Finite Group Databasebeta

← Group #309530

Character table — Group #309530

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888882244444488888888888888884444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-111-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1111-111-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111-1-1111111-1-111-1-1-1-11111-1-1-1-11111-11-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111
χ5111111111111111111111-1-1-1-111111111111-1-1-1-1111111-1-1-1-111111111-1-1-1-11-1-1-111-1-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1111
χ7111111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1111111-1-1-111111-1-1-1
χ911111111111111111-1-1-1-11111111111111-1-11111-1-111111111-1-1-1-11111-1-1-1-1-11-1-1-1-111-1
χ1011111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-111-1-1-1-1-1-111-1-11
χ1111111111111111111-1-1-1-111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-11-111-1-111-1
χ1311111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11
χ1411111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-11111111-1
χ1511111111111111111-1-1-1-1-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111-1-1-11111-1
χ1611111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-1-1-11
χ172222222222-2-222-2-2-200002222-2000022220022-2-20000-2-200000000000000000-20000000
χ182222222222-2-222-2-2-200002222-20000-2-2-2-200-2-2-2-20000220000000000000000020000000
χ192222222222-2-222-2-2-20000-2-2-2-2-20000222200-2-2220000-2-20000000000000000020000000
χ202222222222-2-222-2-2-20000-2-2-2-2-20000-2-2-2-200222200002200000000000000000-20000000
χ2122222222-2-222-2-222-222220000-222220000220000-2-2-2-2000000000000000000-200000000
χ2222222222-2-222-2-222-222220000-2-2-2-2-20000-2-20000-2-222000000000000000000200000000
χ2322222222-2-222-2-222-2-2-2-2-20000-222220000-2-2000022-2-2000000000000000000200000000
χ2422222222-2-222-2-222-2-2-2-2-20000-2-2-2-2-200002200002222000000000000000000-200000000
χ2522-2-222-2-222-2-2-2-222-22i2i−2i−2i00002000000000000002i−2i000022-2-2000000000000002i−2i00000
χ2622-2-222-2-222-2-2-2-222-22i2i−2i−2i00002000000000000002i−2i0000-2-22200000000000000−2i2i00000
χ2722-2-222-2-222-2-2-2-222-2−2i−2i2i2i0000200000000000000−2i2i000022-2-200000000000000−2i2i00000
χ2822-2-222-2-222-2-2-2-222-2−2i−2i2i2i0000200000000000000−2i2i0000-2-222000000000000002i−2i00000
χ2922-2-222-2-2-2-22222-2-2-200002i2i−2i−2i20000000000002i−2i000000000022-2-200002i−2i00000000000
χ3022-2-222-2-2-2-22222-2-2-200002i2i−2i−2i20000000000002i−2i0000000000-2-2220000−2i2i00000000000
χ3122-2-222-2-2-2-22222-2-2-20000−2i−2i2i2i2000000000000−2i2i000000000022-2-20000−2i2i00000000000
χ3222-2-222-2-2-2-22222-2-2-20000−2i−2i2i2i2000000000000−2i2i0000000000-2-22200002i−2i00000000000
χ3322-2-222-2-2-2-2-2-2222222i2i−2i−2i2i2i−2i−2i-2000000000000−2i2i−2i2i0000000000000000002-2000000000
χ3422-2-222-2-2-2-2-2-2222222i2i−2i−2i−2i−2i2i2i-20000000000002i−2i−2i2i000000000000000000-22000000000
χ3522-2-222-2-2-2-2-2-222222−2i−2i2i2i2i2i−2i−2i-2000000000000−2i2i2i−2i000000000000000000-22000000000
χ3622-2-222-2-2-2-2-2-222222−2i−2i2i2i−2i−2i2i2i-20000000000002i−2i2i−2i0000000000000000002-2000000000
χ372-22-22-22-2002-2002-202-22-20000022-2-2i2i2−i2−i22-200000000i2−i20000i2−i2i2−i2i2i2−i2−i200000000i2−i2000
χ382-22-22-22-2002-2002-202-22-20000022-2-2−i2−i2i2i22-200000000−i2i20000−i2i2−i2i2−i2−i2i2i200000000−i2i2000
χ392-22-22-22-2002-2002-202-22-200000-2-222i2i2−i2−i2-2200000000i2−i20000i2−i2i2−i2−i2−i2i2i200000000−i2i2000
χ402-22-22-22-2002-2002-202-22-200000-2-222−i2−i2i2i2-2200000000−i2i20000−i2i2−i2i2i2i2−i2−i200000000i2−i2000
χ412-22-22-22-2002-2002-20-22-220000022-2-2i2i2−i2−i2-2200000000i2−i20000−i2i2−i2i2i2i2−i2−i200000000−i2i2000
χ422-22-22-22-2002-2002-20-22-220000022-2-2−i2−i2i2i2-2200000000−i2i20000i2−i2i2−i2−i2−i2i2i200000000i2−i2000
χ432-22-22-22-2002-2002-20-22-2200000-2-222i2i2−i2−i22-200000000i2−i20000−i2i2−i2i2−i2−i2i2i200000000i2−i2000
χ442-22-22-22-2002-2002-20-22-2200000-2-222−i2−i2i2i22-200000000−i2i20000i2−i2i2−i2i2i2−i2−i200000000−i2i2000
χ452-2-22-222-22-2002-200000002-22-20i2−i2i2−i22i−2i2i−2i002i−2i0000i2−i200i2−i2i2−i200002−22−200000000002−20
χ462-2-22-222-22-2002-200000002-22-20i2−i2i2−i2−2i2i−2i2i00−2i2i0000i2−i200i2−i2i2−i20000−22−220000000000−220
χ472-2-22-222-22-2002-200000002-22-20−i2i2−i2i22i−2i2i−2i002i−2i0000−i2i200−i2i2−i2i20000−22−220000000000−220
χ482-2-22-222-22-2002-200000002-22-20−i2i2−i2i2−2i2i−2i2i00−2i2i0000−i2i200−i2i2−i2i200002−22−200000000002−20
χ492-2-22-222-22-2002-20000000-22-220i2−i2i2−i22i−2i2i−2i00−2i2i0000i2−i200−i2i2−i2i200002−22−20000000000−220
χ502-2-22-222-22-2002-20000000-22-220i2−i2i2−i2−2i2i−2i2i002i−2i0000i2−i200−i2i2−i2i20000−22−2200000000002−20
χ512-2-22-222-22-2002-20000000-22-220−i2i2−i2i22i−2i2i−2i00−2i2i0000−i2i200i2−i2i2−i20000−22−2200000000002−20
χ522-2-22-222-22-2002-20000000-22-220−i2i2−i2i2−2i2i−2i2i002i−2i0000−i2i200i2−i2i2−i200002−22−20000000000−220
χ5344444444-4-4-4-4-4-4-4-44000000004000000000000000000000000000000000000000000000
χ5444-4-444-4-44444-4-4-4-4400000000-4000000000000000000000000000000000000000000000
χ5544-4-4-4-4440000000000000000002i2−2i2−2i22i222−22−222200000000000000000000−2i2i2i−2i0000000000000
χ5644-4-4-4-4440000000000000000002i2−2i2−2i22i2−222222−22000000000000000000002i−2i−2i2i0000000000000
χ5744-4-4-4-444000000000000000000−2i22i22i2−2i222−22−2222000000000000000000002i−2i−2i2i0000000000000
χ5844-4-4-4-444000000000000000000−2i22i22i2−2i2−222222−2200000000000000000000−2i2i2i−2i0000000000000
χ594-44-44-44-400-4400-44000000000000002i22i2−2i2−2i20000000000−2i22i20000000000000000000000000
χ604-44-44-44-400-4400-4400000000000000−2i2−2i22i22i200000000002i2−2i20000000000000000000000000
χ614-44-4-44-444-400-44000000000000000000000000000000002i2−2i2−2i22i2000000000000000000000
χ624-44-4-44-444-400-4400000000000000000000000000000000−2i22i22i2−2i2000000000000000000000
χ634-44-4-44-44-44004-400000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ644-44-4-44-44-44004-40000000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ654-4-444-4-44004-400-4400000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ664-4-444-4-44004-400-440000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ674-4-444-4-4400-44004-404i−4i−4i4i00000000000000000000000000000000000000000000000000
χ684-4-444-4-4400-44004-40−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ694-4-44-444-4-4400-440000000000002i2−2i22i2−2i2000000000000−2i22i2000000000000000000000000000
χ704-4-44-444-4-4400-44000000000000−2i22i2−2i22i20000000000002i2−2i2000000000000000000000000000
χ718888-8-8-8-8000000000000000000000000000000000000000000000000000000000000000

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