Finite Group Databasebeta

← Group #310198

Character table — Group #310198

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888884444444488888888888888884444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-111-1-1111111-1-11111-1-1-1-1-1-1-1-11-1-111-111-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111111111-1-1-1-111-1-1-1-11111-1-1-1-1-111-1-1111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111
χ5111111111111111111111-1-1-1-111111111111-1-1-1-1111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-111-1
χ6111111111111111111111-1-1-1-111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-1-111-1-11
χ7111111111111111111111-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-111-1-1-111-1-11
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-111111-1-1-1-111-1
χ911111111111111111-1-1-1-11111111111111-1-11111-1-111111111-1-1-1-11111-1-1-1-1-11-1-111-1-1-1
χ1011111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1-111-1-1-1-1-1-1-1111
χ1111111111111111111-1-1-1-111111-1-1-1-11111-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-1111
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111-1-1-111-1-1-1
χ1311111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-11111-111-1-1-1-11
χ1411111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1111111111-1
χ1511111111111111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1111-1-1-1111111-1
χ1611111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111111111111-1-1-1-1111-1-1-1-11
χ172222222222-2-22-2-22-200002222-2000022220022-2-20000-2-200000000000000000-20000000
χ182222222222-2-22-2-22-200002222-20000-2-2-2-200-2-2-2-20000220000000000000000020000000
χ192222222222-2-22-2-22-20000-2-2-2-2-20000222200-2-2220000-2-20000000000000000020000000
χ202222222222-2-22-2-22-20000-2-2-2-2-20000-2-2-2-200222200002200000000000000000-20000000
χ2122222222-2-222-222-2-222220000-222220000-2-2000022-2-200000000000000-2000000000000
χ2222222222-2-222-222-2-222220000-2-2-2-2-20000-2-20000-2-222000000000000002000000000000
χ2322222222-2-222-222-2-2-2-2-2-20000-222220000220000-2-2-2-2000000000000002000000000000
χ2422222222-2-222-222-2-2-2-2-2-20000-2-2-2-2-20000220000222200000000000000-2000000000000
χ252-22-2-2-2222-2222-2-2-2-22i2i−2i−2i2i2i−2i−2i2000000002i−2i002i−2i0000000000000000000000002-200000
χ262-22-2-2-2222-2222-2-2-2-22i2i−2i−2i−2i−2i2i2i2000000002i−2i00−2i2i000000000000000000000000-2200000
χ272-22-2-2-2222-2222-2-2-2-2−2i−2i2i2i2i2i−2i−2i200000000−2i2i002i−2i000000000000000000000000-2200000
χ282-22-2-2-2222-2222-2-2-2-2−2i−2i2i2i−2i−2i2i2i200000000−2i2i00−2i2i0000000000000000000000002-200000
χ292-22-2-2-2222-2-2-2222-2200002i2i−2i−2i-2000000000000−2i2i000000000022-2-2000002i−2i0000000000
χ302-22-2-2-2222-2-2-2222-2200002i2i−2i−2i-2000000000000−2i2i0000000000-2-22200000−2i2i0000000000
χ312-22-2-2-2222-2-2-2222-220000−2i−2i2i2i-20000000000002i−2i000000000022-2-200000−2i2i0000000000
χ322-22-2-2-2222-2-2-2222-220000−2i−2i2i2i-20000000000002i−2i0000000000-2-222000002i−2i0000000000
χ332-22-2-2-222-2222-2-2-2222i2i−2i−2i0000-200000000−2i2i00000000002i2i−2i−2i000000000002-200000000
χ342-22-2-2-222-2222-2-2-2222i2i−2i−2i0000-200000000−2i2i0000000000−2i−2i2i2i00000000000-2200000000
χ352-22-2-2-222-2222-2-2-222−2i−2i2i2i0000-2000000002i−2i00000000002i2i−2i−2i00000000000-2200000000
χ362-22-2-2-222-2222-2-2-222−2i−2i2i2i0000-2000000002i−2i0000000000−2i−2i2i2i000000000002-200000000
χ372-2-222-2-22002-202-2002-22-2000002i2i−2i−2ii2i2−i2−i20000002i−2i00i2−i20000i2−i2i2−i222−2−200000000002−20
χ382-2-222-2-22002-202-2002-22-2000002i2i−2i−2i−i2−i2i2i20000002i−2i00−i2i20000−i2i2−i2i2−2−2220000000000−220
χ392-2-222-2-22002-202-2002-22-200000−2i−2i2i2ii2i2−i2−i2000000−2i2i00i2−i20000i2−i2i2−i2−2−2220000000000−220
χ402-2-222-2-22002-202-2002-22-200000−2i−2i2i2i−i2−i2i2i2000000−2i2i00−i2i20000−i2i2−i2i222−2−200000000002−20
χ412-2-222-2-22002-202-200-22-22000002i2i−2i−2ii2i2−i2−i2000000−2i2i00i2−i20000−i2i2−i2i222−2−20000000000−220
χ422-2-222-2-22002-202-200-22-22000002i2i−2i−2i−i2−i2i2i2000000−2i2i00−i2i20000i2−i2i2−i2−2−22200000000002−20
χ432-2-222-2-22002-202-200-22-2200000−2i−2i2i2ii2i2−i2−i20000002i−2i00i2−i20000−i2i2−i2i2−2−22200000000002−20
χ442-2-222-2-22002-202-200-22-2200000−2i−2i2i2i−i2−i2i2i20000002i−2i00−i2i20000i2−i2i2−i222−2−20000000000−220
χ452-2-22-222-2-2200200-2000002-22-20i2−i2i2−i22i−2i2i−2i002i−2i0000i2−i200i2−i2i2−i200002−22−2000000002−2000
χ462-2-22-222-2-2200200-2000002-22-20i2−i2i2−i2−2i2i−2i2i00−2i2i0000i2−i200i2−i2i2−i20000−22−2200000000−22000
χ472-2-22-222-2-2200200-2000002-22-20−i2i2−i2i22i−2i2i−2i002i−2i0000−i2i200−i2i2−i2i20000−22−2200000000−22000
χ482-2-22-222-2-2200200-2000002-22-20−i2i2−i2i2−2i2i−2i2i00−2i2i0000−i2i200−i2i2−i2i200002−22−2000000002−2000
χ492-2-22-222-2-2200200-200000-22-220i2−i2i2−i22i−2i2i−2i00−2i2i0000i2−i200−i2i2−i2i200002−22−200000000−22000
χ502-2-22-222-2-2200200-200000-22-220i2−i2i2−i2−2i2i−2i2i002i−2i0000i2−i200−i2i2−i2i20000−22−22000000002−2000
χ512-2-22-222-2-2200200-200000-22-220−i2i2−i2i22i−2i2i−2i00−2i2i0000−i2i200i2−i2i2−i20000−22−22000000002−2000
χ522-2-22-222-2-2200200-200000-22-220−i2i2−i2i2−2i2i−2i2i002i−2i0000−i2i200i2−i2i2−i200002−22−200000000−22000
χ5344444444-4-4-4-4-4-4-4-44000000004000000000000000000000000000000000000000000000
χ544444-4-4-4-400000000000000000022−22−222222−22−2222000000000000000000002-2-220000000000000
χ554444-4-4-4-400000000000000000022−22−2222−222222−2200000000000000000000-222-20000000000000
χ564444-4-4-4-4000000000000000000−222222−2222−22−222200000000000000000000-222-20000000000000
χ574444-4-4-4-4000000000000000000−222222−22−222222−22000000000000000000002-2-220000000000000
χ5844-4-44-44-44400-400-400000000000000000000000000000022−22−2222000000000000000000000
χ5944-4-44-44-44400-400-4000000000000000000000000000000−222222−22000000000000000000000
χ6044-4-44-44-4-4-4004004000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ6144-4-44-44-4-4-400400400000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ6244-4-4-44-44004-40-44004i−4i−4i4i00000000000000000000000000000000000000000000000000
χ6344-4-4-44-44004-40-4400−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ6444-4-4-44-4400-4404-4000000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ6544-4-4-44-4400-4404-400000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ664-44-4-4-444-44-4-4-4444-4000000004000000000000000000000000000000000000000000000
χ674-4-444-4-4400-440-440000000000000002i22i2−2i2−2i20000000000−2i22i20000000000000000000000000
χ684-4-444-4-4400-440-44000000000000000−2i2−2i22i22i200000000002i2−2i20000000000000000000000000
χ694-4-44-444-44-400-400400000000002i2−2i22i2−2i2000000000000−2i22i2000000000000000000000000000
χ704-4-44-444-44-400-40040000000000−2i22i2−2i22i20000000000002i2−2i2000000000000000000000000000
χ718-88-888-8-8000000000000000000000000000000000000000000000000000000000000000

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