Finite Group Databasebeta

← Group #310621

Character table — Group #310621

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888444444444488888888888888222444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-111111111111111-1-1-11-1-1-1-111-1-1-1-1-1
χ31111111111111111111111111111-1-111111111-1-1-1-11111-1-1-1-1111-111-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111111
χ51111111111111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-1111-1-1-1-111-1-11
χ61111111111111111111111-1-1-1-11111-1-11111-1-11111-1-1-1-1-1-1-1-1-1111-1-111-1-1-1-111-1
χ71111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1111111-1-111-1
χ81111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-1-11111-1-11
χ911111111111111111-1-1-1-111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-1-1-1-11
χ1011111111111111111-1-1-1-111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1111111-1
χ1111111111111111111-1-1-1-111111-1-1-1-1111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-11111-1
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-111-11111-1-1-1-1-1-11
χ1311111111111111111-1-1-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1111
χ1411111111111111111-1-1-1-11-1-1-1-1-1-111-1-11111-1-1-1-1-1-111111111-1-1-111111-1-111-1-1-1
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1111-1-1-1111111-1-1-1
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1111
χ17222222222-222-2-2-22-22222-20000-2-2220000000022-2-200000000000-200000000000
χ18222222222-222-2-2-22-22222-20000-2-2-2-200000000-2-22200000000000200000000000
χ19222222222-222-2-2-22-2-2-2-2-2-20000222200000000-2-22200000000000-200000000000
χ20222222222-222-2-2-22-2-2-2-2-2-2000022-2-20000000022-2-200000000000200000000000
χ2122222222-22-2-2222-2-20000-2222200002222-2-2-2-2000000000000-200000000000000
χ2222222222-22-2-2222-2-20000-222220000-2-2-2-222-2-2000000000000200000000000000
χ2322222222-22-2-2222-2-20000-2-2-2-2-2000022-2-22222000000000000-200000000000000
χ2422222222-22-2-2222-2-20000-2-2-2-2-20000-2-222-2-222000000000000200000000000000
χ2522-2-22-2-2222-2-2-22-2220000-200000000002i−2i2i−2i00000022-2-2000000002i−2i000000000
χ2622-2-22-2-2222-2-2-22-2220000-200000000002i−2i2i−2i000000-2-22200000000−2i2i000000000
χ2722-2-22-2-2222-2-2-22-2220000-20000000000−2i2i−2i2i00000022-2-200000000−2i2i000000000
χ2822-2-22-2-2222-2-2-22-2220000-20000000000−2i2i−2i2i000000-2-222000000002i−2i000000000
χ2922-2-22-2-22-2222-22-2-2-22i2i−2i−2i200002i−2i00002i−2i−2i2i0000000000000002-2000000000000
χ3022-2-22-2-22-2222-22-2-2-22i2i−2i−2i200002i−2i0000−2i2i2i−2i000000000000000-22000000000000
χ3122-2-22-2-22-2222-22-2-2-2−2i−2i2i2i20000−2i2i00002i−2i−2i2i000000000000000-22000000000000
χ3222-2-22-2-22-2222-22-2-2-2−2i−2i2i2i20000−2i2i0000−2i2i2i−2i0000000000000002-2000000000000
χ3322-2-22-2-22-2-2222-22-222i2i−2i−2i-20000−2i2i00000000000000000000000000002-200002i−2i0
χ3422-2-22-2-22-2-2222-22-222i2i−2i−2i-20000−2i2i0000000000000000000000000000-220000−2i2i0
χ3522-2-22-2-22-2-2222-22-22−2i−2i2i2i-200002i−2i00000000000000000000000000002-20000−2i2i0
χ3622-2-22-2-22-2-2222-22-22−2i−2i2i2i-200002i−2i0000000000000000000000000000-2200002i−2i0
χ372-2-2-2222-2202-2000-202-22-2022−2−2002i−2i0000002−22i−2i002−22−2i2i2−i2−i200000000i2−i200000
χ382-2-2-2222-2202-2000-202-22-2022−2−200−2i2i0000002−2−2i2i002−22−2−i2−i2i2i200000000−i2i200000
χ392-2-2-2222-2202-2000-202-22-20−2−222002i−2i000000−222i−2i00−22−22−i2−i2i2i200000000−i2i200000
χ402-2-2-2222-2202-2000-202-22-20−2−22200−2i2i000000−22−2i2i00−22−22i2i2−i2−i200000000i2−i200000
χ412-2-2-2222-2202-2000-20-22-22022−2−2002i−2i0000002−2−2i2i00−22−22−i2−i2i2i200000000i2−i200000
χ422-2-2-2222-2202-2000-20-22-22022−2−200−2i2i0000002−22i−2i00−22−22i2i2−i2−i200000000−i2i200000
χ432-2-2-2222-2202-2000-20-22-220−2−222002i−2i000000−22−2i2i002−22−2i2i2−i2−i200000000−i2i200000
χ442-2-2-2222-2202-2000-20-22-220−2−22200−2i2i000000−222i−2i002−22−2−i2−i2i2i200000000i2−i200000
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000
χ46444-4-4-44-40000000000000022−2222−22000000000000002i2−2i200002i−2i2i−2i000000000000000
χ47444-4-4-44-40000000000000022−2222−2200000000000000−2i22i20000−2i2i−2i2i000000000000000
χ48444-4-4-44-400000000000000−2222−2222000000000000002i2−2i20000−2i2i−2i2i000000000000000
χ49444-4-4-44-400000000000000−2222−222200000000000000−2i22i200002i−2i2i−2i000000000000000
χ5044-4-44-4-444-4-4-44-444-4000040000000000000000000000000000000000000000000
χ514-4444-4-4-440-44000-40000000000000000000000000022−22−22220000000000000000000
χ524-4444-4-4-440-44000-400000000000000000000000000−222222−220000000000000000000
χ534-4444-4-4-4-404-4000404i−4i−4i4i00000000000000000000000000000000000000000000
χ544-4444-4-4-4-404-400040−4i4i4i−4i00000000000000000000000000000000000000000000
χ554-44-4-44-4404004-4-40000000000000004i−4i000000000000000000000000000000000
χ564-44-4-44-4404004-4-4000000000000000−4i4i000000000000000000000000000000000
χ574-44-4-44-440-400-44400000000000000000000000000000000000000000000022−22000
χ584-44-4-44-440-400-444000000000000000000000000000000000000000000000−2222000
χ594-4-44-4-4440400-4-4400000004-4-44000000000000000000000000000000000000000
χ604-4-44-4-4440400-4-440000000-444-4000000000000000000000000000000000000000
χ614-4-44-4-4440-40044-4000000000000000000000000000000022−22−2222000000000000000
χ624-4-44-4-4440-40044-40000000000000000000000000000000−222222−22000000000000000
χ634-4-4-4444-4-40-4400040000002222−22−220000000000−2222000000000000000000000000000
χ644-4-4-4444-4-40-440004000000−22−222222000000000022−22000000000000000000000000000
χ6588-88-88-8-8000000000000000000000000000000000000000000000000000000000

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