Finite Group Databasebeta

← Group #351835

Character table — Group #351835

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444888888888888888888161616161616161632323232
order12222222444444444444448888888888888888444444444488888888888888882444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1-11
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11-1-11
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-111-1
χ91111111111111111-1-1-1-1111111-1-1-1-111111111-1-11111-1-1-1-111-1-1-1-1-1-111-1-111-1-1-11-11
χ101111111111111111-1-1-1-1111111-1-1-1-111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-111-1-1111-11-1
χ111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-111-1-11-11-1
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-111-1-111-11-11
χ131111111111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-11111-1-111-1-1-1-111-1-1-1-11111-1-1
χ141111111111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-111
χ151111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-111-1-111
χ161111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-11111-1-111-1-1
χ172222222222-2-22-2-2222-2-2-2-200000000000000002-222-2-222-2-200000000000000000000
χ182222222222-2-22-2-2222-2-2-2-200000000000000002-2-2-222-2-22200000000000000000000
χ192222222222-2-22-2-22-2-222-2-20000000000000000-2222-2-2-2-22200000000000000000000
χ202222222222-2-22-2-22-2-222-2-20000000000000000-22-2-22222-2-200000000000000000000
χ2122222222-2-222-222-22222-2-22222222200000000-2-200000000-2-2-2-20000000000000000
χ2222222222-2-222-222-22222-2-2-2-2-2-2-2-2-2-200000000-2-20000000022220000000000000000
χ2322222222-2-222-222-2-2-2-2-2-2-22222-2-2-2-2000000002200000000-2-2220000000000000000
χ2422222222-2-222-222-2-2-2-2-2-2-2-2-2-2-2222200000000220000000022-2-20000000000000000
χ2522222222-2-2-2-2-2-2-2-222-2-222000000002i2i2i2i−2i−2i−2i−2i-220000000000002i2i−2i−2i000000000000
χ2622222222-2-2-2-2-2-2-2-222-2-22200000000−2i−2i−2i−2i2i2i2i2i-22000000000000−2i−2i2i2i000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-22222000000002i2i2i2i−2i−2i−2i−2i2-2000000000000−2i−2i2i2i000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2222200000000−2i−2i−2i−2i2i2i2i2i2-20000000000002i2i−2i−2i000000000000
χ292-2-222-22-2002-202-202i−2i2i−2i002i2i−2i−2i22-2-200000000000000000000000000i2−i22−22−2i2−i20000
χ302-2-222-22-2002-202-202i−2i2i−2i002i2i−2i−2i22-2-200000000000000000000000000−i2i2−22−22−i2i20000
χ312-2-222-22-2002-202-202i−2i2i−2i00−2i−2i2i2i-2-22200000000000000000000000000i2−i22−2−22−i2i20000
χ322-2-222-22-2002-202-202i−2i2i−2i00−2i−2i2i2i-2-22200000000000000000000000000−i2i2−222−2i2−i20000
χ332-2-222-22-2002-202-20−2i2i−2i2i002i2i−2i−2i-2-22200000000000000000000000000i2−i2−222−2−i2i20000
χ342-2-222-22-2002-202-20−2i2i−2i2i002i2i−2i−2i-2-22200000000000000000000000000−i2i22−2−22i2−i20000
χ352-2-222-22-2002-202-20−2i2i−2i2i00−2i−2i2i2i22-2-200000000000000000000000000i2−i2−22−22i2−i20000
χ362-2-222-22-2002-202-20−2i2i−2i2i00−2i−2i2i2i22-2-200000000000000000000000000−i2i22−22−2−i2i20000
χ372-2-2-2-2222222-2-2-22-200002-200002-22-200000000002i−2i2i−2i0000002-22i−2i2i−2i000000000000
χ382-2-2-2-2222222-2-2-22-200002-200002-22-20000000000−2i2i−2i2i0000002-2−2i2i−2i2i000000000000
χ392-2-2-2-2222222-2-2-22-200002-20000-22-2200000000002i−2i2i−2i000000-22−2i2i−2i2i000000000000
χ402-2-2-2-2222222-2-2-22-200002-20000-22-220000000000−2i2i−2i2i000000-222i−2i2i−2i000000000000
χ412-2-2-2-222222-22-22-2-20000-222-22-200002i2i−2i−2i2i2i−2i−2i002i−2i−2i2i00002-2000000000000000000
χ422-2-2-2-222222-22-22-2-20000-222-22-20000−2i−2i2i2i−2i−2i2i2i00−2i2i2i−2i00002-2000000000000000000
χ432-2-2-2-222222-22-22-2-20000-22-22-2200002i2i−2i−2i2i2i−2i−2i00−2i2i2i−2i0000-22000000000000000000
χ442-2-2-2-222222-22-22-2-20000-22-22-220000−2i−2i2i2i−2i−2i2i2i002i−2i−2i2i0000-22000000000000000000
χ452-2-2-2-2222-2-22-22-2220000-2200002-22-222-2-2-2-2220000002-22-200-220000000000000000
χ462-2-2-2-2222-2-22-22-2220000-2200002-22-2-2-22222-2-2000000-22-2200-220000000000000000
χ472-2-2-2-2222-2-22-22-2220000-220000-22-2222-2-2-2-222000000-22-22002-20000000000000000
χ482-2-2-2-2222-2-22-22-2220000-220000-22-22-2-22222-2-20000002-22-2002-20000000000000000
χ492-2-2-2-2222-2-2-2222-2200002-22-22-20000000000000000002-2-22-2200-222-2000000000000
χ502-2-2-2-2222-2-2-2222-2200002-22-22-2000000000000000000-222-2-22002-2-22000000000000
χ512-2-2-2-2222-2-2-2222-2200002-2-22-220000000000000000002-2-222-2002-2-22000000000000
χ522-2-2-2-2222-2-2-2222-2200002-2-22-22000000000000000000-222-22-200-222-2000000000000
χ53444-4-4-44-400440-4-4000000000004-4-4400000000000000000000000000000000000000
χ54444-4-4-44-400440-4-400000000000-444-400000000000000000000000000000000000000
χ55444-4-4-44-400-4-404400000004i−4i−4i4i000000000000000000000000000000000000000000
χ56444-4-4-44-400-4-40440000000−4i4i4i−4i000000000000000000000000000000000000000000
χ5744-44-4-4-444-400400-4000000000000002i2−2i22i2−2i22i2−2i22i2−2i2000000000000000000000000000000
χ5844-44-4-4-444-400400-400000000000000−2i22i2−2i22i2−2i22i2−2i22i2000000000000000000000000000000
χ5944-44-4-4-44-4400-40040000000000000022−2222−22−2222−2222000000000000000000000000000000
χ6044-44-4-4-44-4400-400400000000000000−2222−222222−2222−22000000000000000000000000000000
χ614-44-44-4-444-400-40040000000000000022−22−222222−22−2222000000000000000000000000000000
χ624-44-44-4-444-400-400400000000000000−222222−22−222222−22000000000000000000000000000000
χ634-44-44-4-44-4400400-4000000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000
χ644-44-44-4-44-4400400-400000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000
χ654-4-444-44-400-440-4404i−4i−4i4i000000000000000000000000000000000000000000000000
χ664-4-444-44-400-440-440−4i4i4i−4i000000000000000000000000000000000000000000000000
χ6788-8-888-8-8000000000000000000000000000000000000000000000000000000000000
χ688-888-88-8-8000000000000000000000000000000000000000000000000000000000000

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