2-2-2222i−2i2i−2i2-22i−2i2i−2i−2i2i−2i2i002i−2i00000000002-22-200000000000000000000
χ382-22-22-22-2-222-2-2-2222i−2i2i−2i2-2−2i2i−2i2i2i−2i2i−2i002i−2i0000000000-22-2200000000000000000000
χ392-22-22-22-2-222-2-2-222−2i2i−2i2i2-22i−2i2i−2i−2i2i−2i2i00−2i2i0000000000-22-2200000000000000000000
χ402-22-22-22-2-222-2-2-222−2i2i−2i2i2-2−2i2i−2i2i2i−2i2i−2i00−2i2i00000000002-22-200000000000000000000
χ412-22-22-22-2-2-2222-22-22i−2i2i−2i-220000000000−2i2i000000000000002i−2i2i−2i2-22-2000000000000
χ422-22-22-22-2-2-2222-22-22i−2i2i−2i-220000000000−2i2i00000000000000−2i2i−2i2i-22-22000000000000
χ432-22-22-22-2-2-2222-22-2−2i2i−2i2i-2200000000002i−2i000000000000002i−2i2i−2i-22-22000000000000
χ442-22-22-22-2-2-2222-22-2−2i2i−2i2i-2200000000002i−2i00000000000000−2i2i−2i2i2-22-2000000000000
χ452-2-222-2-2220-200-2202i−2i−2i2i00i2−i2−i2i2−i2i2i2−i20000002i−2i00002-22−2−222−2−22−i2i2i2−i2000000000000
χ462-2-222-2-2220-200-2202i−2i−2i2i00i2−i2−i2i2−i2i2i2−i2000000−2i2i0000-222−2−22−222−2i2−i2−i2i2000000000000
χ472-2-222-2-2220-200-2202i−2i−2i2i00−i2i2i2−i2i2−i2−i2i20000002i−2i00002-2−222−2−222−2i2−i2−i2i2000000000000
χ482-2-222-2-2220-200-2202i−2i−2i2i00−i2i2i2−i2i2−i2−i2i2000000−2i2i0000-22−222−22−2−22−i2i2i2−i2000000000000
χ492-2-222-2-2220-200-220−2i2i2i−2i00i2−i2−i2i2−i2i2i2−i20000002i−2i0000-22−222−22−2−22i2−i2−i2i2000000000000
χ502-2-222-2-2220-200-220−2i2i2i−2i00i2−i2−i2i2−i2i2i2−i2000000−2i2i00002-2−222−2−222−2−i2i2i2−i2000000000000
χ512-2-222-2-2220-200-220−2i2i2i−2i00−i2i2i2−i2i2−i2−i2i20000002i−2i0000-222−2−22−222−2−i2i2i2−i2000000000000
χ522-2-222-2-2220-200-220−2i2i2i−2i00−i2i2i2−i2i2−i2−i2i2000000−2i2i00002-22−2−222−2−22i2−i2−i2i2000000000000
χ5344444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000000
χ5444-44-4-44-40404-400-40000000000000000004-400000000000000000000000000000000
χ5544-44-4-44-40404-400-4000000000000000000-4400000000000000000000000000000000
χ5644-44-4-44-40-40-440040000000000000000000000000000000000000000000000002i2−2i200
χ5744-44-4-44-40-40-44004000000000000000000000000000000000000000000000000−2i22i200
χ5844-4-444-4-440400-4-400000002222−22−22−22−22222200000000000000000000000000000000000000
χ5944-4-444-4-440400-4-40000000−22−2222222222−22−2200000000000000000000000000000000000000
χ604-44-44-44-44-4-4444-4-400004-40000000000000000000000000000000000000000000000
χ614-4-444-4-44-404004-400000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000
χ624-4-444-4-44-404004-40000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000
χ634-4-4-4-4444040-4400-4000000000000004i−4i000000000000000000000000000000000000
χ644-4-4-4-4444040-4400-400000000000000−4i4i000000000000000000000000000000000000
χ654-4-4-4-44440-404-4004000000000000000000000000000000000000000000000022−220000
χ664-4-4-4-44440-404-40040000000000000000000000000000000000000000000000−22220000
χ67888-8-8-8-88000000000000000000000000000000000000000000000000000000000000
χ688-888-88-8-8000000000000000000000000000000000000000000000000000000000000

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