Finite Group Databasebeta

← Group #310605

Character table — Group #310605

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888444444444488888888888888244444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1111111-1-1-1-1111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-11111-1-1-1-111111111111111-1-1-1-1-1-1-11-1-1-1-111-1
χ411111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-111-11111-1-11
χ51111111111111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1
χ61111111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-1-1-111111
χ71111111111111111111111-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-11-1-111-1-11
χ81111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111111-1-111-111-1-111-1
χ91111111111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-11-1-1-1-1111-1-1-1-1111
χ101111111111111111-1-1-1-111111111-1-1-1-111111111-1-1-1-11111111-1-1-1-1-1-1-11111-1-1-1
χ111111111111111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11111-1-11111111-1
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1111111-1-1-1-1-1-1-11
χ131111111111111111-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-11111-1-11111-111-1-1111-1-111-1-1-1
χ141111111111111111-1-1-1-111-1-1-1-111-1-1-1-111-1-111111111-1-1-1-1-1-1-111-1-1-1-1-111-1-1111
χ151111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-111111-1-111-1-1111-1-1-1-11
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11-1-11111-1-1-11111-1
χ172222222222-2-22-2-220000-2-22222220000-2-22200000000-2-20000-200000000000000
χ182222222222-2-22-2-220000-2-22222-2-2000022-2-200000000-2-20000200000000000000
χ192222222222-2-22-2-220000-2-2-2-2-2-2220000-2-2-2-200000000220000200000000000000
χ202222222222-2-22-2-220000-2-2-2-2-2-2-2-20000222200000000220000-200000000000000
χ2122222222-2-222-222-22222-2-200000022-2-2000022-2-200000000000000000-20000000
χ2222222222-2-222-222-22222-2-2000000-2-2-2-20000-2-2220000000000000000020000000
χ2322222222-2-222-222-2-2-2-2-2-2-200000022220000-2-22200000000000000000-20000000
χ2422222222-2-222-222-2-2-2-2-2-2-2000000-2-222000022-2-20000000000000000020000000
χ252-222-2-2-22002-202-2022-2-200i2i2−i2−i2002-20000002-200i2i2−i2−i2i2−i2i2i2−i2−i2000000000000i2−i20
χ262-222-2-2-22002-202-2022-2-200i2i2−i2−i200-22000000-2200i2i2−i2−i2i2−i2−i2−i2i2i2000000000000−i2i20
χ272-222-2-2-22002-202-2022-2-200−i2−i2i2i2002-20000002-200−i2−i2i2i2−i2i2−i2−i2i2i2000000000000−i2i20
χ282-222-2-2-22002-202-2022-2-200−i2−i2i2i200-22000000-2200−i2−i2i2i2−i2i2i2i2−i2−i2000000000000i2−i20
χ292-222-2-2-22002-202-20-2-22200i2i2−i2−i2002-2000000-2200−i2−i2i2i2i2−i2−i2−i2i2i2000000000000i2−i20
χ302-222-2-2-22002-202-20-2-22200i2i2−i2−i200-220000002-200−i2−i2i2i2i2−i2i2i2−i2−i2000000000000−i2i20
χ312-222-2-2-22002-202-20-2-22200−i2−i2i2i2002-2000000-2200i2i2−i2−i2−i2i2i2i2−i2−i2000000000000−i2i20
χ322-222-2-2-22002-202-20-2-22200−i2−i2i2i200-220000002-200i2i2−i2−i2−i2i2−i2−i2i2i2000000000000i2−i20
χ332-2-2-222-222-2222-2-2-22i−2i2i−2i-2200002i−2i002i−2i2i−2i00000000000000000002-20000000000
χ342-2-2-222-222-2222-2-2-22i−2i2i−2i-220000−2i2i002i−2i−2i2i0000000000000000000-220000000000
χ352-2-2-222-222-2222-2-2-2−2i2i−2i2i-2200002i−2i00−2i2i2i−2i0000000000000000000-220000000000
χ362-2-2-222-222-2222-2-2-2−2i2i−2i2i-220000−2i2i00−2i2i−2i2i00000000000000000002-20000000000
χ372-2-2-222-222-2-2-2222-200002-200002i−2i0000−2i2i0000002-22-200000002i−2i000000000000
χ382-2-2-222-222-2-2-2222-200002-200002i−2i0000−2i2i000000-22-220000000−2i2i000000000000
χ392-2-2-222-222-2-2-2222-200002-20000−2i2i00002i−2i0000002-22-20000000−2i2i000000000000
χ402-2-2-222-222-2-2-2222-200002-20000−2i2i00002i−2i000000-22-2200000002i−2i000000000000
χ412-2-2-222-22-2222-2-2-222i−2i2i−2i2-200000000−2i2i000000000000000000000002-202i−2i00000
χ422-2-2-222-22-2222-2-2-222i−2i2i−2i2-200000000−2i2i00000000000000000000000-220−2i2i00000
χ432-2-2-222-22-2222-2-2-22−2i2i−2i2i2-2000000002i−2i000000000000000000000002-20−2i2i00000
χ442-2-2-222-22-2222-2-2-22−2i2i−2i2i2-2000000002i−2i00000000000000000000000-2202i−2i00000
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000
χ46444-44-4-4-44400-400-400000000000000000000000000000022−2222−22000000000000000
χ47444-44-4-4-44400-400-4000000000000000000000000000000−2222−2222000000000000000
χ48444-44-4-4-4-4-40040040000004i−4i4i−4i000000000000000000000000000000000000000
χ49444-44-4-4-4-4-4004004000000−4i4i−4i4i000000000000000000000000000000000000000
χ5044-4-4-4-444004-40-4404i−4i−4i4i000000000000000000000000000000000000000000000
χ5144-4-4-4-444004-40-440−4i4i4i−4i000000000000000000000000000000000000000000000
χ5244-4-4-4-44400-4404-400000000000000000000000002i2−2i2−2i22i2000000000000000000000
χ5344-4-4-4-44400-4404-40000000000000000000000000−2i22i22i2−2i2000000000000000000000
χ544-444-4-4-4400-440-4400000002i22i2−2i2−2i2000000000000000000−2i22i20000000000000000000
χ554-444-4-4-4400-440-440000000−2i2−2i22i22i20000000000000000002i2−2i20000000000000000000
χ564-44-4-444-40000000000000022−22−22220000000000002i2−2i20000002i−2i−2i2i000000000000000
χ574-44-4-444-40000000000000022−22−2222000000000000−2i22i2000000−2i2i2i−2i000000000000000
χ584-44-4-444-400000000000000−222222−220000000000002i2−2i2000000−2i2i2i−2i000000000000000
χ594-44-4-444-400000000000000−222222−22000000000000−2i22i20000002i−2i−2i2i000000000000000
χ604-4-444-44-44-400-4004000000000000000000000000000000000000000000002i2−2i2000
χ614-4-444-44-44-400-400400000000000000000000000000000000000000000000−2i22i2000
χ624-4-444-44-4-4400400-40000000000000000004i−4i00000000000000000000000000000
χ634-4-444-44-4-4400400-4000000000000000000−4i4i00000000000000000000000000000
χ644-4-4-444-44-44-4-4-44440000-440000000000000000000000000000000000000000000
χ6588-88-88-8-8000000000000000000000000000000000000000000000000000000000

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