Finite Group Databasebeta

← Group #309889

Character table — Group #309889

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888444444444488888888888888244444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-11-1-11111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-111-1-1-1-111111111111111111-1-1-1-1-1-1-111-1-1-1-1-1
χ411111111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-111111
χ51111111111111111111111-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-11-111-1-111-1-111-1-1-1
χ61111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1111
χ71111111111111111111111-1-1-1-1-1-111-1-11111-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1111
χ81111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-111111-1-11111-1-1-1
χ911111111111111111-1-1-1-11111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11
χ1011111111111111111-1-1-1-11111111-1-11111-1-1111111-1-1-1-11111-11-1-1-1-1-1-1-1-11111-1
χ1111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111111111-1
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1111111-1-1-1-1-1-11
χ1311111111111111111-1-1-1-11-1-1-1-111-1-111-1-111-1-1-1-1-1-1111111111-11111-1-1-1-1-1-111-1
χ1411111111111111111-1-1-1-11-1-1-1-111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-11
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-111-1-111-1-11
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1111-1-11111-1-111-1
χ1722222222222-2-2-2-22-22222-2000000-2-20000220022-2-200000000-200000000000000
χ1822222222222-2-2-2-22-22222-2000000-2-20000-2-200-2-22200000000200000000000000
χ1922222222222-2-2-2-22-2-2-2-2-2-20000002200002200-2-22200000000-200000000000000
χ2022222222222-2-2-2-22-2-2-2-2-2-2000000220000-2-20022-2-200000000200000000000000
χ2122222222-2-2-22222-2-20000-222222200-2-2-2-200-2-2000000000000020000000000000
χ2222222222-2-2-22222-2-20000-22222-2-200222200-2-20000000000000-20000000000000
χ2322222222-2-2-22222-2-20000-2-2-2-2-22200-2-22200220000000000000-20000000000000
χ2422222222-2-2-22222-2-20000-2-2-2-2-2-2-20022-2-20022000000000000020000000000000
χ2522-22-2-2-222-2-222-2-22-22i2i−2i−2i20000002i−2i00000000000000000000002i−2i0000002-2000
χ2622-22-2-2-222-2-222-2-22-22i2i−2i−2i20000002i−2i0000000000000000000000−2i2i000000-22000
χ2722-22-2-2-222-2-222-2-22-2−2i−2i2i2i2000000−2i2i00000000000000000000002i−2i000000-22000
χ2822-22-2-2-222-2-222-2-22-2−2i−2i2i2i2000000−2i2i0000000000000000000000−2i2i0000002-2000
χ2922-22-2-2-222-2-2-2-222222i2i−2i−2i-200002i−2i−2i2i2i−2i0000000000000000000000002-20000000
χ3022-22-2-2-222-2-2-2-222222i2i−2i−2i-20000−2i2i−2i2i−2i2i000000000000000000000000-220000000
χ3122-22-2-2-222-2-2-2-22222−2i−2i2i2i-200002i−2i2i−2i2i−2i000000000000000000000000-220000000
χ3222-22-2-2-222-2-2-2-22222−2i−2i2i2i-20000−2i2i2i−2i−2i2i0000000000000000000000002-20000000
χ3322-22-2-2-22-222-2-222-2-20000200002i−2i00−2i2i000000000022-2-2000000002i−2i000000000
χ3422-22-2-2-22-222-2-222-2-20000200002i−2i00−2i2i0000000000-2-22200000000−2i2i000000000
χ3522-22-2-2-22-222-2-222-2-2000020000−2i2i002i−2i000000000022-2-200000000−2i2i000000000
χ3622-22-2-2-22-222-2-222-2-2000020000−2i2i002i−2i0000000000-2-222000000002i−2i000000000
χ3722-2-222-2-2-22-20000202-22-2022−2−2000000002i−2i2−22i−2i002−22−2i2i2−i2−i200000000i2−i200000
χ3822-2-222-2-2-22-20000202-22-2022−2−200000000−2i2i2−2−2i2i002−22−2−i2−i2i2i200000000−i2i200000
χ3922-2-222-2-2-22-20000202-22-20−2−222000000002i−2i−222i−2i00−22−22−i2−i2i2i200000000−i2i200000
χ4022-2-222-2-2-22-20000202-22-20−2−22200000000−2i2i−22−2i2i00−22−22i2i2−i2−i200000000i2−i200000
χ4122-2-222-2-2-22-2000020-22-22022−2−2000000002i−2i2−2−2i2i00−22−22−i2−i2i2i200000000i2−i200000
χ4222-2-222-2-2-22-2000020-22-22022−2−200000000−2i2i2−22i−2i00−22−22i2i2−i2−i200000000−i2i200000
χ4322-2-222-2-2-22-2000020-22-220−2−222000000002i−2i−22−2i2i002−22−2i2i2−i2−i200000000−i2i200000
χ4422-2-222-2-2-22-2000020-22-220−2−22200000000−2i2i−222i−2i002−22−2−i2−i2i2i200000000i2−i200000
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000
χ46444-4-4-44-444-40000-40000000000000000000000000022−22−22220000000000000000000
χ47444-4-4-44-444-40000-400000000000000000000000000−222222−220000000000000000000
χ48444-4-4-44-4-4-440000404i−4i−4i4i00000000000000000000000000000000000000000000
χ49444-4-4-44-4-4-44000040−4i4i4i−4i00000000000000000000000000000000000000000000
χ5044-44-4-4-44-44444-4-4-440000-40000000000000000000000000000000000000000000
χ5144-4-444-4-44-440000-40000002222−22−220000000000−2222000000000000000000000000000
χ5244-4-444-4-44-440000-4000000−22−222222000000000022−22000000000000000000000000000
χ534-44-44-4-440004-44-400000000000000000000000000000002i2−2i22i2−2i2000000000000000
χ544-44-44-4-440004-44-40000000000000000000000000000000−2i22i2−2i22i2000000000000000
χ554-44-44-4-44000-44-4400000004i−4i4i−4i000000000000000000000000000000000000000
χ564-44-44-4-44000-44-440000000−4i4i−4i4i000000000000000000000000000000000000000
χ574-4-444-44-4000000000000002i2−2i2−2i22i2000000000000002i2−2i200002-2-22000000000000000
χ584-4-444-44-4000000000000002i2−2i2−2i22i200000000000000−2i22i20000-222-2000000000000000
χ594-4-444-44-400000000000000−2i22i22i2−2i2000000000000002i2−2i20000-222-2000000000000000
χ604-4-444-44-400000000000000−2i22i22i2−2i200000000000000−2i22i200002-2-22000000000000000
χ614-4-4-4-44440004-4-44000000000000000004-40000000000000000000000000000000
χ624-4-4-4-44440004-4-4400000000000000000-440000000000000000000000000000000
χ634-4-4-4-4444000-444-40000000000000000000000000000000000000000000000022−220
χ644-4-4-4-4444000-444-400000000000000000000000000000000000000000000000−22220
χ658-888-88-8-8000000000000000000000000000000000000000000000000000000000

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