Finite Group Databasebeta

← Group #351049

Character table — Group #351049

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444888888888888888888161616161616161632323232
order12222222444444444444448888888888888888444444444488888888888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-11-11-1
χ61111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-11111-11-11
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-11-11
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111-11-1
χ91111111111111111-1-1-1-1111111-1-1-1-111111111-111-1-1-111-1-111-1-1-1-1-1-111-1-111-1-111-1-1
χ101111111111111111-1-1-1-1111111-1-1-1-111111111-111-1-1-111-1-111-1-1-1-1-1-1-1-111-1-111-1-111
χ111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11111-1-1111111-1-111-1-1-1-111
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11111-1-11111-1-111-1-11111-1-1
χ131111111111111111-1-1-1-111-1-1-1-1111111111111-1-1-111-1-1-111-1-111-1-1-1-111-1-1-1-1111-1-11
χ141111111111111111-1-1-1-111-1-1-1-1111111111111-1-1-111-1-1-111-1-111-1-1-1-1-1-11111-1-1-111-1
χ151111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-111-1-1-1-111111111-1-1-1-111-111-1
χ161111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-111-1-1-1-1111111-1-11111-1-11-1-11
χ17222222222-2-222-2-2222-2-2-2-20000000000000000-222222-2-2-2-200000000000000000000
χ18222222222-2-222-2-2222-2-2-2-20000000000000000-2-2-2-2-22222200000000000000000000
χ19222222222-2-222-2-22-2-222-2-20000000000000000222-2-2-2-2-22200000000000000000000
χ20222222222-2-222-2-22-2-222-2-200000000000000002-2-222-222-2-200000000000000000000
χ2122222222-222-2-222-22222-2-22222222200000000-20000-20000-2-2-2-20000000000000000
χ2222222222-222-2-222-22222-2-2-2-2-2-2-2-2-2-200000000-20000-2000022220000000000000000
χ2322222222-222-2-222-2-2-2-2-2-2-22222-2-2-2-2000000002000020000-2-2220000000000000000
χ2422222222-222-2-222-2-2-2-2-2-2-2-2-2-2-2222200000000200002000022-2-20000000000000000
χ2522222222-2-2-2-2-2-2-2-222-2-222000000002i2i2i2i−2i−2i−2i−2i20000-2000000002i2i−2i−2i000000000000
χ2622222222-2-2-2-2-2-2-2-222-2-22200000000−2i−2i−2i−2i2i2i2i2i20000-200000000−2i−2i2i2i000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-22222000000002i2i2i2i−2i−2i−2i−2i-20000200000000−2i−2i2i2i000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2222200000000−2i−2i−2i−2i2i2i2i2i-200002000000002i2i−2i−2i000000000000
χ292-22-22-22-202-2002-202i−2i2i−2i002i2i−2i−2i22-2-200000000000000000000000000i2−i22−22−2i2−i20000
χ302-22-22-22-202-2002-202i−2i2i−2i002i2i−2i−2i22-2-200000000000000000000000000−i2i2−22−22−i2i20000
χ312-22-22-22-202-2002-202i−2i2i−2i00−2i−2i2i2i-2-22200000000000000000000000000i2−i22−2−22−i2i20000
χ322-22-22-22-202-2002-202i−2i2i−2i00−2i−2i2i2i-2-22200000000000000000000000000−i2i2−222−2i2−i20000
χ332-22-22-22-202-2002-20−2i2i−2i2i002i2i−2i−2i-2-22200000000000000000000000000i2−i2−222−2−i2i20000
χ342-22-22-22-202-2002-20−2i2i−2i2i002i2i−2i−2i-2-22200000000000000000000000000−i2i22−2−22i2−i20000
χ352-22-22-22-202-2002-20−2i2i−2i2i00−2i−2i2i2i22-2-200000000000000000000000000i2−i2−22−22i2−i20000
χ362-22-22-22-202-2002-20−2i2i−2i2i00−2i−2i2i2i22-2-200000000000000000000000000−i2i22−22−2−i2i20000
χ372-2-222-2-2222-2-2-2-22200002-22i−2i2i−2i0000000000000002i−2i0002i−2i2i−2i002-22-2000000000000
χ382-2-222-2-2222-2-2-2-22200002-22i−2i2i−2i000000000000000−2i2i000−2i2i2i−2i00-22-22000000000000
χ392-2-222-2-2222-2-2-2-22200002-2−2i2i−2i2i0000000000000002i−2i0002i−2i−2i2i00-22-22000000000000
χ402-2-222-2-2222-2-2-2-22200002-2−2i2i−2i2i000000000000000−2i2i000−2i2i−2i2i002-22-2000000000000
χ412-2-222-2-222-22-2-22-220000-2200002i−2i2i−2i22-2-222-2-20002i−2i000−2i2i002i−2i0000000000000000
χ422-2-222-2-222-22-2-22-220000-2200002i−2i2i−2i-2-222-2-222000−2i2i0002i−2i002i−2i0000000000000000
χ432-2-222-2-222-22-2-22-220000-220000−2i2i−2i2i22-2-222-2-2000−2i2i0002i−2i00−2i2i0000000000000000
χ442-2-222-2-222-22-2-22-220000-220000−2i2i−2i2i-2-222-2-2220002i−2i000−2i2i00−2i2i0000000000000000
χ452-2-222-2-22-22-222-22-20000-222i−2i2i−2i00002i2i−2i−2i−2i−2i2i2i02-20002-200−2i2i000000000000000000
χ462-2-222-2-22-22-222-22-20000-222i−2i2i−2i0000−2i−2i2i2i2i2i−2i−2i0-22000-2200−2i2i000000000000000000
χ472-2-222-2-22-22-222-22-20000-22−2i2i−2i2i00002i2i−2i−2i−2i−2i2i2i0-22000-22002i−2i000000000000000000
χ482-2-222-2-22-22-222-22-20000-22−2i2i−2i2i0000−2i−2i2i2i2i2i−2i−2i02-20002-2002i−2i000000000000000000
χ492-2-222-2-22-2-22222-2-200002-200002i−2i2i−2i0000000002-2000-220000−2i2i−2i2i2i−2i000000000000
χ502-2-222-2-22-2-22222-2-200002-200002i−2i2i−2i000000000-220002-20000−2i2i2i−2i−2i2i000000000000
χ512-2-222-2-22-2-22222-2-200002-20000−2i2i−2i2i0000000002-2000-2200002i−2i2i−2i−2i2i000000000000
χ522-2-222-2-22-2-22222-2-200002-20000−2i2i−2i2i000000000-220002-200002i−2i−2i2i2i−2i000000000000
χ5344-44-4-44-44004-400-40000000000000022−2222−2222−2222−22000000000000000000000000000000
χ5444-44-4-44-44004-400-400000000000000−2222−2222−2222−2222000000000000000000000000000000
χ5544-44-4-44-4-400-44004000000000000002i2−2i22i2−2i2−2i22i2−2i22i2000000000000000000000000000000
χ5644-44-4-44-4-400-4400400000000000000−2i22i2−2i22i22i2−2i22i2−2i2000000000000000000000000000000
χ5744-4-444-4-404400-4-400000004-4-44000000000000000000000000000000000000000000
χ5844-4-444-4-404400-4-40000000-444-4000000000000000000000000000000000000000000
χ5944-4-444-4-40-4-40044000000000004i−4i−4i4i00000000000000000000000000000000000000
χ6044-4-444-4-40-4-4004400000000000−4i4i4i−4i00000000000000000000000000000000000000
χ614-444-44-4-4400-4400-40000000000000022−22−222222−22−2222000000000000000000000000000000
χ624-444-44-4-4400-4400-400000000000000−222222−22−222222−22000000000000000000000000000000
χ634-444-44-4-4-4004-4004000000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000
χ644-444-44-4-4-4004-400400000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000
χ654-44-44-44-40-4400-4404i−4i−4i4i000000000000000000000000000000000000000000000000
χ664-44-44-44-40-4400-440−4i4i4i−4i000000000000000000000000000000000000000000000000
χ67888-8-8-8-88000000000000000000000000000000000000000000000000000000000000
χ688-8-8-8-8888000000000000000000000000000000000000000000000000000000000000

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