Finite Group Databasebeta

← Group #310021

Character table — Group #310021

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888884444444488888888888888884444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-11-1-11111-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111-1-1111111-1-1111111-1-1-1-1-1-1-1-1-11111-1-11-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-111111
χ511111111111111111111-1-1-1-111111111111111-1-1-1-111111111-1-1-1-111111-1-1-1-1-1-1-111-1-1-1
χ611111111111111111111-1-1-1-1111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-11-1-1111
χ711111111111111111111-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-111-1-1-1111
χ811111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111-111-1-111111-1-1-1
χ91111111111111111-1-1-1-111111111111111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-11-1-111-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1-111-1-1-1-1-111-1-11
χ111111111111111111-1-1-1-1111111-1-1-1-1111111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111-1-11
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111111-1-111-1-1-111-1
χ131111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1111111-1-1-1-1-11
χ141111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1111111111-1
χ151111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111-1-1-11111-1
χ161111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111111111111-1-111-1-11-1-1-1-11
χ17222222222-222-2-2-2222220000-2-22222000022-2-20000-2-200000000000000-2000000000000
χ18222222222-222-2-2-2222220000-2-2-2-2-2-20000-2-2-2-2000022000000000000002000000000000
χ19222222222-222-2-2-22-2-2-2-20000-2-222220000-2-2220000-2-2000000000000002000000000000
χ20222222222-222-2-2-22-2-2-2-20000-2-2-2-2-2-20000222200002200000000000000-2000000000000
χ2122222222-22-2-2222-200002222-2-2000022220000-2-22200-2-20000000000000000000-200000
χ2222222222-22-2-2222-200002222-2-20000-2-2-2-20000-2-2-2-200220000000000000000000200000
χ2322222222-22-2-2222-20000-2-2-2-2-2-200002222000022-2-200-2-20000000000000000000200000
χ2422222222-22-2-2222-20000-2-2-2-2-2-20000-2-2-2-20000222200220000000000000000000-200000
χ252222-2-2-2-2202-2000-222-2-200000022-2-222−2−22-2000000002−222−2−2000022−2−2000000002−2000
χ262222-2-2-2-2202-2000-222-2-200000022-2-2−2−2222-200000000−22−2−2220000−2−22200000000−22000
χ272222-2-2-2-2202-2000-222-2-2000000-2-22222−2−2-22000000002−222−2−20000−2−22200000000−22000
χ282222-2-2-2-2202-2000-222-2-2000000-2-222−2−222-2200000000−22−2−222000022−2−2000000002−2000
χ292222-2-2-2-2202-2000-2-2-22200000022-2-222−2−2-22000000002−2−2−222000022−2−200000000−22000
χ302222-2-2-2-2202-2000-2-2-22200000022-2-2−2−222-2200000000−2222−2−20000−2−222000000002−2000
χ312222-2-2-2-2202-2000-2-2-222000000-2-22222−2−22-2000000002−2−2−2220000−2−222000000002−2000
χ322222-2-2-2-2202-2000-2-2-222000000-2-222−2−2222-200000000−2222−2−2000022−2−200000000−22000
χ332-22-2-2-22222-2-2-22-2200002i2i−2i−2i2-20000000000002i−2i0000002-22-20000000002i−2i0000000000
χ342-22-2-2-22222-2-2-22-2200002i2i−2i−2i2-20000000000002i−2i000000-22-22000000000−2i2i0000000000
χ352-22-2-2-22222-2-2-22-220000−2i−2i2i2i2-2000000000000−2i2i0000002-22-2000000000−2i2i0000000000
χ362-22-2-2-22222-2-2-22-220000−2i−2i2i2i2-2000000000000−2i2i000000-22-220000000002i−2i0000000000
χ372-22-2-2-222-2222-22-2-22i−2i2i−2i2i2i−2i−2i-2200000000002i−2i−2i2i0000000000000000000002-200000000
χ382-22-2-2-222-2222-22-2-22i−2i2i−2i−2i−2i2i2i-2200000000002i−2i2i−2i000000000000000000000-2200000000
χ392-22-2-2-222-2222-22-2-2−2i2i−2i2i2i2i−2i−2i-220000000000−2i2i−2i2i000000000000000000000-2200000000
χ402-22-2-2-222-2222-22-2-2−2i2i−2i2i−2i−2i2i2i-220000000000−2i2i2i−2i0000000000000000000002-200000000
χ412-22-2-2-222-2-2222-22-22i−2i2i−2i00002-20000000000−2i2i0000000000002i2i−2i−2i0000000002-2000000
χ422-22-2-2-222-2-2222-22-22i−2i2i−2i00002-20000000000−2i2i000000000000−2i−2i2i2i000000000-22000000
χ432-22-2-2-222-2-2222-22-2−2i2i−2i2i00002-200000000002i−2i0000000000002i2i−2i−2i000000000-22000000
χ442-22-2-2-222-2-2222-22-2−2i2i−2i2i00002-200000000002i−2i000000000000−2i−2i2i2i0000000002-2000000
χ452-2-222-2-2202002-2-2000002-22-2002−22−22i−2i2i−2i0000002i−2i2−20000002−22−2i2−i2i2−i20000000000i2−i20
χ462-2-222-2-2202002-2-2000002-22-2002−22−2−2i2i−2i2i000000−2i2i2−20000002−22−2−i2i2−i2i20000000000−i2i20
χ472-2-222-2-2202002-2-2000002-22-200−22−222i−2i2i−2i0000002i−2i−22000000−22−22−i2i2−i2i20000000000−i2i20
χ482-2-222-2-2202002-2-2000002-22-200−22−22−2i2i−2i2i000000−2i2i−22000000−22−22i2−i2i2−i20000000000i2−i20
χ492-2-222-2-2202002-2-200000-22-22002−22−22i−2i2i−2i000000−2i2i2−2000000−22−22i2−i2i2−i20000000000−i2i20
χ502-2-222-2-2202002-2-200000-22-22002−22−2−2i2i−2i2i0000002i−2i2−2000000−22−22−i2i2−i2i20000000000i2−i20
χ512-2-222-2-2202002-2-200000-22-2200−22−222i−2i2i−2i000000−2i2i−220000002−22−2−i2i2−i2i20000000000i2−i20
χ522-2-222-2-2202002-2-200000-22-2200−22−22−2i2i−2i2i0000002i−2i−220000002−22−2i2−i2i2−i20000000000−i2i20
χ5344444444-4-4-4-4-4-4-4-40000000044000000000000000000000000000000000000000000000
χ544444-4-4-4-4-40-440004000000000000002222−22−220000000000−22220000000000000000000000000
χ554444-4-4-4-4-40-44000400000000000000−22−222222000000000022−220000000000000000000000000
χ5644-4-4-44-440400-4-44000004i−4i−4i4i00000000000000000000000000000000000000000000000
χ5744-4-4-44-440400-4-4400000−4i4i4i−4i00000000000000000000000000000000000000000000000
χ5844-4-4-44-440-40044-4000000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ5944-4-4-44-440-40044-400000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ604-44-444-4-440-44000-400000000000000000000000000000022−22−2222000000000000000000000
χ614-44-444-4-440-44000-4000000000000000000000000000000−222222−22000000000000000000000
χ624-44-444-4-4-404-400044i−4i−4i4i000000000000000000000000000000000000000000000000000
χ634-44-444-4-4-404-40004−4i4i4i−4i000000000000000000000000000000000000000000000000000
χ644-44-4-4-4444-4-4-44-44400000000-44000000000000000000000000000000000000000000000
χ654-4-444-4-440-400-4440000000000022−2222−22000000000000−2222000000000000000000000000000
χ664-4-444-4-440-400-44400000000000−2222−222200000000000022−22000000000000000000000000000
χ674-4-44-444-400000000000000000022−22−22222i2−2i2−2i22i2000000000000000000002i−2i−2i2i0000000000000
χ684-4-44-444-400000000000000000022−22−2222−2i22i22i2−2i200000000000000000000−2i2i2i−2i0000000000000
χ694-4-44-444-4000000000000000000−222222−222i2−2i2−2i22i200000000000000000000−2i2i2i−2i0000000000000
χ704-4-44-444-4000000000000000000−222222−22−2i22i22i2−2i2000000000000000000002i−2i−2i2i0000000000000
χ7188-8-88-88-8000000000000000000000000000000000000000000000000000000000000000

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