Finite Group Databasebeta

← Group #310113

Character table — Group #310113

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888884444444488888888888888882244444488882
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-111-1-1111111-1-11111-1-1-1-1-1-1-1-111-1111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111111111-1-1-1-111-1-1-1-11111-1-1-1-1111-1-1-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111
χ5111111111111111111111-1-1-1-11111111111111-1-1-1-111111111-1-1-1-11111-1-11-1-1-1-1-111-1-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1111
χ7111111111111111111111-1-1-1-11-1-1-1-111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-11111111-1-1-1
χ911111111111111111-1-1-1-11111111111111-1-1-1-111111111-1-1-1-111111111-1-1-11-1-1-1-1-1-111-1
χ1011111111111111111-1-1-1-1111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11
χ1111111111111111111-1-1-1-111111-1-1-1-11111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-11
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-11-11111-1-111-1
χ1311111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-11
χ1411111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111-111-1-11111-1
χ1511111111111111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111-11-1-1111111-1
χ1611111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11
χ17222222222-2-22-2-222-222220000-200002222-2-222000000-2-200000000000000-20000000000
χ18222222222-2-22-2-222-222220000-20000-2-2-2-2-2-2-2-2000000220000000000000020000000000
χ19222222222-2-22-2-222-2-2-2-2-20000-20000222222-2-2000000-2-20000000000000020000000000
χ20222222222-2-22-2-222-2-2-2-2-20000-20000-2-2-2-222220000002200000000000000-20000000000
χ2122222222-222-222-2-2-200002222-2222200000000-2-222-2-200000000000000000-2000000000
χ2222222222-222-222-2-2-200002222-2-2-2-2-200000000-2-2-2-222000000000000000002000000000
χ2322222222-222-222-2-2-20000-2-2-2-2-222220000000022-2-2-2-2000000000000000002000000000
χ2422222222-222-222-2-2-20000-2-2-2-2-2-2-2-2-20000000022222200000000000000000-2000000000
χ252-222-22-2-202-202-2000000022-2-202i2i−2i−2ii2i2−i2−i20000002i−2i00i2−i20000i2i2−i2−i222−2−200000000002−20
χ262-222-22-2-202-202-2000000022-2-202i2i−2i−2i−i2−i2i2i20000002i−2i00−i2i20000−i2−i2i2i2−2−2220000000000−220
χ272-222-22-2-202-202-2000000022-2-20−2i−2i2i2ii2i2−i2−i2000000−2i2i00i2−i20000i2i2−i2−i2−2−2220000000000−220
χ282-222-22-2-202-202-2000000022-2-20−2i−2i2i2i−i2−i2i2i2000000−2i2i00−i2i20000−i2−i2i2i222−2−200000000002−20
χ292-222-22-2-202-202-20000000-2-22202i2i−2i−2ii2i2−i2−i2000000−2i2i00i2−i20000−i2−i2i2i222−2−20000000000−220
χ302-222-22-2-202-202-20000000-2-22202i2i−2i−2i−i2−i2i2i2000000−2i2i00−i2i20000i2i2−i2−i2−2−22200000000002−20
χ312-222-22-2-202-202-20000000-2-2220−2i−2i2i2ii2i2−i2−i20000002i−2i00i2−i20000−i2−i2i2i2−2−22200000000002−20
χ322-222-22-2-202-202-20000000-2-2220−2i−2i2i2i−i2−i2i2i20000002i−2i00−i2i20000i2i2−i2−i222−2−20000000000−220
χ332-22-22-22-2222-2-2-22-2-22i2i−2i−2i2i−2i2i−2i2000000002i−2i002i−2i0000000000000000002-200000000000
χ342-22-22-22-2222-2-2-22-2-22i2i−2i−2i−2i2i−2i2i2000000002i−2i00−2i2i000000000000000000-2200000000000
χ352-22-22-22-2222-2-2-22-2-2−2i−2i2i2i2i−2i2i−2i200000000−2i2i002i−2i000000000000000000-2200000000000
χ362-22-22-22-2222-2-2-22-2-2−2i−2i2i2i−2i2i−2i2i200000000−2i2i00−2i2i0000000000000000002-200000000000
χ372-22-22-22-22-2-2-2222-222i2i−2i−2i0000-200000000−2i2i000000000000002-22-200000000002i−2i00000
χ382-22-22-22-22-2-2-2222-222i2i−2i−2i0000-200000000−2i2i00000000000000-22-220000000000−2i2i00000
χ392-22-22-22-22-2-2-2222-22−2i−2i2i2i0000-2000000002i−2i000000000000002-22-20000000000−2i2i00000
χ402-22-22-22-22-2-2-2222-22−2i−2i2i2i0000-2000000002i−2i00000000000000-22-2200000000002i−2i00000
χ412-22-22-22-2-2222-2-2-22200002i−2i2i−2i-2000000000000−2i2i0000002i2i−2i−2i0000000000002-20000000
χ422-22-22-22-2-2222-2-2-22200002i−2i2i−2i-2000000000000−2i2i000000−2i−2i2i2i000000000000-220000000
χ432-22-22-22-2-2222-2-2-2220000−2i2i−2i2i-20000000000002i−2i0000002i2i−2i−2i000000000000-220000000
χ442-22-22-22-2-2222-2-2-2220000−2i2i−2i2i-20000000000002i−2i000000−2i−2i2i2i0000000000002-20000000
χ452-2-2-2-2222-200-2002202-22-2000002−22−22-22-2002-200002−2002−22−200002−22−2000000002−2000
χ462-2-2-2-2222-200-2002202-22-2000002−22−2-22-2200-2200002−2002−22−20000−22−2200000000−22000
χ472-2-2-2-2222-200-2002202-22-200000−22−222-22-2002-20000−2200−22−220000−22−2200000000−22000
χ482-2-2-2-2222-200-2002202-22-200000−22−22-22-2200-220000−2200−22−2200002−22−2000000002−2000
χ492-2-2-2-2222-200-200220-22-22000002−22−22-22-200-2200002−200−22−2200002−22−200000000−22000
χ502-2-2-2-2222-200-200220-22-22000002−22−2-22-22002-200002−200−22−220000−22−22000000002−2000
χ512-2-2-2-2222-200-200220-22-2200000−22−222-22-200-220000−22002−22−20000−22−22000000002−2000
χ522-2-2-2-2222-200-200220-22-2200000−22−22-22-22002-20000−22002−22−200002−22−200000000−22000
χ5344444444-4-4-4-4-4-4-4-44000000004000000000000000000000000000000000000000000000
χ54444-4-4-4-4404-40-4400000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ55444-4-4-4-4404-40-440000000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ56444-4-4-4-440-4404-40000000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ57444-4-4-4-440-4404-4000000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ5844-44-4-44-4400-400-440000000000000000000000000000002i2−2i2−2i22i2000000000000000000000
χ5944-44-4-44-4400-400-44000000000000000000000000000000−2i22i22i2−2i2000000000000000000000
χ6044-44-4-44-4-4004004-404i−4i−4i4i00000000000000000000000000000000000000000000000000
χ6144-44-4-44-4-4004004-40−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ6244-4-444-4-40000000000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000002-2-220000000000000
χ6344-4-444-4-40000000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000-222-20000000000000
χ6444-4-444-4-4000000000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000-222-20000000000000
χ6544-4-444-4-4000000000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000002-2-220000000000000
χ664-444-44-4-40-440-4400000000000000002i22i2−2i2−2i20000000000−2i22i20000000000000000000000000
χ674-444-44-4-40-440-440000000000000000−2i2−2i22i22i200000000002i2−2i20000000000000000000000000
χ684-44-44-44-4-4-4-4444-44-4000000004000000000000000000000000000000000000000000000
χ694-4-4-4-4444400400-4-4000000000022−2222−22000000000000−2222000000000000000000000000000
χ704-4-4-4-4444400400-4-40000000000−2222−222200000000000022−22000000000000000000000000000
χ718-8-888-8-88000000000000000000000000000000000000000000000000000000000000000

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