Finite Group Databasebeta

← Group #305313

Character table — Group #305313

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888882244444488888888888888884444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-11111-1-111-1-1111111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111-1-1111111-1-1-1-1-1-11111-1-1-1-11-1-111-111-1-1-1-1-1
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
χ5111111111111111111111-1-1-1-1111111111-1-1-1-1111111111111-1-1-1-111111-1-1-1-1-1-1-111-1-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1111
χ7111111111111111111111-1-1-1-11-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-1-1-1-1111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111-111-1-111111-1-1-1
χ911111111111111111-1-1-1-111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-11-1-1-1-111-1
χ1011111111111111111-1-1-1-1111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111-1-11
χ1111111111111111111-1-1-1-111111-1-1-1-1111111-1-1-1-1-1-111-1-111111111-1-1-1-1-111-1-1-1-1-111-1-11
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111111-1-1-111-1-111-1
χ1311111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-11111-111-1-1-1-11
χ1411111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-111111-1-1-11111-1
χ1511111111111111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1111111111-1
χ1611111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111111-1-1111-1-1-1-1-1-11
χ172222222222-2-22-22-2-200002222-222220000-2-222000000-2-200000000000000000-20000000
χ182222222222-2-22-22-2-200002222-2-2-2-2-20000-2-2-2-2000000220000000000000000020000000
χ192222222222-2-22-22-2-20000-2-2-2-2-22222000022-2-2000000-2-20000000000000000020000000
χ202222222222-2-22-22-2-20000-2-2-2-2-2-2-2-2-2000022220000002200000000000000000-20000000
χ2122222222-2-222-22-22-222220000-200002222000022-2-2-2-200000000000000-2000000000000
χ2222222222-2-222-22-22-222220000-20000-2-2-2-20000-2-2-2-222000000000000002000000000000
χ2322222222-2-222-22-22-2-2-2-2-20000-2000022220000-2-222-2-2000000000000002000000000000
χ2422222222-2-222-22-22-2-2-2-2-20000-20000-2-2-2-2000022222200000000000000-2000000000000
χ252-22-2-222-22222-2-2-2-2222-2-222-2-2-2000000002-200002-200000000000000000002-200000000
χ262-22-2-222-22222-2-2-2-2222-2-2-2-222-200000000-2200002-20000000000000000000-2200000000
χ272-22-2-222-22222-2-2-2-22-2-22222-2-2-2000000002-20000-220000000000000000000-2200000000
χ282-22-2-222-22222-2-2-2-22-2-222-2-222-200000000-220000-2200000000000000000002-200000000
χ292-22-2-222-222-2-2-22-22-2000022-2-2200000000-2200000000002i2i−2i−2i0000000002i−2i0000000000
χ302-22-2-222-222-2-2-22-22-2000022-2-2200000000-220000000000−2i−2i2i2i000000000−2i2i0000000000
χ312-22-2-222-222-2-2-22-22-20000-2-2222000000002-200000000002i2i−2i−2i000000000−2i2i0000000000
χ322-22-2-222-222-2-2-22-22-20000-2-2222000000002-20000000000−2i−2i2i2i0000000002i−2i0000000000
χ332-22-2-222-2-2-2222-22-2-222-2-20000200000000000000-22000000002i2i−2i−2i00000000002i−2i00000
χ342-22-2-222-2-2-2222-22-2-222-2-20000200000000000000-2200000000−2i−2i2i2i0000000000−2i2i00000
χ352-22-2-222-2-2-2222-22-2-2-2-22200002000000000000002-2000000002i2i−2i−2i0000000000−2i2i00000
χ362-22-2-222-2-2-2222-22-2-2-2-22200002000000000000002-200000000−2i−2i2i2i00000000002i−2i00000
χ372-2-22-22-22002-2020-202i−2i2i−2i0000022−2−22i2i−2i−2i00002-200002−2i2−i2i2−i20000i2i2−i2−i2000000002−2000
χ382-2-22-22-22002-2020-202i−2i2i−2i0000022−2−2−2i−2i2i2i0000-2200002−2i2−i2i2−i20000−i2−i2i2i200000000−22000
χ392-2-22-22-22002-2020-202i−2i2i−2i00000−2−2222i2i−2i−2i00002-20000−22−i2i2−i2i20000−i2−i2i2i200000000−22000
χ402-2-22-22-22002-2020-202i−2i2i−2i00000−2−222−2i−2i2i2i0000-220000−22−i2i2−i2i20000i2i2−i2−i2000000002−2000
χ412-2-22-22-22002-2020-20−2i2i−2i2i0000022−2−22i2i−2i−2i0000-2200002−2−i2i2−i2i20000i2i2−i2−i200000000−22000
χ422-2-22-22-22002-2020-20−2i2i−2i2i0000022−2−2−2i−2i2i2i00002-200002−2−i2i2−i2i20000−i2−i2i2i2000000002−2000
χ432-2-22-22-22002-2020-20−2i2i−2i2i00000−2−2222i2i−2i−2i0000-220000−22i2−i2i2−i20000−i2−i2i2i2000000002−2000
χ442-2-22-22-22002-2020-20−2i2i−2i2i00000−2−222−2i−2i2i2i00002-20000−22i2−i2i2−i20000i2i2−i2−i200000000−22000
χ452-2-2-22-2222-20020-20000002i−2i2i−2i02-22-22−22−2002i−2i00002−2000000i2−i2i2−i22−22−20000000000i2−i20
χ462-2-2-22-2222-20020-20000002i−2i2i−2i02-22-2−22−22002i−2i0000−22000000−i2i2−i2i2−22−220000000000−i2i20
χ472-2-2-22-2222-20020-20000002i−2i2i−2i0-22-222−22−200−2i2i00002−2000000i2−i2i2−i2−22−220000000000−i2i20
χ482-2-2-22-2222-20020-20000002i−2i2i−2i0-22-22−22−2200−2i2i0000−22000000−i2i2−i2i22−22−20000000000i2−i20
χ492-2-2-22-2222-20020-2000000−2i2i−2i2i02-22-22−22−200−2i2i00002−2000000−i2i2−i2i22−22−20000000000−i2i20
χ502-2-2-22-2222-20020-2000000−2i2i−2i2i02-22-2−22−2200−2i2i0000−22000000i2−i2i2−i2−22−220000000000i2−i20
χ512-2-2-22-2222-20020-2000000−2i2i−2i2i0-22-222−22−2002i−2i00002−2000000−i2i2−i2i2−22−220000000000i2−i20
χ522-2-2-22-2222-20020-2000000−2i2i−2i2i0-22-22−22−22002i−2i0000−22000000i2−i2i2−i22−22−20000000000−i2i20
χ5344444444-4-4-4-4-4-4-4-44000000004000000000000000000000000000000000000000000000
χ54444-4-4-4-4400000000000000000022−22−22222i2−2i2−2i22i2000000000000000000002i−2i−2i2i0000000000000
χ55444-4-4-4-4400000000000000000022−22−2222−2i22i22i2−2i200000000000000000000−2i2i2i−2i0000000000000
χ56444-4-4-4-44000000000000000000−222222−222i2−2i2−2i22i200000000000000000000−2i2i2i−2i0000000000000
χ57444-4-4-4-44000000000000000000−222222−22−2i22i22i2−2i2000000000000000000002i−2i−2i2i0000000000000
χ5844-44-4-44-44-400-4040000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ5944-44-4-44-44-400-404000000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ6044-44-4-44-4-440040-40000000000000000000000000000000000022−22−222200000000000000000
χ6144-44-4-44-4-440040-400000000000000000000000000000000000−222222−2200000000000000000
χ6244-4-444-4-4004-40-40404i−4i−4i4i00000000000000000000000000000000000000000000000000
χ6344-4-444-4-4004-40-4040−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ6444-4-444-4-400-44040-400000000000000000000000000000022−22−2222000000000000000000000
χ6544-4-444-4-400-44040-4000000000000000000000000000000−222222−22000000000000000000000
χ664-44-4-444-4-4-4-4-44444400000000-4000000000000000000000000000000000000000000000
χ674-4-44-44-4400-440-40400000000002222−22−2200000000000000−22220000000000000000000000000
χ684-4-44-44-4400-440-4040000000000−22−2222220000000000000022−220000000000000000000000000
χ694-4-4-44-444-4400-40400000000000000022−2222−2200000000−2222000000000000000000000000000
χ704-4-4-44-444-4400-404000000000000000−2222−22220000000022−22000000000000000000000000000
χ718-8888-8-8-8000000000000000000000000000000000000000000000000000000000000000

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