Finite Group Databasebeta

← Group #282673

Character table — Group #282673

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888882244444488888888888888882224444488882
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-1111-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-111111
χ511111111111111111111-1-1-1-1111111111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1111-1-1-1
χ611111111111111111111-1-1-1-1111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-1-1111
χ711111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1111
χ811111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111111111111-1-1-111-1-1-1
χ91111111111111111-1-1-1-111111111111111-1-11111-1-11111-1-1-1-111111111-1-11-1-1-1-1-1-1-111-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-111-1-111111111-1-1-1-1-1-1-111-1-1-111-1-11
χ111111111111111111-1-1-1-1111111-1-1-1-11111-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1111-1-11
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1111111-111-1-11-1-111-1
χ131111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-11111-1-1-1-1-11
χ141111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1111-1-111-11111-1
χ151111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1111111111-1
χ161111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-11-1-1111-1-1-1-11
χ172222222222-2-2-222-200002222-2-20000222200-2-2220000-2-200000000000000-20000000000
χ182222222222-2-2-222-200002222-2-20000-2-2-2-200-2-2-2-20000220000000000000020000000000
χ192222222222-2-2-222-20000-2-2-2-2-2-2000022220022-2-20000-2-20000000000000020000000000
χ202222222222-2-2-222-20000-2-2-2-2-2-20000-2-2-2-200222200002200000000000000-20000000000
χ2122222222-2-2222-2-2222220000-2-222220000-2-2000022-2-2000000000000000000000-200000
χ2222222222-2-2222-2-2222220000-2-2-2-2-2-20000-2-20000-2-222000000000000000000000200000
χ2322222222-2-2222-2-22-2-2-2-20000-2-222220000220000-2-2-2-2000000000000000000000200000
χ2422222222-2-2222-2-22-2-2-2-20000-2-2-2-2-2-200002200002222000000000000000000000-200000
χ252222-2-2-2-22-20002-2000002i2i−2i−2i00i2i2−i2−i222-2-200002i−2i00i2−i200000022−2−2i2i2−i2−i200000000002−20
χ262222-2-2-2-22-20002-2000002i2i−2i−2i00i2i2−i2−i2-2-2220000−2i2i00i2−i200000022−2−2−i2−i2i2i20000000000−220
χ272222-2-2-2-22-20002-2000002i2i−2i−2i00−i2−i2i2i222-2-200002i−2i00−i2i2000000−2−222−i2−i2i2i20000000000−220
χ282222-2-2-2-22-20002-2000002i2i−2i−2i00−i2−i2i2i2-2-2220000−2i2i00−i2i2000000−2−222i2i2−i2−i200000000002−20
χ292222-2-2-2-22-20002-200000−2i−2i2i2i00i2i2−i2−i222-2-20000−2i2i00i2−i2000000−2−222i2i2−i2−i20000000000−220
χ302222-2-2-2-22-20002-200000−2i−2i2i2i00i2i2−i2−i2-2-22200002i−2i00i2−i2000000−2−222−i2−i2i2i200000000002−20
χ312222-2-2-2-22-20002-200000−2i−2i2i2i00−i2−i2i2i222-2-20000−2i2i00−i2i200000022−2−2−i2−i2i2i200000000002−20
χ322222-2-2-2-22-20002-200000−2i−2i2i2i00−i2−i2i2i2-2-22200002i−2i00−i2i200000022−2−2i2i2−i2−i20000000000−220
χ332-22-222-2-20022-200-22i2i−2i−2i0000002i−2i2i−2i2−22−20000002-2002−2i2i2−i2−i20000i2−i2i2−i2000000002−2000
χ342-22-222-2-20022-200-22i2i−2i−2i0000002i−2i2i−2i−22−220000002-200−22−i2−i2i2i20000−i2i2−i2i200000000−22000
χ352-22-222-2-20022-200-22i2i−2i−2i000000−2i2i−2i2i2−22−2000000-22002−2i2i2−i2−i20000−i2i2−i2i200000000−22000
χ362-22-222-2-20022-200-22i2i−2i−2i000000−2i2i−2i2i−22−22000000-2200−22−i2−i2i2i20000i2−i2i2−i2000000002−2000
χ372-22-222-2-20022-200-2−2i−2i2i2i0000002i−2i2i−2i2−22−2000000-22002−2−i2−i2i2i20000i2−i2i2−i200000000−22000
χ382-22-222-2-20022-200-2−2i−2i2i2i0000002i−2i2i−2i−22−22000000-2200−22i2i2−i2−i20000−i2i2−i2i2000000002−2000
χ392-22-222-2-20022-200-2−2i−2i2i2i000000−2i2i−2i2i2−22−20000002-2002−2−i2−i2i2i20000−i2i2−i2i2000000002−2000
χ402-22-222-2-20022-200-2−2i−2i2i2i000000−2i2i−2i2i−22−220000002-200−22i2i2−i2−i20000i2−i2i2−i200000000−22000
χ412-2-222-22-2222-2-2-2-222-22-22i−2i2i−2i2-2000000002-22i−2i00000000000000000000000002i−2i000000
χ422-2-222-22-2222-2-2-2-222-22-2−2i2i−2i2i2-2000000002-2−2i2i0000000000000000000000000−2i2i000000
χ432-2-222-22-2222-2-2-2-22-22-222i−2i2i−2i2-200000000-222i−2i0000000000000000000000000−2i2i000000
χ442-2-222-22-2222-2-2-2-22-22-22−2i2i−2i2i2-200000000-22−2i2i00000000000000000000000002i−2i000000
χ452-2-222-22-222-222-2-2-200002i−2i2i−2i-220000000000−2i2i000000002i−2i2i−2i000000000002-200000000
χ462-2-222-22-222-222-2-2-200002i−2i2i−2i-220000000000−2i2i00000000−2i2i−2i2i00000000000-2200000000
χ472-2-222-22-222-222-2-2-20000−2i2i−2i2i-2200000000002i−2i000000002i−2i2i−2i00000000000-2200000000
χ482-2-222-22-222-222-2-2-20000−2i2i−2i2i-2200000000002i−2i00000000−2i2i−2i2i000000000002-200000000
χ492-2-222-22-2-2-22-2-22222-22-20000-2200000000-22000000000000002-22-200002-200000000000
χ502-2-222-22-2-2-22-2-22222-22-20000-2200000000-2200000000000000-22-220000-2200000000000
χ512-2-222-22-2-2-22-2-2222-22-220000-22000000002-2000000000000002-22-20000-2200000000000
χ522-2-222-22-2-2-22-2-2222-22-220000-22000000002-200000000000000-22-2200002-200000000000
χ5344444444-4-4-4-4-4-4-4-40000000044000000000000000000000000000000000000000000000
χ544444-4-4-4-4-44000-44000000000002i22i2−2i2−2i2000000000000−2i22i2000000000000000000000000000
χ554444-4-4-4-4-44000-4400000000000−2i2−2i22i22i20000000000002i2−2i2000000000000000000000000000
χ5644-4-44-4-44004-4400-44i−4i−4i4i000000000000000000000000000000000000000000000000000
χ5744-4-44-4-44004-4400-4−4i4i4i−4i000000000000000000000000000000000000000000000000000
χ5844-4-44-4-4400-44-400400000000000000000000000000000022−22−2222000000000000000000000
χ5944-4-44-4-4400-44-4004000000000000000000000000000000−222222−22000000000000000000000
χ604-44-444-4-400-4-440040000000000000022−2222−220000000000−22220000000000000000000000000
χ614-44-444-4-400-4-4400400000000000000−2222−2222000000000022−220000000000000000000000000
χ624-44-4-4-44400000000000000000022−22−222222−22−2222000000000000000000002-2-220000000000000
χ634-44-4-4-44400000000000000000022−22−2222−222222−2200000000000000000000-222-20000000000000
χ644-44-4-4-444000000000000000000−222222−2222−22−222200000000000000000000-222-20000000000000
χ654-44-4-4-444000000000000000000−222222−22−222222−22000000000000000000002-2-220000000000000
χ664-4-444-44-4-4-4-44444-4000000004-4000000000000000000000000000000000000000000000
χ674-4-44-44-444-4000-44000004-4-4400000000000000000000000000000000000000000000000
χ684-4-44-44-444-4000-4400000-444-400000000000000000000000000000000000000000000000
χ694-4-44-44-44-440004-40000000000000000000000000000000000022−22−222200000000000000000
χ704-4-44-44-44-440004-400000000000000000000000000000000000−222222−2200000000000000000
χ7188-8-8-888-8000000000000000000000000000000000000000000000000000000000000000

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