Finite Group Databasebeta

← Group #310237

Character table — Group #310237

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888444444444488888888888888222224448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-111-1
χ31111111111111111111111111111-1-111111111-1-1-1-11111-1-1-1-1-111111-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-11
χ51111111111111111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1111-1-1-11111-1-1-1-1-1
χ61111111111111111111111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11-1-1111-1-1-1-111-1-11
χ71111111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-1-1-1-111111
χ81111111111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-11111111-1-111-1
χ911111111111111111-1-1-1-111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1111-1-1-1-1111
χ1011111111111111111-1-1-1-111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1111111-1
χ1111111111111111111-1-1-1-111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-11-1-11111-1-1-1
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-11111-111-1-1-1-1-1-11
χ1311111111111111111-1-1-1-11-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111-1-111-111-1-111-1-1-1
χ1411111111111111111-1-1-1-11-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-111111111111-1-11-1-111-1-1-1-11
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-111-1-1-111-1-1111
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-111-1-1111-1-11111-1
χ17222222222-22-2-222-2-22222-20000-2-22200000000-2-22200000000-200000000000000
χ18222222222-22-2-222-2-22222-20000-2-2-2-20000000022-2-200000000200000000000000
χ19222222222-22-2-222-2-2-2-2-2-2-2000022220000000022-2-200000000-200000000000000
χ20222222222-22-2-222-2-2-2-2-2-2-2000022-2-200000000-2-22200000000200000000000000
χ2122222222-22-222-2-22-20000-22222000022-2-2-2-2-2-2000000000000000002000000000
χ2222222222-22-222-2-22-20000-222220000-2-22222-2-200000000000000000-2000000000
χ2322222222-22-222-2-22-20000-2-2-2-2-2000022-2-2222200000000000000000-2000000000
χ2422222222-22-222-2-22-20000-2-2-2-2-20000-2-222-2-222000000000000000002000000000
χ2522-22-2-22-222-2-2-22-2222i2i−2i−2i-200002i−2i00000000000000000000000000002i−2i2-200000
χ2622-22-2-22-222-2-2-22-2222i2i−2i−2i-200002i−2i0000000000000000000000000000−2i2i-2200000
χ2722-22-2-22-222-2-2-22-222−2i−2i2i2i-20000−2i2i00000000000000000000000000002i−2i-2200000
χ2822-22-2-22-222-2-2-22-222−2i−2i2i2i-20000−2i2i0000000000000000000000000000−2i2i2-200000
χ2922-22-2-22-22-2-2222-2-2-22i2i−2i−2i20000−2i2i002i−2i2i−2i000000000000000002-2000000000000
χ3022-22-2-22-22-2-2222-2-2-22i2i−2i−2i20000−2i2i00−2i2i−2i2i00000000000000000-22000000000000
χ3122-22-2-22-22-2-2222-2-2-2−2i−2i2i2i200002i−2i002i−2i2i−2i00000000000000000-22000000000000
χ3222-22-2-22-22-2-2222-2-2-2−2i−2i2i2i200002i−2i00−2i2i−2i2i000000000000000002-2000000000000
χ3322-22-2-22-2-2-2222-22-220000-2000000002i−2i−2i2i000000002i2i−2i−2i00000002-20000000000
χ3422-22-2-22-2-2-2222-22-220000-2000000002i−2i−2i2i00000000−2i−2i2i2i0000000-220000000000
χ3522-22-2-22-2-2-2222-22-220000-200000000−2i2i2i−2i000000002i2i−2i−2i0000000-220000000000
χ3622-22-2-22-2-2-2222-22-220000-200000000−2i2i2i−2i00000000−2i−2i2i2i00000002-20000000000
χ3722-2-22-2-2220200-2-2002-22-2022−2−2002i−2i0000002−2002i−2i2−22−2i2i2−i2−i2000000000000i2−i20
χ3822-2-22-2-2220200-2-2002-22-2022−2−200−2i2i0000002−200−2i2i2−22−2−i2−i2i2i2000000000000−i2i20
χ3922-2-22-2-2220200-2-2002-22-20−2−222002i−2i000000−22002i−2i−22−22−i2−i2i2i2000000000000−i2i20
χ4022-2-22-2-2220200-2-2002-22-20−2−22200−2i2i000000−2200−2i2i−22−22i2i2−i2−i2000000000000i2−i20
χ4122-2-22-2-2220200-2-200-22-22022−2−2002i−2i0000002−200−2i2i−22−22−i2−i2i2i2000000000000i2−i20
χ4222-2-22-2-2220200-2-200-22-22022−2−200−2i2i0000002−2002i−2i−22−22i2i2−i2−i2000000000000−i2i20
χ4322-2-22-2-2220200-2-200-22-220−2−222002i−2i000000−2200−2i2i2−22−2i2i2−i2−i2000000000000−i2i20
χ4422-2-22-2-2220200-2-200-22-220−2−22200−2i2i000000−22002i−2i2−22−2−i2−i2i2i2000000000000i2−i20
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000
χ46444-4-44-4-440-400-44004i−4i−4i4i00000000000000000000000000000000000000000000
χ47444-4-44-4-440-400-4400−4i4i4i−4i00000000000000000000000000000000000000000000
χ48444-4-44-4-4-404004-40000000000000000000000000002i2−2i2−2i22i20000000000000000000
χ49444-4-44-4-4-404004-4000000000000000000000000000−2i22i22i2−2i20000000000000000000
χ5044-44-4-44-4-444-4-4-444-4000040000000000000000000000000000000000000000000
χ5144-4-44-4-44-40-4004400000002222−22−220000000000−2222000000000000000000000000000
χ5244-4-44-4-44-40-400440000000−22−222222000000000022−22000000000000000000000000000
χ534-444-4-4-440404-400-40000000000000000000000000000002i2−2i22i2−2i2000000000000000
χ544-444-4-4-440404-400-4000000000000000000000000000000−2i22i2−2i22i2000000000000000
χ554-444-4-4-440-40-440040000004-44-4000000000000000000000000000000000000000
χ564-444-4-4-440-40-44004000000-44-44000000000000000000000000000000000000000
χ574-4-4444-4-4040-4400-40000000000000000004i−4i00000000000000000000000000000
χ584-4-4444-4-4040-4400-4000000000000000000−4i4i00000000000000000000000000000
χ594-4-4444-4-40-404-40040000000000000000000000000000000000000000000022−22000
χ604-4-4444-4-40-404-400400000000000000000000000000000000000000000000−2222000
χ614-4-4-4-44440000000000000022−22−222200000000000022−220000002-2-22000000000000000
χ624-4-4-4-44440000000000000022−22−2222000000000000−2222000000-222-2000000000000000
χ634-4-4-4-444400000000000000−222222−2200000000000022−22000000-222-2000000000000000
χ644-4-4-4-444400000000000000−222222−22000000000000−22220000002-2-22000000000000000
χ658-88-88-88-8000000000000000000000000000000000000000000000000000000000

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