Finite Group Databasebeta

← Group #305568

Character table — Group #305568

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888224444444488888888888888444444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1111111-1-1111111-1-1-1-1-1-1111-111-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-11111-1-1-1-111111111111111-1-1-11-1-1-1-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111
χ51111111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-111111-1-111-1-1-1
χ61111111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1111
χ71111111111111111111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111
χ81111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111111-1-1-1111111-1-1-1
χ911111111111111111-1-1-1-1111111111-1-11111-1-111-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-1-1-1-11
χ1011111111111111111-1-1-1-11111111-1-1-1-111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-11111-1
χ1111111111111111111-1-1-1-111111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111111-1-1111111-1
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-111-11111-1-1-1-1-1-11
χ1311111111111111111-1-1-1-11-1-1-1-11111-1-111-1-1-1-1-1-11111-1-11111-1111-1-111-1-1-1-111-1
χ1411111111111111111-1-1-1-11-1-1-1-111-1-1-1-111-1-111-1-1111111-1-1-1-1-111-1-1-1-1-11111-1-11
χ1511111111111111111-1-1-1-11-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-111111-1-1111-1-1-1-111-1-11
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-11-1-1-1111111-1-111-1
χ172222222222-2-22-22-2-20000-22222220000-2-22200-2-20000000000-200000000000000
χ182222222222-2-22-22-2-20000-22222-2-2000022-2-200-2-20000000000200000000000000
χ192222222222-2-22-22-2-20000-2-2-2-2-2220000-2-2-2-200220000000000200000000000000
χ202222222222-2-22-22-2-20000-2-2-2-2-2-2-20000222200220000000000-200000000000000
χ2122222222-2-222-22-22-22222-200000022-2-20000-2-2000000220000000-200000000000
χ2222222222-2-222-22-22-22222-2000000-2-2-2-2000022000000-2-20000000200000000000
χ2322222222-2-222-22-22-2-2-2-2-2-20000002222000022000000-2-20000000-200000000000
χ2422222222-2-222-22-22-2-2-2-2-2-2000000-2-2220000-2-2000000220000000200000000000
χ252-22-22-22-22222-2-2-2-2222-2-2-200002-2002-22-2000000000000000000002-2000000000
χ262-22-22-22-22222-2-2-2-2222-2-2-20000-22002-2-2200000000000000000000-22000000000
χ272-22-22-22-22222-2-2-2-22-2-222-200002-200-222-200000000000000000000-22000000000
χ282-22-22-22-22222-2-2-2-22-2-222-20000-2200-22-22000000000000000000002-2000000000
χ292-22-22-22-222-2-2-22-22-20000200002-20000-220000002i2i−2i−2i00000002i−2i000000000000
χ302-22-22-22-222-2-2-22-22-20000200002-20000-22000000−2i−2i2i2i0000000−2i2i000000000000
χ312-22-22-22-222-2-2-22-22-2000020000-2200002-20000002i2i−2i−2i0000000−2i2i000000000000
χ322-22-22-22-222-2-2-22-22-2000020000-2200002-2000000−2i−2i2i2i00000002i−2i000000000000
χ332-22-22-22-2-2-2222-22-2-222-2-2200000000-220000000000000000000000002i−2i002i−2i000
χ342-22-22-22-2-2-2222-22-2-222-2-2200000000-22000000000000000000000000−2i2i00−2i2i000
χ352-22-22-22-2-2-2222-22-2-2-2-2222000000002-20000000000000000000000002i−2i00−2i2i000
χ362-22-22-22-2-2-2222-22-2-2-2-2222000000002-2000000000000000000000000−2i2i002i−2i000
χ372-2-222-2-22002-2020-202i−2i2i−2i022−2−2002-2000000002−2i2−i2i2−i22i−2ii2i2−i2−i2000000002−200000
χ382-2-222-2-22002-2020-202i−2i2i−2i022−2−200-22000000002−2i2−i2i2−i2−2i2i−i2−i2i2i200000000−2200000
χ392-2-222-2-22002-2020-202i−2i2i−2i0−2−222002-200000000−22−i2i2−i2i22i−2i−i2−i2i2i200000000−2200000
χ402-2-222-2-22002-2020-202i−2i2i−2i0−2−22200-2200000000−22−i2i2−i2i2−2i2ii2i2−i2−i2000000002−200000
χ412-2-222-2-22002-2020-20−2i2i−2i2i022−2−2002-2000000002−2−i2i2−i2i2−2i2i−i2−i2i2i2000000002−200000
χ422-2-222-2-22002-2020-20−2i2i−2i2i022−2−200-22000000002−2−i2i2−i2i22i−2ii2i2−i2−i200000000−2200000
χ432-2-222-2-22002-2020-20−2i2i−2i2i0−2−222002-200000000−22i2−i2i2−i2−2i2ii2i2−i2−i200000000−2200000
χ442-2-222-2-22002-2020-20−2i2i−2i2i0−2−22200-2200000000−22i2−i2i2−i22i−2i−i2−i2i2i2000000002−200000
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000
χ46444-4-4-4-444-40040-400000004-44-4000000000000000000000000000000000000000
χ47444-4-4-4-444-40040-40000000-44-44000000000000000000000000000000000000000
χ48444-4-4-4-44-4400-40400000000000000000000000000000002i2−2i22i2−2i2000000000000000
χ49444-4-4-4-44-4400-4040000000000000000000000000000000−2i22i2−2i22i2000000000000000
χ5044-4-444-4-4004-40-40404i−4i−4i4i00000000000000000000000000000000000000000000
χ5144-4-444-4-4004-40-4040−4i4i4i−4i00000000000000000000000000000000000000000000
χ5244-4-444-4-400-44040-400000000000000000000000022−22−2222000000000000000000000
χ5344-4-444-4-400-44040-4000000000000000000000000−222222−22000000000000000000000
χ544-444-44-4-44-400-40400000000000000000004i−4i00000000000000000000000000000
χ554-444-44-4-44-400-4040000000000000000000−4i4i00000000000000000000000000000
χ564-444-44-4-4-440040-40000000000000000000000000000000000000000000000022−220
χ574-444-44-4-4-440040-400000000000000000000000000000000000000000000000−22220
χ584-44-44-44-4-4-4-4-4444440000-40000000000000000000000000000000000000000000
χ594-4-444-4-4400-440-4040000002222−22−22000000000000−22220000000000000000000000000
χ604-4-444-4-4400-440-404000000−22−22222200000000000022−220000000000000000000000000
χ614-4-4-4-44440000000000000022−22−2222000000000022−22000000002-2-22000000000000000
χ624-4-4-4-44440000000000000022−22−22220000000000−222200000000-222-2000000000000000
χ634-4-4-4-444400000000000000−222222−22000000000022−2200000000-222-2000000000000000
χ644-4-4-4-444400000000000000−222222−220000000000−2222000000002-2-22000000000000000
χ6588-88-8-88-8000000000000000000000000000000000000000000000000000000000

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