Finite Group Databasebeta

← Group #306884

Character table — Group #306884

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888224444444488888888888888444444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-111-1-111111111111111-1-1-11-1-1-1-111-1-1-1-1-1
χ311111111111111111111111111-1-111111111-1-1111111-1-1-1-1-1-1111-111-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111
χ51111111111111111111111-1-1-1-11111-1-1111111-1-1-1-1-1-111-1-1-1-111-11-1-111-1-111-1-1-1
χ61111111111111111111111-1-1-1-111-1-11111-1-111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1111
χ71111111111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1111
χ81111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11-111111111-1-1-1
χ911111111111111111-1-1-1-111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11
χ1011111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1111-1-1111111-1
χ1111111111111111111-1-1-1-111111-1-11111-1-1111111-1-1-1-1111111-1-11-1-1-1-1-1-1-11111-1
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-11111-1-1-1-1-1-11
χ1311111111111111111-1-1-1-11-1-1-1-11111-1-1-1-111-1-1-1-11111-1-11111-1-1-111111-1-1-1-111-1
χ1411111111111111111-1-1-1-11-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-111-1-11
χ1511111111111111111-1-1-1-11-1-1-1-1-1-111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-111-1-11111-1-11
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1111-1-1-11111-1-111-1
χ17222222222-22-22-22-2-22222-20000220000-2-20022000000-2-20000000-200000000000
χ18222222222-22-22-22-2-22222-20000-2-20000-2-200-2-2000000220000000200000000000
χ19222222222-22-22-22-2-2-2-2-2-2-200002200002200-2-2000000220000000-200000000000
χ20222222222-22-22-22-2-2-2-2-2-2-20000-2-20000220022000000-2-20000000200000000000
χ2122222222-22-22-22-22-20000-2222200222200-2-200-2-2000000000000-2000000000000
χ2222222222-22-22-22-22-20000-2222200-2-2-2-2002200-2-20000000000002000000000000
χ2322222222-22-22-22-22-20000-2-2-2-2-20022-2-200-2-200220000000000002000000000000
χ2422222222-22-22-22-22-20000-2-2-2-2-200-2-22200220022000000000000-2000000000000
χ2522-22-2-2-2220-20-202002i2i−2i−2i0i2i2−i2−i22-2000000002i−2ii2−i222−2−20022−2−200000000i2−i200000
χ2622-22-2-2-2220-20-202002i2i−2i−2i0i2i2−i2−i2-2200000000−2i2ii2−i222−2−200−2−22200000000−i2i200000
χ2722-22-2-2-2220-20-202002i2i−2i−2i0−i2−i2i2i22-2000000002i−2i−i2i2−2−22200−2−22200000000−i2i200000
χ2822-22-2-2-2220-20-202002i2i−2i−2i0−i2−i2i2i2-2200000000−2i2i−i2i2−2−2220022−2−200000000i2−i200000
χ2922-22-2-2-2220-20-20200−2i−2i2i2i0i2i2−i2−i22-200000000−2i2ii2−i2−2−22200−2−22200000000i2−i200000
χ3022-22-2-2-2220-20-20200−2i−2i2i2i0i2i2−i2−i2-22000000002i−2ii2−i2−2−2220022−2−200000000−i2i200000
χ3122-22-2-2-2220-20-20200−2i−2i2i2i0−i2−i2i2i22-200000000−2i2i−i2i222−2−20022−2−200000000−i2i200000
χ3222-22-2-2-2220-20-20200−2i−2i2i2i0−i2−i2i2i2-22000000002i−2i−i2i222−2−200−2−22200000000i2−i200000
χ332-2-222-22-22-2-222-2-22-2000020000002i−2i00002i−2i00002-22-200000000002i−2i000000000
χ342-2-222-22-22-2-222-2-22-2000020000002i−2i00002i−2i0000-22-220000000000−2i2i000000000
χ352-2-222-22-22-2-222-2-22-200002000000−2i2i0000−2i2i00002-22-20000000000−2i2i000000000
χ362-2-222-22-22-2-222-2-22-200002000000−2i2i0000−2i2i0000-22-2200000000002i−2i000000000
χ372-2-222-22-2-222-2-222-2-22-22-2200000000002-200000000000000000000002i−2i002i−2i000
χ382-2-222-22-2-222-2-222-2-22-22-2200000000002-20000000000000000000000−2i2i00−2i2i000
χ392-2-222-22-2-222-2-222-2-2-22-2220000000000-2200000000000000000000002i−2i00−2i2i000
χ402-2-222-22-2-222-2-222-2-2-22-2220000000000-220000000000000000000000−2i2i002i−2i000
χ412-2-222-22-2-2-222-2-22222-22-2-20000002i−2i00-22−2i2i000000000000002i−2i0000000000000
χ422-2-222-22-2-2-222-2-22222-22-2-2000000−2i2i00-222i−2i00000000000000−2i2i0000000000000
χ432-2-222-22-2-2-222-2-2222-22-22-20000002i−2i002-2−2i2i00000000000000−2i2i0000000000000
χ442-2-222-22-2-2-222-2-2222-22-22-2000000−2i2i002-22i−2i000000000000002i−2i0000000000000
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000
χ46444-4-4-44-404040-40-4000000000000004-4000000000000000000000000000000000
χ47444-4-4-44-404040-40-400000000000000-44000000000000000000000000000000000
χ48444-4-4-44-40-40-4040400000000000000000000000000000000000000000000002i2−2i20
χ49444-4-4-44-40-40-404040000000000000000000000000000000000000000000000−2i22i20
χ5044-44-4-4-44-404040-400000002i22i2−2i2−2i2000000000000−2i22i20000000000000000000000000
χ5144-44-4-4-44-404040-40000000−2i2−2i22i22i20000000000002i2−2i20000000000000000000000000
χ524-444-44-4-44040-40-4000000000000000000000000022−22−2222000000000000000000000
χ534-444-44-4-44040-40-40000000000000000000000000−222222−22000000000000000000000
χ544-444-44-4-4-40-40404004i−4i−4i4i00000000000000000000000000000000000000000000
χ554-444-44-4-4-40-4040400−4i4i4i−4i00000000000000000000000000000000000000000000
χ564-44-44-4-44000000000000002i2−2i22i2−2i20000000000000000002i2−2i22-22-2000000000000000
χ574-44-44-4-44000000000000002i2−2i22i2−2i2000000000000000000−2i22i2-22-22000000000000000
χ584-44-44-4-4400000000000000−2i22i2−2i22i20000000000000000002i2−2i2-22-22000000000000000
χ594-44-44-4-4400000000000000−2i22i2−2i22i2000000000000000000−2i22i22-22-2000000000000000
χ604-4-444-44-444-4-444-4-440000-40000000000000000000000000000000000000000000
χ614-4-4-4-4444040-40-40400000000000000000000000000000022−22−2222000000000000000
χ624-4-4-4-4444040-40-404000000000000000000000000000000−222222−22000000000000000
χ634-4-4-4-44440-404040-40000004-4-44000000000000000000000000000000000000000
χ644-4-4-4-44440-404040-4000000-444-4000000000000000000000000000000000000000
χ6588-8-888-8-8000000000000000000000000000000000000000000000000000000000

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