Finite Group Databasebeta

← Group #282747

Character table — Group #282747

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444442222444444888888882244444488888888888888882244444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-111111-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111-1-11111-1-1111111-1-1-1-1-1-1-1-1111-111-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111111
χ511111111111111111111-1-1-1-11111111111-1-11111-1-111111111-1-1-1-11111-1-1-11-1-1-1-111-1-1-1
χ611111111111111111111-1-1-1-1111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111
χ711111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1111
χ811111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111111-1-1-11111-1-1-1
χ91111111111111111-1-1-1-11111111111111111-1-1-1-1111111-1-1-1-111111111-1-11-1-1-1-1-1-1-111-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-111-1-1-1-1-1-111-1-11
χ111111111111111111-1-1-1-1111111-1-1-1-111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1111111-11-1-111-1-111-1
χ131111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-11
χ141111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-11-111111111-1
χ151111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1111-1-11111-1
χ161111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-1-1-11
χ172222222222-2-2-222-200002222-2-200002222220000-2-200-2-200000000000000-20000000000
χ182222222222-2-2-222-200002222-2-20000-2-2-2-2-2-20000-2-200220000000000000020000000000
χ192222222222-2-2-222-20000-2-2-2-2-2-200002222-2-200002200-2-20000000000000020000000000
χ202222222222-2-2-222-20000-2-2-2-2-2-20000-2-2-2-222000022002200000000000000-20000000000
χ2122222222-2-2222-2-2222220000-2-2222200000022-2-200-2-200000000000000000-2000000000
χ2222222222-2-2222-2-2222220000-2-2-2-2-2-2000000-2-2-2-20022000000000000000002000000000
χ2322222222-2-2222-2-22-2-2-2-20000-2-22222000000-2-22200-2-2000000000000000002000000000
χ2422222222-2-2222-2-22-2-2-2-20000-2-2-2-2-2-20000002222002200000000000000000-2000000000
χ2522-22-2-22-22-20002-20000022-2-200i2i2−i2−i222-2-22-2000000i2−i2000000i2i2−i2−i2i2i2−i2−i20000000000i2−i20
χ2622-22-2-22-22-20002-20000022-2-200i2i2−i2−i2-2-222-22000000i2−i2000000i2i2−i2−i2−i2−i2i2i20000000000−i2i20
χ2722-22-2-22-22-20002-20000022-2-200−i2−i2i2i222-2-22-2000000−i2i2000000−i2−i2i2i2−i2−i2i2i20000000000−i2i20
χ2822-22-2-22-22-20002-20000022-2-200−i2−i2i2i2-2-222-22000000−i2i2000000−i2−i2i2i2i2i2−i2−i20000000000i2−i20
χ2922-22-2-22-22-20002-200000-2-22200i2i2−i2−i222-2-2-22000000i2−i2000000−i2−i2i2i2i2i2−i2−i20000000000−i2i20
χ3022-22-2-22-22-20002-200000-2-22200i2i2−i2−i2-2-2222-2000000i2−i2000000−i2−i2i2i2−i2−i2i2i20000000000i2−i20
χ3122-22-2-22-22-20002-200000-2-22200−i2−i2i2i222-2-2-22000000−i2i2000000i2i2−i2−i2−i2−i2i2i20000000000i2−i20
χ3222-22-2-22-22-20002-200000-2-22200−i2−i2i2i2-2-2222-2000000−i2i2000000i2i2−i2−i2i2i2−i2−i20000000000−i2i20
χ332-2-222-2-22222-2-2-2-2222-2-22i−2i2i−2i2-20000000000002-22i−2i000000000000000000002i−2i0000000
χ342-2-222-2-22222-2-2-2-2222-2-2−2i2i−2i2i2-20000000000002-2−2i2i00000000000000000000−2i2i0000000
χ352-2-222-2-22222-2-2-2-22-2-2222i−2i2i−2i2-2000000000000-222i−2i00000000000000000000−2i2i0000000
χ362-2-222-2-22222-2-2-2-22-2-222−2i2i−2i2i2-2000000000000-22−2i2i000000000000000000002i−2i0000000
χ372-2-222-2-2222-222-2-2-200002i−2i2i−2i-2200000000000000−2i2i00002i2i−2i−2i000000002-200000000000
χ382-2-222-2-2222-222-2-2-200002i−2i2i−2i-2200000000000000−2i2i0000−2i−2i2i2i00000000-2200000000000
χ392-2-222-2-2222-222-2-2-20000−2i2i−2i2i-22000000000000002i−2i00002i2i−2i−2i00000000-2200000000000
χ402-2-222-2-2222-222-2-2-20000−2i2i−2i2i-22000000000000002i−2i0000−2i−2i2i2i000000002-200000000000
χ412-2-222-2-22-2-22-2-222222-2-20000-22000000000000-2200000000002-22-200000000002-200000
χ422-2-222-2-22-2-22-2-222222-2-20000-22000000000000-220000000000-22-220000000000-2200000
χ432-2-222-2-22-2-22-2-2222-2-2220000-220000000000002-200000000002-22-20000000000-2200000
χ442-2-222-2-22-2-22-2-2222-2-2220000-220000000000002-20000000000-22-2200000000002-200000
χ452-2-2-2222-20022-200-22-22-20000002i−2i2i−2i2−22−2002i−2i0000002−22−22−20000i2−i2i2−i200000000i2−i2000
χ462-2-2-2222-20022-200-22-22-20000002i−2i2i−2i−22−22002i−2i000000−22−22−220000−i2i2−i2i200000000−i2i2000
χ472-2-2-2222-20022-200-22-22-2000000−2i2i−2i2i2−22−200−2i2i0000002−22−22−20000−i2i2−i2i200000000−i2i2000
χ482-2-2-2222-20022-200-22-22-2000000−2i2i−2i2i−22−2200−2i2i000000−22−22−220000i2−i2i2−i200000000i2−i2000
χ492-2-2-2222-20022-200-2-22-220000002i−2i2i−2i2−22−200−2i2i0000002−2−22−220000i2−i2i2−i200000000−i2i2000
χ502-2-2-2222-20022-200-2-22-220000002i−2i2i−2i−22−2200−2i2i000000−222−22−20000−i2i2−i2i200000000i2−i2000
χ512-2-2-2222-20022-200-2-22-22000000−2i2i−2i2i2−22−2002i−2i0000002−2−22−220000−i2i2−i2i200000000i2−i2000
χ522-2-2-2222-20022-200-2-22-22000000−2i2i−2i2i−22−22002i−2i000000−222−22−20000i2−i2i2−i200000000−i2i2000
χ5344444444-4-4-4-4-4-4-4-40000000044000000000000000000000000000000000000000000000
χ54444-44-4-4-4004-4400-44-4-44000000000000000000000000000000000000000000000000000
χ55444-44-4-4-4004-4400-4-444-4000000000000000000000000000000000000000000000000000
χ56444-44-4-4-400-44-40040000000000000000000000000000002i2−2i2−2i22i2000000000000000000000
χ57444-44-4-4-400-44-4004000000000000000000000000000000−2i22i22i2−2i2000000000000000000000
χ5844-44-4-44-4-44000-44000000000002i22i2−2i2−2i2000000000000−2i22i2000000000000000000000000000
χ5944-44-4-44-4-44000-4400000000000−2i2−2i22i22i20000000000002i2−2i2000000000000000000000000000
χ604-444-44-4-44-4000-44000004i−4i−4i4i00000000000000000000000000000000000000000000000
χ614-444-44-4-44-4000-4400000−4i4i4i−4i00000000000000000000000000000000000000000000000
χ624-444-44-4-4-440004-4000000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ634-444-44-4-4-440004-400000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ644-44-4-4-44400000000000000000022−22−222222−22−2222000000000000000000002-2-220000000000000
χ654-44-4-4-44400000000000000000022−22−2222−222222−2200000000000000000000-222-20000000000000
χ664-44-4-4-444000000000000000000−222222−2222−22−222200000000000000000000-222-20000000000000
χ674-44-4-4-444000000000000000000−222222−22−222222−22000000000000000000002-2-220000000000000
χ684-4-444-4-44-4-4-44444-4000000004-4000000000000000000000000000000000000000000000
χ694-4-4-4444-400-4-440040000000000000022−2222−220000000000−22220000000000000000000000000
χ704-4-4-4444-400-4-4400400000000000000−2222−2222000000000022−220000000000000000000000000
χ7188-8-8-88-88000000000000000000000000000000000000000000000000000000000000000

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