Finite Group Databasebeta

← Group #309508

Character table — Group #309508

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888882244444488888888888888884444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-1-1111-1-111-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111-1-1111111-1-1111111-1-1-1-1-1-1-1-1111-111-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-1-111111
χ5111111111111111111111-1-1-1-111111111111-1-1-1-11111111111-1-1-1-11111-1-1-11-1-1-1-111-1-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-1111
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
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1-1111111-1-1-1
χ911111111111111111-1-1-1-11111111111111-1-11111-1-11111-1-1-1-1111111111-1-1-1-1-1-1-1-1-111-1
χ1011111111111111111-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11
χ1111111111111111111-1-1-1-111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-1-11
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-111111-1-111-1
χ1311111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-111-11111-1-1-1-11
χ1411111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1111-1-1-1111111-1
χ1511111111111111111-1-1-1-1-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-111111-1-11111-1
χ1611111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11
χ1722222222222-2-2-2-22-222220000-222220000220000-2-2-2-200000000000000000-2000000000
χ1822222222222-2-2-2-22-222220000-2-2-2-2-20000-2-20000-2-222000000000000000002000000000
χ1922222222222-2-2-2-22-2-2-2-2-20000-222220000-2-2000022-2-2000000000000000002000000000
χ2022222222222-2-2-2-22-2-2-2-2-20000-2-2-2-2-20000220000222200000000000000000-2000000000
χ2122222222-2-2-22222-2-200002222-20000222200-2-2220000-2-2000000000000-2000000000000
χ2222222222-2-2-22222-2-200002222-20000-2-2-2-200-2-2-2-20000220000000000002000000000000
χ2322222222-2-2-22222-2-20000-2-2-2-2-2000022220022-2-20000-2-20000000000002000000000000
χ2422222222-2-2-22222-2-20000-2-2-2-2-20000-2-2-2-2002222000022000000000000-2000000000000
χ2522-2-22-22-2-22-20000202i2i−2i−2i000002i2i−2i−2i22−2−22-2000000002−2i2i2−i2−i20000i2i2−i2−i2000000002−2000
χ2622-2-22-22-2-22-20000202i2i−2i−2i000002i2i−2i−2i−2−2222-200000000−22−i2−i2i2i20000−i2−i2i2i200000000−22000
χ2722-2-22-22-2-22-20000202i2i−2i−2i00000−2i−2i2i2i22−2−2-22000000002−2i2i2−i2−i20000−i2−i2i2i200000000−22000
χ2822-2-22-22-2-22-20000202i2i−2i−2i00000−2i−2i2i2i−2−222-2200000000−22−i2−i2i2i20000i2i2−i2−i2000000002−2000
χ2922-2-22-22-2-22-2000020−2i−2i2i2i000002i2i−2i−2i22−2−2-22000000002−2−i2−i2i2i20000i2i2−i2−i200000000−22000
χ3022-2-22-22-2-22-2000020−2i−2i2i2i000002i2i−2i−2i−2−222-2200000000−22i2i2−i2−i20000−i2−i2i2i2000000002−2000
χ3122-2-22-22-2-22-2000020−2i−2i2i2i00000−2i−2i2i2i22−2−22-2000000002−2−i2−i2i2i20000−i2−i2i2i2000000002−2000
χ3222-2-22-22-2-22-2000020−2i−2i2i2i00000−2i−2i2i2i−2−2222-200000000−22i2i2−i2−i20000i2i2−i2−i200000000−22000
χ3322-2-2-22-220002-22-200000022-2-20i2−i2i2−i22-22-200002-200i2−i2000000i2i2−i2−i2i2−i2i2−i20000000000i2−i20
χ3422-2-2-22-220002-22-200000022-2-20i2−i2i2−i2-22-220000-2200i2−i2000000i2i2−i2−i2−i2i2−i2i20000000000−i2i20
χ3522-2-2-22-220002-22-200000022-2-20−i2i2−i2i22-22-200002-200−i2i2000000−i2−i2i2i2−i2i2−i2i20000000000−i2i20
χ3622-2-2-22-220002-22-200000022-2-20−i2i2−i2i2-22-220000-2200−i2i2000000−i2−i2i2i2i2−i2i2−i20000000000i2−i20
χ3722-2-2-22-220002-22-2000000-2-2220i2−i2i2−i22-22-20000-2200i2−i2000000−i2−i2i2i2i2−i2i2−i20000000000−i2i20
χ3822-2-2-22-220002-22-2000000-2-2220i2−i2i2−i2-22-2200002-200i2−i2000000−i2−i2i2i2−i2i2−i2i20000000000i2−i20
χ3922-2-2-22-220002-22-2000000-2-2220−i2i2−i2i22-22-20000-2200−i2i2000000i2i2−i2−i2−i2i2−i2i20000000000i2−i20
χ4022-2-2-22-220002-22-2000000-2-2220−i2i2−i2i2-22-2200002-200−i2i2000000i2i2−i2−i2i2−i2i2−i20000000000−i2i20
χ412-22-222-2-22-2-222-2-22-22i−2i2i−2i00002000000000000002i−2i000000002-22-200000000002i−2i00000
χ422-22-222-2-22-2-222-2-22-22i−2i2i−2i00002000000000000002i−2i00000000-22-220000000000−2i2i00000
χ432-22-222-2-22-2-222-2-22-2−2i2i−2i2i0000200000000000000−2i2i000000002-22-20000000000−2i2i00000
χ442-22-222-2-22-2-222-2-22-2−2i2i−2i2i0000200000000000000−2i2i00000000-22-2200000000002i−2i00000
χ452-22-222-2-22-2-2-2-222222i−2i2i−2i2i−2i2i−2i-200000000002i−2i00−2i2i000000000000000002-20000000000
χ462-22-222-2-22-2-2-2-222222i−2i2i−2i−2i2i−2i2i-20000000000−2i2i00−2i2i00000000000000000-220000000000
χ472-22-222-2-22-2-2-2-22222−2i2i−2i2i2i−2i2i−2i-200000000002i−2i002i−2i00000000000000000-220000000000
χ482-22-222-2-22-2-2-2-22222−2i2i−2i2i−2i2i−2i2i-20000000000−2i2i002i−2i000000000000000002-20000000000
χ492-22-222-2-2-222-2-222-2-200002i−2i2i−2i20000000000−2i2i000000002-22-20000000000002i−2i0000000
χ502-22-222-2-2-222-2-222-2-200002i−2i2i−2i20000000000−2i2i00000000-22-22000000000000−2i2i0000000
χ512-22-222-2-2-222-2-222-2-20000−2i2i−2i2i200000000002i−2i000000002-22-2000000000000−2i2i0000000
χ522-22-222-2-2-222-2-222-2-20000−2i2i−2i2i200000000002i−2i00000000-22-220000000000002i−2i0000000
χ5344444444-4-4-4-4-4-4-4-44000000004000000000000000000000000000000000000000000000
χ544444-4-4-4-400000000000000000022−22−222222−22−2222000000000000000000002-2-220000000000000
χ554444-4-4-4-400000000000000000022−22−2222−222222−2200000000000000000000-222-20000000000000
χ564444-4-4-4-4000000000000000000−222222−2222−22−222200000000000000000000-222-20000000000000
χ574444-4-4-4-4000000000000000000−222222−22−222222−22000000000000000000002-2-220000000000000
χ5844-4-44-44-44-440000-4000000000000002222−22−220000000000−22220000000000000000000000000
χ5944-4-44-44-44-440000-400000000000000−22−222222000000000022−220000000000000000000000000
χ6044-4-4-44-44000-44-44000000000002i2−2i22i2−2i2000000000000−2i22i2000000000000000000000000000
χ6144-4-4-44-44000-44-4400000000000−2i22i2−2i22i20000000000002i2−2i2000000000000000000000000000
χ624-44-444-4-4-44444-4-4-4400000000-4000000000000000000000000000000000000000000000
χ634-4-444-4-4444-40000-40000000000000000000000000000002i2−2i2−2i22i2000000000000000000000
χ644-4-444-4-4444-40000-4000000000000000000000000000000−2i22i22i2−2i2000000000000000000000
χ654-4-444-4-44-4-440000404-4-4400000000000000000000000000000000000000000000000000
χ664-4-444-4-44-4-44000040-444-400000000000000000000000000000000000000000000000000
χ674-4-44-444-40004-4-44000000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ684-4-44-444-40004-4-4400000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ694-4-44-444-4000-444-40000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ704-4-44-444-4000-444-4000000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ718-88-8-8-888000000000000000000000000000000000000000000000000000000000000000

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