Finite Group Databasebeta

← Group #306458

Character table — Group #306458

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888884444444488888888888888882444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-111111-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111-1-11111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-111111
χ5111111111111111111111-1-1-1-111111111111-1-111-1-111-1-1-1-111111111111-1-1-1-1-1-1-111-1-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-111-1-1-1-1-1-1-1111
χ7111111111111111111111-1-1-1-11-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1111-1-1111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111-111-1-111111-1-1-1
χ911111111111111111-1-1-1-11111111111111-1-111-1-11111111111-1-1-1-11111-1-1-1-1-11-1-1-1-111-1
χ1011111111111111111-1-1-1-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111-1-11-1-111-1-11
χ1111111111111111111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-11
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111-1-1-111-1-111-1
χ1311111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-11111-111-1-1-1-11
χ1411111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11-1-111-1111111-1
χ1511111111111111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-111111-1-11111-1
χ1611111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1111111111-1-1111-1-1-1-1-1-11
χ17222222222-22-22-22-2-222220000-200002222-2-2002200-2-200000000000000-2000000000000
χ18222222222-22-22-22-2-222220000-20000-2-2-2-2-2-200-2-20022000000000000002000000000000
χ19222222222-22-22-22-2-2-2-2-2-20000-2000022222200-2-200-2-2000000000000002000000000000
χ20222222222-22-22-22-2-2-2-2-2-20000-20000-2-2-2-2220022002200000000000000-2000000000000
χ2122222222-22-22-22-22-200002222-222220000002200-2-2000000-2-20000000000000-20000000
χ2222222222-22-22-22-22-200002222-2-2-2-2-2000000-2-200-2-200000022000000000000020000000
χ2322222222-22-22-22-22-20000-2-2-2-2-22222000000-2-20022000000-2-2000000000000020000000
χ2422222222-22-22-22-22-20000-2-2-2-2-2-2-2-2-2000000220022000000220000000000000-20000000
χ252-222-2-22-22-2-222-2-22-200002i2i−2i−2i2000000000000002i−2i0000000022-2-200000000002i−2i00000
χ262-222-2-22-22-2-222-2-22-200002i2i−2i−2i2000000000000002i−2i00000000-2-2220000000000−2i2i00000
χ272-222-2-22-22-2-222-2-22-20000−2i−2i2i2i200000000000000−2i2i0000000022-2-20000000000−2i2i00000
χ282-222-2-22-22-2-222-2-22-20000−2i−2i2i2i200000000000000−2i2i00000000-2-22200000000002i−2i00000
χ292-222-2-22-2-222-2-222-2-222-2-200002000000002-2000000002i2i−2i−2i000000000002i−2i0000000000
χ302-222-2-22-2-222-2-222-2-222-2-200002000000002-200000000−2i−2i2i2i00000000000−2i2i0000000000
χ312-222-2-22-2-222-2-222-2-2-2-2220000200000000-22000000002i2i−2i−2i00000000000−2i2i0000000000
χ322-222-2-22-2-222-2-222-2-2-2-2220000200000000-2200000000−2i−2i2i2i000000000002i−2i0000000000
χ332-222-2-22-2-2-222-2-222222-2-22i2i−2i−2i-200000000-220000−2i2i00000000000000000002i−2i00000000
χ342-222-2-22-2-2-222-2-222222-2-2−2i−2i2i2i-200000000-2200002i−2i0000000000000000000−2i2i00000000
χ352-222-2-22-2-2-222-2-2222-2-2222i2i−2i−2i-2000000002-20000−2i2i0000000000000000000−2i2i00000000
χ362-222-2-22-2-2-222-2-2222-2-222−2i−2i2i2i-2000000002-200002i−2i00000000000000000002i−2i00000000
χ372-22-22-2-222020-20-2002-22-20000022−2−22i2i−2i−2i00002i−2i000000002−22−22−2i2i2−i2−i200000000i2−i2000
χ382-22-22-2-222020-20-2002-22-20000022−2−2−2i−2i2i2i0000−2i2i000000002−22−22−2−i2−i2i2i200000000−i2i2000
χ392-22-22-2-222020-20-2002-22-200000−2−2222i2i−2i−2i00002i−2i00000000−22−22−22−i2−i2i2i200000000−i2i2000
χ402-22-22-2-222020-20-2002-22-200000−2−222−2i−2i2i2i0000−2i2i00000000−22−22−22i2i2−i2−i200000000i2−i2000
χ412-22-22-2-222020-20-200-22-220000022−2−22i2i−2i−2i0000−2i2i000000002−2−22−22i2i2−i2−i200000000−i2i2000
χ422-22-22-2-222020-20-200-22-220000022−2−2−2i−2i2i2i00002i−2i000000002−2−22−22−i2−i2i2i200000000i2−i2000
χ432-22-22-2-222020-20-200-22-2200000−2−2222i2i−2i−2i0000−2i2i00000000−222−22−2−i2−i2i2i200000000i2−i2000
χ442-22-22-2-222020-20-200-22-2200000−2−222−2i−2i2i2i00002i−2i00000000−222−22−2i2i2−i2−i200000000−i2i2000
χ452-2-2-2222-20-202020-2000002-22-202-22-2i2−i2i2−i2002-20000i2−i2i2−i2i2−i2000000i2−i2i2−i20000000000i2−i20
χ462-2-2-2222-20-202020-2000002-22-202-22-2−i2i2−i2i2002-20000−i2i2−i2i2−i2i2000000−i2i2−i2i20000000000−i2i20
χ472-2-2-2222-20-202020-2000002-22-20-22-22i2−i2i2−i200-220000i2−i2i2−i2i2−i2000000−i2i2−i2i20000000000−i2i20
χ482-2-2-2222-20-202020-2000002-22-20-22-22−i2i2−i2i200-220000−i2i2−i2i2−i2i2000000i2−i2i2−i20000000000i2−i20
χ492-2-2-2222-20-202020-200000-22-2202-22-2i2−i2i2−i200-220000i2−i2−i2i2−i2i2000000i2−i2i2−i20000000000−i2i20
χ502-2-2-2222-20-202020-200000-22-2202-22-2−i2i2−i2i200-220000−i2i2i2−i2i2−i2000000−i2i2−i2i20000000000i2−i20
χ512-2-2-2222-20-202020-200000-22-220-22-22i2−i2i2−i2002-20000i2−i2−i2i2−i2i2000000−i2i2−i2i20000000000i2−i20
χ522-2-2-2222-20-202020-200000-22-220-22-22−i2i2−i2i2002-20000−i2i2i2−i2i2−i2000000i2−i2i2−i20000000000−i2i20
χ5344444444-4-4-4-4-4-4-4-44000000004000000000000000000000000000000000000000000000
χ54444-4-44-4-440-40-4040000000000000000000000000000000000022−22−222200000000000000000
χ55444-4-44-4-440-40-40400000000000000000000000000000000000−222222−2200000000000000000
χ56444-4-44-4-4-404040-4004-4-4400000000000000000000000000000000000000000000000000
χ57444-4-44-4-4-404040-400-444-400000000000000000000000000000000000000000000000000
χ5844-444-4-4-400000000000000000022−22−222222−22−2222000000000000000000002-2-220000000000000
χ5944-444-4-4-400000000000000000022−22−2222−222222−2200000000000000000000-222-20000000000000
χ6044-444-4-4-4000000000000000000−222222−2222−22−222200000000000000000000-222-20000000000000
χ6144-444-4-4-4000000000000000000−222222−22−222222−22000000000000000000002-2-220000000000000
χ6244-4-4-4-44404040-40-4000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ6344-4-4-4-44404040-40-400000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ6444-4-4-4-4440-40-40404000000000000000000000000000022−22−222200000000000000000000000
χ6544-4-4-4-4440-40-404040000000000000000000000000000−222222−2200000000000000000000000
χ664-444-4-44-444-4-444-4-4400000000-4000000000000000000000000000000000000000000000
χ674-44-44-4-44-40-40404000000000002222−22−22000000000000000000−2222000000000000000000000
χ684-44-44-4-44-40-4040400000000000−22−22222200000000000000000022−22000000000000000000000
χ694-4-4-4444-4040-40-404000000000000002i2−2i22i2−2i200000000−2i22i2000000000000000000000000000
χ704-4-4-4444-4040-40-40400000000000000−2i22i2−2i22i2000000002i2−2i2000000000000000000000000000
χ718-8-88-88-88000000000000000000000000000000000000000000000000000000000000000

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