Finite Group Databasebeta

← Group #312432

Character table — Group #312432

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888444444444488888888888888224444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-11-1-111-1-1-1
χ31111111111111111111111111111-1-1111111-1-1111111-1-1-1-1-1-11111-1-11-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1111
χ51111111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-111-1-1-1-111-1-111-1111-1-1-1-1-1
χ61111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-111-1-111-1-1-1-1111
χ71111111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111
χ81111111111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-111111-11111-1-1-1
χ911111111111111111-1-1-1-111111-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-111-1-11
χ1011111111111111111-1-1-1-111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-11111111-1
χ1111111111111111111-1-1-1-111111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-11-111-1-111-1
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111111111-1-1-1-1-1-1-1-11
χ1311111111111111111-1-1-1-11-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-11111-11-1-1-1-111-1
χ1411111111111111111-1-1-1-11-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-11
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1111111-1-111-1-1-1-1-1-111-1-1-1-11111-1-11
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-1111-1-1-11111-1
χ17222222222-22-22-22-2-20000-22222000022-2-222000000-2-2000000000000-200000000
χ18222222222-22-22-22-2-20000-222220000-2-222-2-2000000-2-2000000000000200000000
χ19222222222-22-22-22-2-20000-2-2-2-2-2000022-2-2-2-200000022000000000000200000000
χ20222222222-22-22-22-2-20000-2-2-2-2-20000-2-2222200000022000000000000-200000000
χ2122222222-22-22-22-22-22222-20000-2-22200000022000000-2-200000000000-20000000
χ2222222222-22-22-22-22-22222-20000-2-2-2-2000000-2-2000000220000000000020000000
χ2322222222-22-22-22-22-2-2-2-2-2-200002222000000-2-20000002200000000000-20000000
χ2422222222-22-22-22-22-2-2-2-2-2-2000022-2-200000022000000-2-20000000000020000000
χ2522-2-222-2-22-2-222-2-22-22i2i−2i−2i200002i−2i000000000000000000000000002-2002i−2i00000
χ2622-2-222-2-22-2-222-2-22-22i2i−2i−2i200002i−2i00000000000000000000000000-2200−2i2i00000
χ2722-2-222-2-22-2-222-2-22-2−2i−2i2i2i20000−2i2i000000000000000000000000002-200−2i2i00000
χ2822-2-222-2-22-2-222-2-22-2−2i−2i2i2i20000−2i2i00000000000000000000000000-22002i−2i00000
χ2922-2-222-2-2-222-2-222-2-200002000000002i−2i2i−2i00002i2i−2i−2i00000000002-200000000000
χ3022-2-222-2-2-222-2-222-2-200002000000002i−2i2i−2i0000−2i−2i2i2i0000000000-2200000000000
χ3122-2-222-2-2-222-2-222-2-20000200000000−2i2i−2i2i00002i2i−2i−2i0000000000-2200000000000
χ3222-2-222-2-2-222-2-222-2-20000200000000−2i2i−2i2i0000−2i−2i2i2i00000000002-200000000000
χ3322-2-222-2-2-2-222-2-22222i2i−2i−2i-20000−2i2i002i−2i−2i2i00000000000000002-20000000000000
χ3422-2-222-2-2-2-222-2-22222i2i−2i−2i-20000−2i2i00−2i2i2i−2i0000000000000000-220000000000000
χ3522-2-222-2-2-2-222-2-2222−2i−2i2i2i-200002i−2i002i−2i−2i2i0000000000000000-220000000000000
χ3622-2-222-2-2-2-222-2-2222−2i−2i2i2i-200002i−2i00−2i2i2i−2i00000000000000002-20000000000000
χ372-2222-2-2-20-20-2020202i−2i2i−2i022−2−2002-20000002i−2ii2−i2i2−i22−200i2i2−i2−i200000000002−2000
χ382-2222-2-2-20-20-2020202i−2i2i−2i022−2−200-22000000−2i2ii2−i2i2−i22−200−i2−i2i2i20000000000−22000
χ392-2222-2-2-20-20-2020202i−2i2i−2i0−2−222002-20000002i−2i−i2i2−i2i2−2200−i2−i2i2i20000000000−22000
χ402-2222-2-2-20-20-2020202i−2i2i−2i0−2−22200-22000000−2i2i−i2i2−i2i2−2200i2i2−i2−i200000000002−2000
χ412-2222-2-2-20-20-202020−2i2i−2i2i022−2−2002-2000000−2i2i−i2i2−i2i22−200−i2−i2i2i200000000002−2000
χ422-2222-2-2-20-20-202020−2i2i−2i2i022−2−200-220000002i−2i−i2i2−i2i22−200i2i2−i2−i20000000000−22000
χ432-2222-2-2-20-20-202020−2i2i−2i2i0−2−222002-2000000−2i2ii2−i2i2−i2−2200i2i2−i2−i20000000000−22000
χ442-2222-2-2-20-20-202020−2i2i−2i2i0−2−22200-220000002i−2ii2−i2i2−i2−2200−i2−i2i2i200000000002−2000
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000
χ46444-4-4-4-44000000000000002i2−2i22i2−2i20000000000000000002i2−2i22-22-2000000000000000
χ47444-4-4-4-44000000000000002i2−2i22i2−2i2000000000000000000−2i22i2-22-22000000000000000
χ48444-4-4-4-4400000000000000−2i22i2−2i22i20000000000000000002i2−2i2-22-22000000000000000
χ49444-4-4-4-4400000000000000−2i22i2−2i22i2000000000000000000−2i22i22-22-2000000000000000
χ5044-4-444-4-444-4-444-4-440000-40000000000000000000000000000000000000000000
χ514-4444-4-4-404040-40-40000002222−22−220000000000000000−2222000000000000000000000
χ524-4444-4-4-404040-40-4000000−22−222222000000000000000022−22000000000000000000000
χ534-44-4-444-440-40-40400000004i−4i−4i4i000000000000000000000000000000000000000
χ544-44-4-444-440-40-4040000000−4i4i4i−4i000000000000000000000000000000000000000
χ554-44-4-444-4-404040-400000000000000000000000000000002i2−2i2−2i22i2000000000000000
χ564-44-4-444-4-404040-40000000000000000000000000000000−2i22i22i2−2i2000000000000000
χ574-4-44-44-444040-40-4000000000000000000000000000000000000000000000002i2−2i20
χ584-4-44-44-444040-40-400000000000000000000000000000000000000000000000−2i22i20
χ594-4-44-44-44-40-4040400000000000000000004-400000000000000000000000000000
χ604-4-44-44-44-40-404040000000000000000000-4400000000000000000000000000000
χ614-4-4-44-444040-40-40404-4-4400000000000000000000000000000000000000000000
χ624-4-4-44-444040-40-4040-444-400000000000000000000000000000000000000000000
χ634-4-4-44-4440-404040-4000000000000000000000022−22−222200000000000000000000000
χ644-4-4-44-4440-404040-40000000000000000000000−222222−2200000000000000000000000
χ6588-88-8-88-8000000000000000000000000000000000000000000000000000000000

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