Finite Group Databasebeta

← Group #305672

Character table — Group #305672

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888444444444488888888888888444444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-11111-1-1111111-1-1-1-1-1-1111-111-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111-1-11111111111111111-1-1-11-1-1-1-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111
χ51111111111111111111111-1-1-1-111-1-111-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-11
χ61111111111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111-1-1-11111-1-111-1
χ71111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-1-111111-1-1-1-111-1
χ81111111111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-11
χ911111111111111111-1-1-1-11111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-1-1-1-11
χ1011111111111111111-1-1-1-1111111111-1-111-1-11111-1-1-1-11111111-1-1-1-1-1-1-1-1-11111-1
χ1111111111111111111-1-1-1-111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111111-1-1111111-1
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
χ1311111111111111111-1-1-1-11-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-111111-1-1111-1-1-1-1-1-1111
χ1411111111111111111-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11-1-1-111111111-1-1-1
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-11111-1111-1-111-1-111-1-1-1
χ1611111111111111111-1-1-1-11-1-1-1-1-1-111-1-111-1-111-1-1111111-1-1-1-1-111-1-1-1-1-111-1-1111
χ172222222222-2-22-22-2-20000-22222222200-2-20000-2-20000000000-200000000000000
χ182222222222-2-22-22-2-20000-22222-2-2-2-200220000-2-20000000000200000000000000
χ192222222222-2-22-22-2-20000-2-2-2-2-222-2-200220000220000000000-200000000000000
χ202222222222-2-22-22-2-20000-2-2-2-2-2-2-22200-2-20000220000000000200000000000000
χ2122222222-2-222-22-22-22222-2000000002200-2-222000000-2-20000000-200000000000
χ2222222222-2-222-22-22-22222-200000000-2-200-2-2-2-2000000220000000200000000000
χ2322222222-2-222-22-22-2-2-2-2-2-200000000220022-2-2000000220000000-200000000000
χ2422222222-2-222-22-22-2-2-2-2-2-200000000-2-2002222000000-2-20000000200000000000
χ252-22-22-22-22222-2-2-2-2222-2-2-20000002-2002-22-20000000000000000002-2000000000
χ262-22-22-22-22222-2-2-2-2222-2-2-2000000-2200-222-2000000000000000000-22000000000
χ272-22-22-22-22222-2-2-2-22-2-222-20000002-2002-2-22000000000000000000-22000000000
χ282-22-22-22-22222-2-2-2-22-2-222-2000000-2200-22-220000000000000000002-2000000000
χ292-22-22-22-222-2-2-22-22-2000020000002-200-220000002i2i−2i−2i00000002i−2i000000000000
χ302-22-22-22-222-2-2-22-22-2000020000002-200-22000000−2i−2i2i2i0000000−2i2i000000000000
χ312-22-22-22-222-2-2-22-22-200002000000-22002-20000002i2i−2i−2i0000000−2i2i000000000000
χ322-22-22-22-222-2-2-22-22-200002000000-22002-2000000−2i−2i2i2i00000002i−2i000000000000
χ332-22-22-22-2-2-2222-22-2-222-2-22000000000000-22000000000000000000002i−2i00002i−2i0
χ342-22-22-22-2-2-2222-22-2-222-2-22000000000000-2200000000000000000000−2i2i0000−2i2i0
χ352-22-22-22-2-2-2222-22-2-2-2-22220000000000002-2000000000000000000002i−2i0000−2i2i0
χ362-22-22-22-2-2-2222-22-2-2-2-22220000000000002-200000000000000000000−2i2i00002i−2i0
χ372-2-2-2-2222002-2020-202i−2i2i−2i022−2−200002i−2i00002-22−2i2−i2i2−i20022−2−200000000i2−i200000
χ382-2-2-2-2222002-2020-202i−2i2i−2i022−2−20000−2i2i0000-222−2i2−i2i2−i200−2−22200000000−i2i200000
χ392-2-2-2-2222002-2020-202i−2i2i−2i0−2−22200002i−2i00002-2−22−i2i2−i2i200−2−22200000000−i2i200000
χ402-2-2-2-2222002-2020-202i−2i2i−2i0−2−2220000−2i2i0000-22−22−i2i2−i2i20022−2−200000000i2−i200000
χ412-2-2-2-2222002-2020-20−2i2i−2i2i022−2−200002i−2i0000-222−2−i2i2−i2i200−2−22200000000i2−i200000
χ422-2-2-2-2222002-2020-20−2i2i−2i2i022−2−20000−2i2i00002-22−2−i2i2−i2i20022−2−200000000−i2i200000
χ432-2-2-2-2222002-2020-20−2i2i−2i2i0−2−22200002i−2i0000-22−22i2−i2i2−i20022−2−200000000−i2i200000
χ442-2-2-2-2222002-2020-20−2i2i−2i2i0−2−2220000−2i2i00002-2−22i2−i2i2−i200−2−22200000000i2−i200000
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
χ5044-44-4-44-4004-40-40404i−4i−4i4i00000000000000000000000000000000000000000000
χ5144-44-4-44-4004-40-4040−4i4i4i−4i00000000000000000000000000000000000000000000
χ5244-44-4-44-400-44040-400000000000000000000000022−22−2222000000000000000000000
χ5344-44-4-44-400-44040-4000000000000000000000000−222222−22000000000000000000000
χ544-444-44-4-44-400-404000000000004i−4i0000000000000000000000000000000000000
χ554-444-44-4-44-400-40400000000000−4i4i0000000000000000000000000000000000000
χ564-444-44-4-4-440040-400000000000000000000000000000000000000000000022−22000
χ574-444-44-4-4-440040-4000000000000000000000000000000000000000000000−2222000
χ584-44-44-44-4-4-4-4-4444440000-40000000000000000000000000000000000000000000
χ594-4-444-4-440000000000000022−22−22220000000000000000002i2−2i22i−2i−2i2i000000000000000
χ604-4-444-4-440000000000000022−22−2222000000000000000000−2i22i2−2i2i2i−2i000000000000000
χ614-4-444-4-4400000000000000−222222−220000000000000000002i2−2i2−2i2i2i−2i000000000000000
χ624-4-444-4-4400000000000000−222222−22000000000000000000−2i22i22i−2i−2i2i000000000000000
χ634-4-4-4-444400-440-4040000002222−22−22000000000000−22220000000000000000000000000
χ644-4-4-4-444400-440-404000000−22−22222200000000000022−220000000000000000000000000
χ6588-8-888-8-8000000000000000000000000000000000000000000000000000000000

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