Finite Group Databasebeta

← Group #306954

Character table — Group #306954

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888444444444488888888888888244444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-111-1-1-1-1-1
χ31111111111111111111111111111-1-1111111-1-1111111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-111-1-1-1-1-1-1-111111
χ51111111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-111-1-1-1-111111-1-1-1-1-111-1-1-1
χ61111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11-1-1-1-1111-1-1-1-1111
χ71111111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-111-1-1111
χ81111111111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-111-1-11111111-1-1-1
χ911111111111111111-1-1-1-111111-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1111-1-11-1-111-1-1-1-11
χ1011111111111111111-1-1-1-111111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1-111-111111111-1
χ1111111111111111111-1-1-1-111111-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-11-1-1-1-11111-1
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-11111-111-1-1-1-1-1-11
χ1311111111111111111-1-1-1-11-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-11111111-1-1-111-1-1-1-111-1
χ1411111111111111111-1-1-1-11-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-111111-1-1111-1-1-1-111-1-11
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-11
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-111111-1-111-1-111-1
χ17222222222-22-22-22-2-22222-20000-2-222000000-2-2000000220000-200000000000000
χ18222222222-22-22-22-2-22222-20000-2-2-2-200000022000000-2-20000200000000000000
χ19222222222-22-22-22-2-2-2-2-2-2-20000222200000022000000-2-20000-200000000000000
χ20222222222-22-22-22-2-2-2-2-2-2-2000022-2-2000000-2-2000000220000200000000000000
χ2122222222-22-22-22-22-20000-22222000022-2-22200-2-2000000000000000-2000000000
χ2222222222-22-22-22-22-20000-222220000-2-222-2-200-2-20000000000000002000000000
χ2322222222-22-22-22-22-20000-2-2-2-2-2000022-2-2-2-200220000000000000002000000000
χ2422222222-22-22-22-22-20000-2-2-2-2-20000-2-222220022000000000000000-2000000000
χ252-222-22-2-22-2-222-2-22-200002000000002i−2i2i−2i00000022-2-20000000000002i−2i0000000
χ262-222-22-2-22-2-222-2-22-200002000000002i−2i2i−2i000000-2-222000000000000−2i2i0000000
χ272-222-22-2-22-2-222-2-22-20000200000000−2i2i−2i2i00000022-2-2000000000000−2i2i0000000
χ282-222-22-2-22-2-222-2-22-20000200000000−2i2i−2i2i000000-2-2220000000000002i−2i0000000
χ292-222-22-2-2-222-2-222-2-222-2-2200002-2000000000000000000000002i−2i00000002i−2i000
χ302-222-22-2-2-222-2-222-2-222-2-2200002-200000000000000000000000−2i2i0000000−2i2i000
χ312-222-22-2-2-222-2-222-2-2-2-22220000-22000000000000000000000002i−2i0000000−2i2i000
χ322-222-22-2-2-222-2-222-2-2-2-22220000-2200000000000000000000000−2i2i00000002i−2i000
χ332-222-22-2-2-2-222-2-222222-2-2-20000-22002i−2i−2i2i00000000000000000002i−2i0000000000
χ342-222-22-2-2-2-222-2-222222-2-2-20000-2200−2i2i2i−2i0000000000000000000−2i2i0000000000
χ352-222-22-2-2-2-222-2-2222-2-222-200002-2002i−2i−2i2i0000000000000000000−2i2i0000000000
χ362-222-22-2-2-2-222-2-2222-2-222-200002-200−2i2i2i−2i00000000000000000002i−2i0000000000
χ372-22-2-2-2222020-20-2002-22-2022−2−2002i−2i000000002−22−22−22i−2ii2i2−i2−i200000000i2−i200000
χ382-22-2-2-2222020-20-2002-22-2022−2−200−2i2i000000002−22−22−2−2i2i−i2−i2i2i200000000−i2i200000
χ392-22-2-2-2222020-20-2002-22-20−2−222002i−2i00000000−22−22−222i−2i−i2−i2i2i200000000−i2i200000
χ402-22-2-2-2222020-20-2002-22-20−2−22200−2i2i00000000−22−22−22−2i2ii2i2−i2−i200000000i2−i200000
χ412-22-2-2-2222020-20-200-22-22022−2−2002i−2i000000002−2−22−22−2i2i−i2−i2i2i200000000i2−i200000
χ422-22-2-2-2222020-20-200-22-22022−2−200−2i2i000000002−2−22−222i−2ii2i2−i2−i200000000−i2i200000
χ432-22-2-2-2222020-20-200-22-220−2−222002i−2i00000000−222−22−2−2i2ii2i2−i2−i200000000−i2i200000
χ442-22-2-2-2222020-20-200-22-220−2−22200−2i2i00000000−222−22−22i−2i−i2−i2i2i200000000i2−i200000
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000
χ46444-44-4-4-440-40-404000000000000000000000000022−22−2222000000000000000000000
χ47444-44-4-4-440-40-4040000000000000000000000000−222222−22000000000000000000000
χ48444-44-4-4-4-404040-4004-4-4400000000000000000000000000000000000000000000
χ49444-44-4-4-4-404040-400-444-400000000000000000000000000000000000000000000
χ5044-4-4-444-4040-40-4040000004i−4i4i−4i000000000000000000000000000000000000000
χ5144-4-4-444-4040-40-404000000−4i4i−4i4i000000000000000000000000000000000000000
χ5244-4-4-444-40-404040-40000000000000000000000000000002i2−2i22i2−2i2000000000000000
χ5344-4-4-444-40-404040-4000000000000000000000000000000−2i22i2−2i22i2000000000000000
χ544-444-44-4-444-4-444-4-440000-40000000000000000000000000000000000000000000
χ554-44-4-4-444-40-4040400000002222−22−22000000000000−22220000000000000000000000000
χ564-44-4-4-444-40-404040000000−22−22222200000000000022−220000000000000000000000000
χ574-4-444-44-4000000000000002i2−2i2−2i22i200000000002i2−2i2000000002-2-22000000000000000
χ584-4-444-44-4000000000000002i2−2i2−2i22i20000000000−2i22i200000000-222-2000000000000000
χ594-4-444-44-400000000000000−2i22i22i2−2i200000000002i2−2i200000000-222-2000000000000000
χ604-4-444-44-400000000000000−2i22i22i2−2i20000000000−2i22i2000000002-2-22000000000000000
χ614-4-4-444-4404040-40-400000000000000000000000000000000000000000000002i2−2i20
χ624-4-4-444-4404040-40-40000000000000000000000000000000000000000000000−2i22i20
χ634-4-4-444-440-40-404040000000000000000004-400000000000000000000000000000
χ644-4-4-444-440-40-40404000000000000000000-4400000000000000000000000000000
χ6588-88-8-8-88000000000000000000000000000000000000000000000000000000000

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