Finite Group Databasebeta

← Group #306613

Character table — Group #306613

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888222244444488888888888888444444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-11111-1-11111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111-1-111111111111111-1-1-1-1-1-1-11-1-111-1-1-1
χ411111111111111111111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-1-1-111-1-1111
χ51111111111111111111111-1-1-1-111-1-1111111-1-111-1-1-1-111-1-1-1-111-111-1-11-1-1-1-111-1
χ61111111111111111111111-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-11111-1-11
χ71111111111111111111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-111-1-1-1-1-1-11-1-111111-1-1-1-11
χ81111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-111-1-1-11111-1
χ911111111111111111-1-1-1-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-11-1-111-1-11
χ1011111111111111111-1-1-1-1111111111-1-1-1-1111111-1-1-1-1111111-1-11-1-1-1-1-111-1-111-1
χ1111111111111111111-1-1-1-111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-11111-1-1-1-1-1-1-11
χ1311111111111111111-1-1-1-11-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1111111-1-1-111111-1-1-1-1-1
χ1411111111111111111-1-1-1-11-1-1-1-111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-111-1-1-111111
χ1511111111111111111-1-1-1-11-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-11111-1-1111-1-11-1-1-1-1111
χ1611111111111111111-1-1-1-11-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111111-1-1-11111-1-1-1
χ17222222222-22-22-22-2-20000-2222222220000-2-2-2-200000000000000-2000000000000
χ18222222222-22-22-22-2-20000-22222-2-2-2-2000022-2-2000000000000002000000000000
χ19222222222-22-22-22-2-20000-2-2-2-2-222-2-20000-2-222000000000000002000000000000
χ20222222222-22-22-22-2-20000-2-2-2-2-2-2-2220000222200000000000000-2000000000000
χ2122222222-22-22-22-22-22222-200000000-2-2220000-2-200002200000000000-20000000
χ2222222222-22-22-22-22-22222-200000000-2-2-2-20000220000-2-20000000000020000000
χ2322222222-22-22-22-22-2-2-2-2-2-20000000022220000220000-2-200000000000-20000000
χ2422222222-22-22-22-22-2-2-2-2-2-20000000022-2-20000-2-20000220000000000020000000
χ2522-2-2-22-2202020-20-2022-2-2022−2−20000002i−2i002−20022−2−22i−2ii2i2−i2−i20000000000i2−i2000
χ2622-2-2-22-2202020-20-2022-2-2022−2−2000000−2i2i002−20022−2−2−2i2i−i2−i2i2i20000000000−i2i2000
χ2722-2-2-22-2202020-20-2022-2-20−2−2220000002i−2i00−2200−2−2222i−2i−i2−i2i2i20000000000−i2i2000
χ2822-2-2-22-2202020-20-2022-2-20−2−222000000−2i2i00−2200−2−222−2i2ii2i2−i2−i20000000000i2−i2000
χ2922-2-2-22-2202020-20-20-2-222022−2−20000002i−2i002−200−2−222−2i2i−i2−i2i2i20000000000i2−i2000
χ3022-2-2-22-2202020-20-20-2-222022−2−2000000−2i2i002−200−2−2222i−2ii2i2−i2−i20000000000−i2i2000
χ3122-2-2-22-2202020-20-20-2-2220−2−2220000002i−2i00−220022−2−2−2i2ii2i2−i2−i20000000000−i2i2000
χ3222-2-2-22-2202020-20-20-2-2220−2−222000000−2i2i00−220022−2−22i−2i−i2−i2i2i20000000000i2−i2000
χ332-22-2-222-22-2-222-2-22-22i−2i2i−2i2000000002i−2i0000000000000000002i−2i00000000002-20
χ342-22-2-222-22-2-222-2-22-22i−2i2i−2i2000000002i−2i000000000000000000−2i2i0000000000-220
χ352-22-2-222-22-2-222-2-22-2−2i2i−2i2i200000000−2i2i0000000000000000002i−2i0000000000-220
χ362-22-2-222-22-2-222-2-22-2−2i2i−2i2i200000000−2i2i000000000000000000−2i2i00000000002-20
χ372-22-2-222-2-222-2-222-2-20000200002-20000002-200002i−2i2i−2i000000000002i−2i00000000
χ382-22-2-222-2-222-2-222-2-20000200002-20000002-20000−2i2i−2i2i00000000000−2i2i00000000
χ392-22-2-222-2-222-2-222-2-2000020000-22000000-2200002i−2i2i−2i00000000000−2i2i00000000
χ402-22-2-222-2-222-2-222-2-2000020000-22000000-220000−2i2i−2i2i000000000002i−2i00000000
χ412-22-2-222-2-2-222-2-22222i−2i2i−2i-200002-200−2i2i00-22000000000000000002i−2i0000000000
χ422-22-2-222-2-2-222-2-22222i−2i2i−2i-20000-2200−2i2i002-200000000000000000−2i2i0000000000
χ432-22-2-222-2-2-222-2-2222−2i2i−2i2i-200002-2002i−2i00-2200000000000000000−2i2i0000000000
χ442-22-2-222-2-2-222-2-2222−2i2i−2i2i-20000-22002i−2i002-2000000000000000002i−2i0000000000
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000
χ464444-4-4-4-440-40-40400000000000004-400000000000000000000000000000000000
χ474444-4-4-4-440-40-4040000000000000-4400000000000000000000000000000000000
χ484444-4-4-4-4-404040-4000000000000000000000000000000000000000000022−2200000
χ494444-4-4-4-4-404040-40000000000000000000000000000000000000000000−222200000
χ5044-4-4-44-440-40-404040000002222−22−220000000000−2222000000000000000000000000000
χ5144-4-4-44-440-40-40404000000−22−222222000000000022−22000000000000000000000000000
χ524-44-44-4-444040-40-400000000000000000000000000000002i2−2i22i2−2i2000000000000000
χ534-44-44-4-444040-40-40000000000000000000000000000000−2i22i2−2i22i2000000000000000
χ544-44-44-4-44-40-4040400000004-44-4000000000000000000000000000000000000000
χ554-44-44-4-44-40-404040000000-44-44000000000000000000000000000000000000000
χ564-44-4-444-444-4-444-4-440000-40000000000000000000000000000000000000000000
χ574-4-4444-4-4040-40-4040000000000000000000000002i2−2i2−2i22i2000000000000000000000
χ584-4-4444-4-4040-40-404000000000000000000000000−2i22i22i2−2i2000000000000000000000
χ594-4-4444-4-40-404040-404i−4i−4i4i00000000000000000000000000000000000000000000
χ604-4-4444-4-40-404040-40−4i4i4i−4i00000000000000000000000000000000000000000000
χ614-4-44-4-4440000000000000022−22−222200000000000022−220000002-2-22000000000000000
χ624-4-44-4-4440000000000000022−22−2222000000000000−2222000000-222-2000000000000000
χ634-4-44-4-44400000000000000−222222−2200000000000022−22000000-222-2000000000000000
χ644-4-44-4-44400000000000000−222222−22000000000000−22220000002-2-22000000000000000
χ6588-8-88-88-8000000000000000000000000000000000000000000000000000000000

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