Finite Group Databasebeta

← Group #310091

Character table — Group #310091

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888882244444488888888888888884444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-111-1-11111-1-1111111-1-1-1-1-1-1-1-11-1-1-11111-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111-1-111111111-1-1-1-1-1-11111-1-1-1-1-1111-1-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111
χ511111111111111111111-1-1-1-1111111111111-1-111-1-111-1-1-1-111111111111-1-1-1-1-1-1-1-1-111-1
χ611111111111111111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11
χ711111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1111111-1-11111-1-1-1-1-1-1-1-111-1-111-1-11
χ811111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-111111-1-1-1-111-1
χ91111111111111111-1-1-1-111111111111111-1-111-1-11111111111-1-1-1-11111-11-1-1-1-1-1-111-1-1-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-1111
χ111111111111111111-1-1-1-1111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1111
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1111111111-11111-1-111-1-1-1
χ131111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1111111-1-1-1-11
χ141111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-11-1-111111111-1
χ151111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11-111-1-1111111-1
χ161111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111111111-1-1-1-111-1-1-1-11
χ17222222222-222-2-2-2200002222-2-200002222002200-2-2-2-2000000000000000-200000000000
χ18222222222-222-2-2-2200002222-2-20000-2-2-2-200-2-200-2-222000000000000000200000000000
χ19222222222-222-2-2-220000-2-2-2-2-2-20000222200-2-20022-2-2000000000000000200000000000
χ20222222222-222-2-2-220000-2-2-2-2-2-20000-2-2-2-20022002222000000000000000-200000000000
χ2122222222-22-2-2222-222220000-2-2222200002200-2-200000000-2-200000000-2000000000000
χ2222222222-22-2-2222-222220000-2-2-2-2-2-20000-2-200-2-20000000022000000002000000000000
χ2322222222-22-2-2222-2-2-2-2-20000-2-222220000-2-2002200000000-2-2000000002000000000000
χ2422222222-22-2-2222-2-2-2-2-20000-2-2-2-2-2-20000220022000000002200000000-2000000000000
χ252-2222-2-2-2-202-2000200002i2i−2i−2i0022−2−222-2-2002i−2i000000i2i2−i2−i22−2000022−2−200000000i2−i2000
χ262-2222-2-2-2-202-2000200002i2i−2i−2i0022−2−2-2-22200−2i2i000000i2i2−i2−i22−20000−2−22200000000−i2i2000
χ272-2222-2-2-2-202-2000200002i2i−2i−2i00−2−22222-2-2002i−2i000000−i2−i2i2i2−220000−2−22200000000−i2i2000
χ282-2222-2-2-2-202-2000200002i2i−2i−2i00−2−222-2-22200−2i2i000000−i2−i2i2i2−22000022−2−200000000i2−i2000
χ292-2222-2-2-2-202-200020000−2i−2i2i2i0022−2−222-2-200−2i2i000000−i2−i2i2i22−2000022−2−200000000−i2i2000
χ302-2222-2-2-2-202-200020000−2i−2i2i2i0022−2−2-2-222002i−2i000000−i2−i2i2i22−20000−2−22200000000i2−i2000
χ312-2222-2-2-2-202-200020000−2i−2i2i2i00−2−22222-2-200−2i2i000000i2i2−i2−i2−220000−2−22200000000i2−i2000
χ322-2222-2-2-2-202-200020000−2i−2i2i2i00−2−222-2-222002i−2i000000i2i2−i2−i2−22000022−2−200000000−i2i2000
χ332-22-2-22-2222-2-2-22-222i2i−2i−2i00002-20000000000002i−2i00002-22-2000000000000002i−2i0000000
χ342-22-2-22-2222-2-2-22-222i2i−2i−2i00002-20000000000002i−2i0000-22-2200000000000000−2i2i0000000
χ352-22-2-22-2222-2-2-22-22−2i−2i2i2i00002-2000000000000−2i2i00002-22-200000000000000−2i2i0000000
χ362-22-2-22-2222-2-2-22-22−2i−2i2i2i00002-2000000000000−2i2i0000-22-22000000000000002i−2i0000000
χ372-22-2-22-22-2222-22-2-22i2i−2i−2i2i−2i2i−2i-22000000000000−2i2i2i−2i00000000000000000000002-200000
χ382-22-2-22-22-2222-22-2-22i2i−2i−2i−2i2i−2i2i-22000000000000−2i2i−2i2i0000000000000000000000-2200000
χ392-22-2-22-22-2222-22-2-2−2i−2i2i2i2i−2i2i−2i-220000000000002i−2i2i−2i0000000000000000000000-2200000
χ402-22-2-22-22-2222-22-2-2−2i−2i2i2i−2i2i−2i2i-220000000000002i−2i−2i2i00000000000000000000002-200000
χ412-22-2-22-22-2-2222-22-200002i−2i2i−2i2-200000000000000−2i2i000000002i2i−2i−2i0000002-2000000000
χ422-22-2-22-22-2-2222-22-200002i−2i2i−2i2-200000000000000−2i2i00000000−2i−2i2i2i000000-22000000000
χ432-22-2-22-22-2-2222-22-20000−2i2i−2i2i2-2000000000000002i−2i000000002i2i−2i−2i000000-22000000000
χ442-22-2-22-22-2-2222-22-20000−2i2i−2i2i2-2000000000000002i−2i00000000−2i−2i2i2i0000002-2000000000
χ452-2-22-222-20200-2-2202i−2i2i−2i0000002i−2i2i−2ii2−i2i2−i22-2000000i2−i20000002−22−22−22−20000000000i2−i20
χ462-2-22-222-20200-2-2202i−2i2i−2i0000002i−2i2i−2i−i2i2−i2i22-2000000−i2i2000000−22−22−22−220000000000−i2i20
χ472-2-22-222-20200-2-2202i−2i2i−2i000000−2i2i−2i2ii2−i2i2−i2-22000000i2−i20000002−22−2−22−220000000000−i2i20
χ482-2-22-222-20200-2-2202i−2i2i−2i000000−2i2i−2i2i−i2i2−i2i2-22000000−i2i2000000−22−222−22−20000000000i2−i20
χ492-2-22-222-20200-2-220−2i2i−2i2i0000002i−2i2i−2ii2−i2i2−i2-22000000i2−i2000000−22−222−22−20000000000−i2i20
χ502-2-22-222-20200-2-220−2i2i−2i2i0000002i−2i2i−2i−i2i2−i2i2-22000000−i2i20000002−22−2−22−220000000000i2−i20
χ512-2-22-222-20200-2-220−2i2i−2i2i000000−2i2i−2i2ii2−i2i2−i22-2000000i2−i2000000−22−22−22−220000000000i2−i20
χ522-2-22-222-20200-2-220−2i2i−2i2i000000−2i2i−2i2i−i2i2−i2i22-2000000−i2i20000002−22−22−22−20000000000−i2i20
χ5344444444-4-4-4-4-4-4-4-40000000044000000000000000000000000000000000000000000000
χ54444-4-4-44-4404-4000-400004-4-4400000000000000000000000000000000000000000000000
χ55444-4-4-44-4404-4000-40000-444-400000000000000000000000000000000000000000000000
χ56444-4-4-44-4-40-44000400000000000000000000000000002i2−2i2−2i22i200000000000000000000000
χ57444-4-4-44-4-40-4400040000000000000000000000000000−2i22i22i2−2i200000000000000000000000
χ5844-44-4-4-440000000000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000002-2-220000000000000
χ5944-44-4-4-440000000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000-222-20000000000000
χ6044-44-4-4-44000000000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000-222-20000000000000
χ6144-44-4-4-44000000000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000002-2-220000000000000
χ6244-4-444-4-404004-4-404-4-44000000000000000000000000000000000000000000000000000
χ6344-4-444-4-404004-4-40-444-4000000000000000000000000000000000000000000000000000
χ6444-4-444-4-40-400-444000000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ6544-4-444-4-40-400-44400000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ664-4444-4-4-440-44000-400000000002222−22−22000000000000000000−2222000000000000000000000
χ674-4444-4-4-440-44000-40000000000−22−22222200000000000000000022−22000000000000000000000
χ684-44-4-44-444-4-4-44-44400000000-44000000000000000000000000000000000000000000000
χ694-4-44-444-40-40044-40000000000000002i2−2i22i2−2i200000000−2i22i2000000000000000000000000000
χ704-4-44-444-40-40044-4000000000000000−2i22i2−2i22i2000000002i2−2i2000000000000000000000000000
χ718-8-8-88-888000000000000000000000000000000000000000000000000000000000000000

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