Finite Group Databasebeta

← Group #309513

Character table — Group #309513

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888882222444488888888888888884444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-111-1-1111111-1-11111-1-1-1-1-1-1-1-11-11111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111-1-1111111-1-111-1-1-1-11111-1-1-1-1-1111-1-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111
χ5111111111111111111111-1-1-1-111111111111-1-111-1-11111-1-1-1-1111111111-1-1-1-1-1-1-111-1-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1111
χ7111111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-11-1-1111111-1-1-1
χ911111111111111111-1-1-1-11111111111111-1-111-1-11111111111-1-1-1-11111-11-1-1-1-1-1-1-1-111-1
χ1011111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-11
χ1111111111111111111-1-1-1-111111-1-1-1-111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-11
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-1-11111-1-111-1
χ1311111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-11
χ1411111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-111111-1-11111-1
χ1511111111111111111-1-1-1-1-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-111-1-1111111-1
χ1611111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11
χ17222222222-222-2-22-2-200002222-200002222002200-2-200-2-20000000000000-200000000000
χ18222222222-222-2-22-2-200002222-20000-2-2-2-200-2-200-2-200220000000000000200000000000
χ19222222222-222-2-22-2-20000-2-2-2-2-20000222200-2-2002200-2-20000000000000200000000000
χ20222222222-222-2-22-2-20000-2-2-2-2-20000-2-2-2-20022002200220000000000000-200000000000
χ2122222222-22-2-222-22-222220000-2222200002200-2-200-2-200000000000000-2000000000000
χ2222222222-22-2-222-22-222220000-2-2-2-2-20000-2-200-2-20022000000000000002000000000000
χ2322222222-22-2-222-22-2-2-2-2-20000-222220000-2-2002200-2-2000000000000002000000000000
χ2422222222-22-2-222-22-2-2-2-2-20000-2-2-2-2-20000220022002200000000000000-2000000000000
χ252-2222-2-2-222-2-2-2-22222i2i−2i−2i2i2i−2i−2i-20000000000002i−2i2i−2i0000000000000000002-2000000000
χ262-2222-2-2-222-2-2-2-22222i2i−2i−2i−2i−2i2i2i-20000000000002i−2i−2i2i000000000000000000-22000000000
χ272-2222-2-2-222-2-2-2-2222−2i−2i2i2i2i2i−2i−2i-2000000000000−2i2i2i−2i000000000000000000-22000000000
χ282-2222-2-2-222-2-2-2-2222−2i−2i2i2i−2i−2i2i2i-2000000000000−2i2i−2i2i0000000000000000002-2000000000
χ292-2222-2-2-22-2-2-2222-2-200002i2i−2i−2i200000000000000−2i2i0000000022-2-200000000002i−2i00000
χ302-2222-2-2-22-2-2-2222-2-200002i2i−2i−2i200000000000000−2i2i00000000-2-2220000000000−2i2i00000
χ312-2222-2-2-22-2-2-2222-2-20000−2i−2i2i2i2000000000000002i−2i0000000022-2-20000000000−2i2i00000
χ322-2222-2-2-22-2-2-2222-2-20000−2i−2i2i2i2000000000000002i−2i00000000-2-22200000000002i−2i00000
χ332-2222-2-2-2-2222-2-2-22-22i2i−2i−2i00002000000000000−2i2i00000022-2-20000000000002i−2i0000000
χ342-2222-2-2-2-2222-2-2-22-22i2i−2i−2i00002000000000000−2i2i000000-2-222000000000000−2i2i0000000
χ352-2222-2-2-2-2222-2-2-22-2−2i−2i2i2i000020000000000002i−2i00000022-2-2000000000000−2i2i0000000
χ362-2222-2-2-2-2222-2-2-22-2−2i−2i2i2i000020000000000002i−2i000000-2-2220000000000002i−2i0000000
χ372-22-2-22-2202002-20-202i−2i2i−2i000002i2i−2i−2i22−2−22-2000000002−20000i2−i2i2−i2i2i2−i2−i2000000002−2000
χ382-22-2-22-2202002-20-202i−2i2i−2i000002i2i−2i−2i−2−2222-200000000−220000−i2i2−i2i2−i2−i2i2i200000000−22000
χ392-22-2-22-2202002-20-202i−2i2i−2i00000−2i−2i2i2i22−2−2-22000000002−20000i2−i2i2−i2−i2−i2i2i200000000−22000
χ402-22-2-22-2202002-20-202i−2i2i−2i00000−2i−2i2i2i−2−222-2200000000−220000−i2i2−i2i2i2i2−i2−i2000000002−2000
χ412-22-2-22-2202002-20-20−2i2i−2i2i000002i2i−2i−2i22−2−2-22000000002−20000−i2i2−i2i2i2i2−i2−i200000000−22000
χ422-22-2-22-2202002-20-20−2i2i−2i2i000002i2i−2i−2i−2−222-2200000000−220000i2−i2i2−i2−i2−i2i2i2000000002−2000
χ432-22-2-22-2202002-20-20−2i2i−2i2i00000−2i−2i2i2i22−2−22-2000000002−20000−i2i2−i2i2−i2−i2i2i2000000002−2000
χ442-22-2-22-2202002-20-20−2i2i−2i2i00000−2i−2i2i2i−2−2222-200000000−220000i2−i2i2−i2i2i2−i2−i200000000−22000
χ452-2-22-2-222202-200-20000002i−2i2i−2i02−22−22i−2i2i−2i002-200002−200i2−i2i2−i20000i2−i2i2−i200000000002−20
χ462-2-22-2-222202-200-20000002i−2i2i−2i02−22−2−2i2i−2i2i00-2200002−200i2−i2i2−i20000−i2i2−i2i20000000000−220
χ472-2-22-2-222202-200-20000002i−2i2i−2i0−22−222i−2i2i−2i002-20000−2200−i2i2−i2i20000−i2i2−i2i20000000000−220
χ482-2-22-2-222202-200-20000002i−2i2i−2i0−22−22−2i2i−2i2i00-220000−2200−i2i2−i2i20000i2−i2i2−i200000000002−20
χ492-2-22-2-222202-200-2000000−2i2i−2i2i02−22−22i−2i2i−2i00-2200002−200−i2i2−i2i20000i2−i2i2−i20000000000−220
χ502-2-22-2-222202-200-2000000−2i2i−2i2i02−22−2−2i2i−2i2i002-200002−200−i2i2−i2i20000−i2i2−i2i200000000002−20
χ512-2-22-2-222202-200-2000000−2i2i−2i2i0−22−222i−2i2i−2i00-220000−2200i2−i2i2−i20000−i2i2−i2i200000000002−20
χ522-2-22-2-222202-200-2000000−2i2i−2i2i0−22−22−2i2i−2i2i002-20000−2200i2−i2i2−i20000i2−i2i2−i20000000000−220
χ5344444444-4-4-4-4-4-4-4-44000000004000000000000000000000000000000000000000000000
χ54444-4-4-44-40400-440-404-4-4400000000000000000000000000000000000000000000000000
χ55444-4-4-44-40400-440-40-444-400000000000000000000000000000000000000000000000000
χ56444-4-4-44-40-4004-40400000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ57444-4-4-44-40-4004-4040000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ5844-44-44-4-440-4400-40000004-4-440000000000000000000000000000000000000000000000
χ5944-44-44-4-440-4400-4000000-444-40000000000000000000000000000000000000000000000
χ6044-44-44-4-4-404-400400000000000000000000000000000002i2−2i2−2i22i2000000000000000000000
χ6144-44-44-4-4-404-40040000000000000000000000000000000−2i22i22i2−2i2000000000000000000000
χ6244-4-44-4-440000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000-222-20000000000000
χ6344-4-44-4-440000000000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000002-2-220000000000000
χ6444-4-44-4-44000000000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000002-2-220000000000000
χ6544-4-44-4-44000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000-222-20000000000000
χ664-4444-4-4-4-4-44444-4-4400000000-4000000000000000000000000000000000000000000000
χ674-44-4-44-440-400-4404000000000000002222−22−220000000000−22220000000000000000000000000
χ684-44-4-44-440-400-440400000000000000−22−222222000000000022−220000000000000000000000000
χ694-4-44-4-444-40-440040000000000022−2222−22000000000000−2222000000000000000000000000000
χ704-4-44-4-444-40-4400400000000000−2222−222200000000000022−22000000000000000000000000000
χ718-8-8-8888-8000000000000000000000000000000000000000000000000000000000000000

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