Finite Group Databasebeta

← Group #312775

Character table — Group #312775

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111111112222222244444444448888888888888888888816161616161616161616161616163232
order12222222444444444444448888444444888888888888882224444488888844
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1111111-1-1-1-1-1-1111-1111-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-111-1-111111111111111-1-1-11-1-1-11-1-111-1-1-1-1
χ411111111111111111111111111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111
χ51111111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-111-1-1-1-111-111-1-11-1-1-1-111-11
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11-1-1-11111-1-11-1
χ71111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-111-111111-1-1-1-11-1
χ81111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-11-1-111-1-1-11111-11
χ911111111111111111-1-1-1-11111111-1-11111-1-1-1-111111111-1-11-11-1-1-111-1-111-1-1
χ1011111111111111111-1-1-1-11111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111-1-11-1-111-1-111
χ1111111111111111111-1-1-1-111111-1-1-1-1-1-111-1-1-1-11111111111-1-1-111-1-1-1-1-1-1-111
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-11-1111111111-1-1
χ1311111111111111111-1-1-1-11-1-1-1-111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1111-1-1-111111-1
χ1411111111111111111-1-1-1-11-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-11111111-1-1-1-1-11
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1111-1-1-1-1-11111-1-1-11
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-11-1-1-1-1111-1
χ17222222222-22-22-22-2-20000-22222220022000000-2-200000000-20-200000000000
χ18222222222-22-22-22-2-20000-22222-2-200-2-2000000-2-20000000020200000000000
χ19222222222-22-22-22-2-20000-2-2-2-2-22200-2-2000000220000000020-200000000000
χ20222222222-22-22-22-2-20000-2-2-2-2-2-2-200220000002200000000-20200000000000
χ2122222222-22-22-22-22-22222-2000000-2-20022000000-2-200000002000-200000000
χ2222222222-22-22-22-22-22222-2000000-2-200-2-2000000220000000-2000200000000
χ2322222222-22-22-22-22-2-2-2-2-2-2000000220022000000-2-20000000-2000200000000
χ2422222222-22-22-22-22-2-2-2-2-2-20000002200-2-20000002200000002000-200000000
χ252-222-2-2-2222-2-222-2-2-22i2i−2i−2i22i2i−2i−2i002i−2i000022-2-22i−2i0000000000000000000000
χ262-222-2-2-2222-2-222-2-2-22i2i−2i−2i2−2i−2i2i2i002i−2i0000-2-222−2i2i0000000000000000000000
χ272-222-2-2-2222-2-222-2-2-2−2i−2i2i2i22i2i−2i−2i00−2i2i0000-2-2222i−2i0000000000000000000000
χ282-222-2-2-2222-2-222-2-2-2−2i−2i2i2i2−2i−2i2i2i00−2i2i000022-2-2−2i2i0000000000000000000000
χ292-222-2-2-222-2-222-2-2220000-22i2i−2i−2i000000000000−2i2i0000002-20002i−2i000000000
χ302-222-2-2-222-2-222-2-2220000-22i2i−2i−2i000000000000−2i2i000000-22000−2i2i000000000
χ312-222-2-2-222-2-222-2-2220000-2−2i−2i2i2i0000000000002i−2i0000002-2000−2i2i000000000
χ322-222-2-2-222-2-222-2-2220000-2−2i−2i2i2i0000000000002i−2i000000-220002i−2i000000000
χ332-222-2-2-22-222-2-222-222i2i−2i−2i-2000000−2i2i0000000000002i2i−2i−2i00000000002-20000
χ342-222-2-2-22-222-2-222-222i2i−2i−2i-2000000−2i2i000000000000−2i−2i2i2i0000000000-220000
χ352-222-2-2-22-222-2-222-22−2i−2i2i2i-20000002i−2i0000000000002i2i−2i−2i0000000000-220000
χ362-222-2-2-22-222-2-222-22−2i−2i2i2i-20000002i−2i000000000000−2i−2i2i2i00000000002-20000
χ372-22-222-2-220-20-20200000002i−2i2i−2i2-2002i−2ii2−i2000000i2−i22−22−2000000002−200i2−i200
χ382-22-222-2-220-20-20200000002i−2i2i−2i2-2002i−2i−i2i2000000−i2i2−22−2200000000−2200−i2i200
χ392-22-222-2-220-20-20200000002i−2i2i−2i-2200−2i2ii2−i2000000i2−i22−22−200000000−2200−i2i200
χ402-22-222-2-220-20-20200000002i−2i2i−2i-2200−2i2i−i2i2000000−i2i2−22−22000000002−200i2−i200
χ412-22-222-2-220-20-2020000000−2i2i−2i2i2-200−2i2ii2−i2000000i2−i2−22−2200000000−2200i2−i200
χ422-22-222-2-220-20-2020000000−2i2i−2i2i2-200−2i2i−i2i2000000−i2i22−22−2000000002−200−i2i200
χ432-22-222-2-220-20-2020000000−2i2i−2i2i-22002i−2ii2−i2000000i2−i2−22−22000000002−200−i2i200
χ442-22-222-2-220-20-2020000000−2i2i−2i2i-22002i−2i−i2i2000000−i2i22−22−200000000−2200i2−i200
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000
χ46444-4-4-44-44040-40-400000004-4-44000000000000000000000000000000000000
χ47444-4-4-44-44040-40-40000000-444-4000000000000000000000000000000000000
χ48444-4-4-44-4-40-404040000000000000000000000000002i2−2i2−2i22i20000000000000000
χ49444-4-4-44-4-40-40404000000000000000000000000000−2i22i22i2−2i20000000000000000
χ5044-4-4-44-4404040-40-404i−4i4i−4i00000000000000000000000000000000000000000
χ5144-4-4-44-4404040-40-40−4i4i−4i4i00000000000000000000000000000000000000000
χ5244-4-4-44-440-40-4040400000000000000000022−2222−22000000000000000000000000
χ5344-4-4-44-440-40-40404000000000000000000−2222−2222000000000000000000000000
χ544-444-4-4-44-4-444-4-444-4000040000000000000000000000000000000000000000
χ554-44-444-4-4-404040-4000000000000000002i2−2i2000000−2i22i200000000000000000000
χ564-44-444-4-4-404040-400000000000000000−2i22i20000002i2−2i200000000000000000000
χ574-4-4-44-444040-40-40404-4-4400000000000000000000000000000000000000000
χ584-4-4-44-444040-40-4040-444-400000000000000000000000000000000000000000
χ594-4-4-44-4440-404040-400000000000000000022−22−2222000000000000000000000000
χ604-4-4-44-4440-404040-4000000000000000000−222222−22000000000000000000000000
χ6188-888-8-8-8000000000000000000000000000000000000000000000000000000
χ628-8-88-888-8000000000000000000000000000000000000000000000000000000

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