Finite Group Databasebeta

← Group #306521

Character table — Group #306521

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444442222444444888888884444444488888888888888884444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111-1-11111-1-111-1-1-1-11111-1-1-1-1-1-1-111111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-111111
χ5111111111111111111111-1-1-1-11111111111111-1-1-1-11111-1-1-1-1111111111-1-1-1-1-1-1-111-1-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1111-1-1111
χ7111111111111111111111-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-111-1-1-1-1-1-1-1111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-11111-111-1-111111-1-1-1
χ91111111111111111-1-1-1-111111111111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-11-1-1-1-111-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-11
χ111111111111111111-1-1-1-1111111-1-1-1-11111-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-1-111-1-11
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111111-1-1-111-1-111-1
χ131111111111111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-11111-111-1-1-1-11
χ141111111111111111-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-111111-1-11111-1
χ151111111111111111-1-1-1-11-1-1-1-11-1-1-1-11111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-1-111-1111111-1
χ161111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111111111111-1-1111-1-1-1-1-1-11
χ17222222222-22-22-22-20000-22222-2000022220000-2-22200-2-200000000000000000-20000000
χ18222222222-22-22-22-20000-22222-20000-2-2-2-20000-2-2-2-200220000000000000000020000000
χ19222222222-22-22-22-20000-2-2-2-2-2-200002222000022-2-200-2-20000000000000000020000000
χ20222222222-22-22-22-20000-2-2-2-2-2-20000-2-2-2-200002222002200000000000000000-20000000
χ2122222222-22-22-22-222222-20000-222220000-2-2220000-2-200000000000000-2000000000000
χ2222222222-22-22-22-222222-20000-2-2-2-2-20000-2-2-2-2000022000000000000002000000000000
χ2322222222-22-22-22-22-2-2-2-2-20000-22222000022-2-20000-2-2000000000000002000000000000
χ2422222222-22-22-22-22-2-2-2-2-20000-2-2-2-2-20000222200002200000000000000-2000000000000
χ252-222-22-2-22-2-222-2-2222-2-2-200002000000002-200000000002i2i−2i−2i0000000002i−2i0000000000
χ262-222-22-2-22-2-222-2-2222-2-2-200002000000002-20000000000−2i−2i2i2i000000000−2i2i0000000000
χ272-222-22-2-22-2-222-2-22-2-222-20000200000000-2200000000002i2i−2i−2i000000000−2i2i0000000000
χ282-222-22-2-22-2-222-2-22-2-222-20000200000000-220000000000−2i−2i2i2i0000000002i−2i0000000000
χ292-222-22-2-2-222-2-222-20000-22i2i−2i−2i20000000000002i−2i000000000022-2-200000000002i−2i00000
χ302-222-22-2-2-222-2-222-20000-22i2i−2i−2i20000000000002i−2i0000000000-2-2220000000000−2i2i00000
χ312-222-22-2-2-222-2-222-20000-2−2i−2i2i2i2000000000000−2i2i000000000022-2-20000000000−2i2i00000
χ322-222-22-2-2-222-2-222-20000-2−2i−2i2i2i2000000000000−2i2i0000000000-2-22200000000002i−2i00000
χ332-222-22-2-2-2-222-2-22222-2-222i2i−2i−2i-200000000-2200−2i2i0000000000000000000002i−2i00000000
χ342-222-22-2-2-2-222-2-22222-2-22−2i−2i2i2i-200000000-22002i−2i000000000000000000000−2i2i00000000
χ352-222-22-2-2-2-222-2-222-2-22222i2i−2i−2i-2000000002-200−2i2i000000000000000000000−2i2i00000000
χ362-222-22-2-2-2-222-2-222-2-2222−2i−2i2i2i-2000000002-2002i−2i0000000000000000000002i−2i00000000
χ372-22-22-22-2-202020-20000002i−2i2i−2i0i2i2−i2−i22i2i−2i−2i0000002-2i2−i2002−22−2000022−2−20000000000i2−i20
χ382-22-22-22-2-202020-20000002i−2i2i−2i0i2i2−i2−i2−2i−2i2i2i000000-22i2−i2002−22−20000−2−2220000000000−i2i20
χ392-22-22-22-2-202020-20000002i−2i2i−2i0−i2−i2i2i22i2i−2i−2i0000002-2−i2i200−22−220000−2−2220000000000−i2i20
χ402-22-22-22-2-202020-20000002i−2i2i−2i0−i2−i2i2i2−2i−2i2i2i000000-22−i2i200−22−22000022−2−20000000000i2−i20
χ412-22-22-22-2-202020-2000000−2i2i−2i2i0i2i2−i2−i22i2i−2i−2i000000-22i2−i200−22−22000022−2−20000000000−i2i20
χ422-22-22-22-2-202020-2000000−2i2i−2i2i0i2i2−i2−i2−2i−2i2i2i0000002-2i2−i200−22−220000−2−2220000000000i2−i20
χ432-22-22-22-2-202020-2000000−2i2i−2i2i0−i2−i2i2i22i2i−2i−2i000000-22−i2i2002−22−20000−2−2220000000000i2−i20
χ442-22-22-22-2-202020-2000000−2i2i−2i2i0−i2−i2i2i2−2i−2i2i2i0000002-2−i2i2002−22−2000022−2−20000000000−i2i20
χ452-2-22-2-22202020-20-22-22-20000002i−2i2i−2i2−22−2002i−2i0000002−200002−22−2i2−i2i2−i200000000i2−i2000
χ462-2-22-2-22202020-20-22-22-20000002i−2i2i−2i−22−22002i−2i000000−220000−22−22−i2i2−i2i200000000−i2i2000
χ472-2-22-2-22202020-20-22-22-2000000−2i2i−2i2i2−22−200−2i2i0000002−200002−22−2−i2i2−i2i200000000−i2i2000
χ482-2-22-2-22202020-20-22-22-2000000−2i2i−2i2i−22−2200−2i2i000000−220000−22−22i2−i2i2−i200000000i2−i2000
χ492-2-22-2-22202020-20-2-22-220000002i−2i2i−2i2−22−200−2i2i0000002−20000−22−22i2−i2i2−i200000000−i2i2000
χ502-2-22-2-22202020-20-2-22-220000002i−2i2i−2i−22−2200−2i2i000000−2200002−22−2−i2i2−i2i200000000i2−i2000
χ512-2-22-2-22202020-20-2-22-22000000−2i2i−2i2i2−22−2002i−2i0000002−20000−22−22−i2i2−i2i200000000i2−i2000
χ522-2-22-2-22202020-20-2-22-22000000−2i2i−2i2i−22−22002i−2i000000−2200002−22−2i2−i2i2−i200000000−i2i2000
χ5344444444-4-4-4-4-4-4-4-40000400004000000000000000000000000000000000000000000000
χ54444-4-4-4-444040-40-40000004-4-440000000000000000000000000000000000000000000000
χ55444-4-4-4-444040-40-4000000-444-40000000000000000000000000000000000000000000000
χ56444-4-4-4-44-40-4040400000000000000000000000000000002i2−2i2−2i22i2000000000000000000000
χ57444-4-4-4-44-40-404040000000000000000000000000000000−2i22i22i2−2i2000000000000000000000
χ5844-444-4-4-4040-40-404000000000000000000000000000000000022−22−222200000000000000000
χ5944-444-4-4-4040-40-4040000000000000000000000000000000000−222222−2200000000000000000
χ6044-444-4-4-40-404040-44-4-44000000000000000000000000000000000000000000000000000
χ6144-444-4-4-40-404040-4-444-4000000000000000000000000000000000000000000000000000
χ6244-4-4-444-400000000000000000022−22−22222i2−2i2−2i22i200000000000000000000−2i2i2i−2i0000000000000
χ6344-4-4-444-400000000000000000022−22−2222−2i22i22i2−2i2000000000000000000002i−2i−2i2i0000000000000
χ6444-4-4-444-4000000000000000000−222222−222i2−2i2−2i22i2000000000000000000002i−2i−2i2i0000000000000
χ6544-4-4-444-4000000000000000000−222222−22−2i22i22i2−2i200000000000000000000−2i2i2i−2i0000000000000
χ664-444-44-4-444-4-444-4-4000040000-4000000000000000000000000000000000000000000000
χ674-44-44-44-440-40-404000000000002i22i2−2i2−2i2000000000000−2i22i2000000000000000000000000000
χ684-44-44-44-440-40-40400000000000−2i2−2i22i22i20000000000002i2−2i2000000000000000000000000000
χ694-4-44-4-4440-40-404040000000000000022−2222−220000000000−22220000000000000000000000000
χ704-4-44-4-4440-40-4040400000000000000−2222−2222000000000022−220000000000000000000000000
χ718-8-8-888-88000000000000000000000000000000000000000000000000000000000000000

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