Finite Group Databasebeta

← Group #280056

Character table — Group #280056

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888884444444488888888888888884444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-1111-1-1-111-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-1-111111
χ511111111111111111111-1-1-1-1111111111111-1-1-1-1111111-1-1-1-111111111-1-1-11-1-1-1-1-1-111-1
χ611111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11
χ711111111111111111111-1-1-1-111-1-1-1-1111111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-1-11
χ811111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-111111-1-1-11111-1-111-1
χ91111111111111111-1-1-1-111111111111111-1-11111-1-111111111-1-1-1-111111-1-1-1-1-1-1-111-1-1-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-1111
χ111111111111111111-1-1-1-1111111-1-1-1-11111-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1111
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-11111111-1-1-1
χ131111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-111-11111-1-1-1-11
χ141111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1111-1-1111111-1
χ151111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1111-111-1-11111-1
χ161111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11
χ17222222222-222-2-2-2200002222-2-22222000000-2-22200-2-200000000000000-2000000000000
χ18222222222-222-2-2-2200002222-2-2-2-2-2-2000000-2-2-2-20022000000000000002000000000000
χ19222222222-222-2-2-220000-2-2-2-2-2-2222200000022-2-200-2-2000000000000002000000000000
χ20222222222-222-2-2-220000-2-2-2-2-2-2-2-2-2-20000002222002200000000000000-2000000000000
χ2122222222-22-2-2222-222220000-2-200002222-2-200002200-2-2000000000000000-2000000000
χ2222222222-22-2-2222-222220000-2-20000-2-2-2-2-2-20000-2-200220000000000000002000000000
χ2322222222-22-2-2222-2-2-2-2-20000-2-200002222220000-2-200-2-20000000000000002000000000
χ2422222222-22-2-2222-2-2-2-2-20000-2-20000-2-2-2-2220000220022000000000000000-2000000000
χ2522-22-2-2-22-202-20002000022-2-2002i2i−2i−2i22−2−200002i−2i00002−222−2−20000i2i2−i2−i200000000i2−i2000
χ2622-22-2-2-22-202-20002000022-2-2002i2i−2i−2i−2−22200002i−2i0000−22−2−2220000−i2−i2i2i200000000−i2i2000
χ2722-22-2-2-22-202-20002000022-2-200−2i−2i2i2i22−2−20000−2i2i00002−222−2−20000−i2−i2i2i200000000−i2i2000
χ2822-22-2-2-22-202-20002000022-2-200−2i−2i2i2i−2−2220000−2i2i0000−22−2−2220000i2i2−i2−i200000000i2−i2000
χ2922-22-2-2-22-202-200020000-2-222002i2i−2i−2i22−2−20000−2i2i00002−2−2−2220000i2i2−i2−i200000000−i2i2000
χ3022-22-2-2-22-202-200020000-2-222002i2i−2i−2i−2−2220000−2i2i0000−2222−2−20000−i2−i2i2i200000000i2−i2000
χ3122-22-2-2-22-202-200020000-2-22200−2i−2i2i2i22−2−200002i−2i00002−2−2−2220000−i2−i2i2i200000000i2−i2000
χ3222-22-2-2-22-202-200020000-2-22200−2i−2i2i2i−2−22200002i−2i0000−2222−2−20000i2i2−i2−i200000000−i2i2000
χ332-2-22-222-222-2-2-22-222i2i−2i−2i00002-2000000002i−2i00000000002i−2i2i−2i0000000000002-20000000
χ342-2-22-222-222-2-2-22-222i2i−2i−2i00002-2000000002i−2i0000000000−2i2i−2i2i000000000000-220000000
χ352-2-22-222-222-2-2-22-22−2i−2i2i2i00002-200000000−2i2i00000000002i−2i2i−2i000000000000-220000000
χ362-2-22-222-222-2-2-22-22−2i−2i2i2i00002-200000000−2i2i0000000000−2i2i−2i2i0000000000002-20000000
χ372-2-22-222-2-2222-22-2-22i2i−2i−2i2-22-2-2200000000−2i2i2-20000000000000000000002i−2i0000000000
χ382-2-22-222-2-2222-22-2-22i2i−2i−2i-22-22-2200000000−2i2i-22000000000000000000000−2i2i0000000000
χ392-2-22-222-2-2222-22-2-2−2i−2i2i2i2-22-2-22000000002i−2i2-2000000000000000000000−2i2i0000000000
χ402-2-22-222-2-2222-22-2-2−2i−2i2i2i-22-22-22000000002i−2i-220000000000000000000002i−2i0000000000
χ412-2-22-222-2-2-2222-22-200002-22-22-20000000000-220000000000002i2i−2i−2i00000000002i−2i00000
χ422-2-22-222-2-2-2222-22-200002-22-22-20000000000-22000000000000−2i−2i2i2i0000000000−2i2i00000
χ432-2-22-222-2-2-2222-22-20000-22-222-200000000002-20000000000002i2i−2i−2i0000000000−2i2i00000
χ442-2-22-222-2-2-2222-22-20000-22-222-200000000002-2000000000000−2i−2i2i2i00000000002i−2i00000
χ452-2-2-222-2202002-2-202i−2i2i−2i0000002−22−22-22-20000002i−2i2−2000000i2−i2i2−i22−22−20000000000i2−i20
χ462-2-2-222-2202002-2-202i−2i2i−2i0000002−22−2-22-22000000−2i2i2−2000000i2−i2i2−i2−22−220000000000−i2i20
χ472-2-2-222-2202002-2-202i−2i2i−2i000000−22−222-22-20000002i−2i−22000000−i2i2−i2i2−22−220000000000−i2i20
χ482-2-2-222-2202002-2-202i−2i2i−2i000000−22−22-22-22000000−2i2i−22000000−i2i2−i2i22−22−20000000000i2−i20
χ492-2-2-222-2202002-2-20−2i2i−2i2i0000002−22−22-22-2000000−2i2i2−2000000−i2i2−i2i22−22−20000000000−i2i20
χ502-2-2-222-2202002-2-20−2i2i−2i2i0000002−22−2-22-220000002i−2i2−2000000−i2i2−i2i2−22−220000000000i2−i20
χ512-2-2-222-2202002-2-20−2i2i−2i2i000000−22−222-22-2000000−2i2i−22000000i2−i2i2−i2−22−220000000000i2−i20
χ522-2-2-222-2202002-2-20−2i2i−2i2i000000−22−22-22-220000002i−2i−22000000i2−i2i2−i22−22−20000000000−i2i20
χ5344444444-4-4-4-4-4-4-4-40000000044000000000000000000000000000000000000000000000
χ54444-4-44-4-40400-4-4404-4-44000000000000000000000000000000000000000000000000000
χ55444-4-44-4-40400-4-440-444-4000000000000000000000000000000000000000000000000000
χ56444-4-44-4-40-40044-40000000000000000000000000000000000022−22−222200000000000000000
χ57444-4-44-4-40-40044-400000000000000000000000000000000000−222222−2200000000000000000
χ5844-44-4-4-4440-44000-4000000000000002222−22−220000000000−22220000000000000000000000000
χ5944-44-4-4-4440-44000-400000000000000−22−222222000000000022−220000000000000000000000000
χ604-4444-4-4-4404-4000-400004-4-4400000000000000000000000000000000000000000000000
χ614-4444-4-4-4404-4000-40000-444-400000000000000000000000000000000000000000000000
χ624-4444-4-4-4-40-4400040000000000000000000000000000002i2−2i2−2i22i2000000000000000000000
χ634-4444-4-4-4-40-440004000000000000000000000000000000−2i22i22i2−2i2000000000000000000000
χ644-44-4-4-4440000000000000000002i2−2i2−2i22i222−22−2222000000000000000000002i−2i−2i2i0000000000000
χ654-44-4-4-4440000000000000000002i2−2i2−2i22i2−222222−2200000000000000000000−2i2i2i−2i0000000000000
χ664-44-4-4-444000000000000000000−2i22i22i2−2i222−22−222200000000000000000000−2i2i2i−2i0000000000000
χ674-44-4-4-444000000000000000000−2i22i22i2−2i2−222222−22000000000000000000002i−2i−2i2i0000000000000
χ684-4-44-444-44-4-4-44-44400000000-44000000000000000000000000000000000000000000000
χ694-4-4-444-440-400-4440000000000022−2222−22000000000000−2222000000000000000000000000000
χ704-4-4-444-440-400-44400000000000−2222−222200000000000022−22000000000000000000000000000
χ7188-8-88-88-8000000000000000000000000000000000000000000000000000000000000000

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