Finite Group Databasebeta

← Group #307004

Character table — Group #307004

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888444444444488888888888888244444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-111-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111
χ51111111111111111111111-1-1-1-1111111-1-11111-1-1-1-1-1-111-1-1-1-11-111-1-111-1-111-1-1-1
χ61111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-1111
χ71111111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-1111
χ81111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-111111111-1-1-1
χ911111111111111111-1-1-1-111111-1-111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11
χ1011111111111111111-1-1-1-111111-1-1111111-1-11111-1-1-1-1111111-11-1-1-1-1-1-1-1-11111-1
χ1111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11-11111-1-1111111-1
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1111111-1-1-1-1-1-11
χ1311111111111111111-1-1-1-11-1-1-1-1-1-11111-1-111-1-1-1-11111-1-111111-1-1-11111-1-1-1-111-1
χ1411111111111111111-1-1-1-11-1-1-1-1-1-11111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111-1-11111-1-11
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111111111-1-1-1-1-1-111-1-11
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-111-1-1111111-1-1-1-1-1111-1-11111-1-111-1
χ17222222222-22-22-22-2-22222-20000-2-200000022-2-2000000220000-200000000000000
χ18222222222-22-22-22-2-22222-20000-2-2000000-2-222000000-2-20000200000000000000
χ19222222222-22-22-22-2-2-2-2-2-2-20000220000002222000000-2-20000-200000000000000
χ20222222222-22-22-22-2-2-2-2-2-2-2000022000000-2-2-2-2000000220000200000000000000
χ2122222222-22-22-22-22-20000-222220022-2-2220000-2-200000000000-20000000000000
χ2222222222-22-22-22-22-20000-2222200-2-222-2-20000-2-20000000000020000000000000
χ2322222222-22-22-22-22-20000-2-2-2-2-20022-2-2-2-20000220000000000020000000000000
χ2422222222-22-22-22-22-20000-2-2-2-2-200-2-2222200002200000000000-20000000000000
χ252-222-2-22-22-2-222-2-22-2000020000002i−2i2i−2i0000000022-2-200000000002i−2i000000000
χ262-222-2-22-22-2-222-2-22-2000020000002i−2i2i−2i00000000-2-2220000000000−2i2i000000000
χ272-222-2-22-22-2-222-2-22-200002000000−2i2i−2i2i0000000022-2-20000000000−2i2i000000000
χ282-222-2-22-22-2-222-2-22-200002000000−2i2i−2i2i00000000-2-22200000000002i−2i000000000
χ292-222-2-22-2-222-2-222-2-222-2-2200002-200000000000000000000000000002i−2i002i−2i000
χ302-222-2-22-2-222-2-222-2-222-2-2200002-20000000000000000000000000000−2i2i00−2i2i000
χ312-222-2-22-2-222-2-222-2-2-2-22220000-2200000000000000000000000000002i−2i00−2i2i000
χ322-222-2-22-2-222-2-222-2-2-2-22220000-220000000000000000000000000000−2i2i002i−2i000
χ332-222-2-22-2-2-222-2-222222-2-2-20000-222i−2i−2i2i000000000000000000002i−2i00000000000
χ342-222-2-22-2-2-222-2-222222-2-2-20000-22−2i2i2i−2i00000000000000000000−2i2i00000000000
χ352-222-2-22-2-2-222-2-2222-2-222-200002-22i−2i−2i2i00000000000000000000−2i2i00000000000
χ362-222-2-22-2-2-222-2-2222-2-222-200002-2−2i2i2i−2i000000000000000000002i−2i00000000000
χ372-22-222-2-2-20-20202002i−2i2i−2i022−2−2000000002i−2i002−2i2−i2i2−i22-222−2−200000000i2−i200000
χ382-22-222-2-2-20-20202002i−2i2i−2i022−2−200000000−2i2i002−2i2−i2i2−i2-22−2−22200000000−i2i200000
χ392-22-222-2-2-20-20202002i−2i2i−2i0−2−222000000002i−2i00−22−i2i2−i2i22-2−2−22200000000−i2i200000
χ402-22-222-2-2-20-20202002i−2i2i−2i0−2−22200000000−2i2i00−22−i2i2−i2i2-2222−2−200000000i2−i200000
χ412-22-222-2-2-20-2020200−2i2i−2i2i022−2−2000000002i−2i002−2−i2i2−i2i2-22−2−22200000000i2−i200000
χ422-22-222-2-2-20-2020200−2i2i−2i2i022−2−200000000−2i2i002−2−i2i2−i2i22-222−2−200000000−i2i200000
χ432-22-222-2-2-20-2020200−2i2i−2i2i0−2−222000000002i−2i00−22i2−i2i2−i2-2222−2−200000000−i2i200000
χ442-22-222-2-2-20-2020200−2i2i−2i2i0−2−22200000000−2i2i00−22i2−i2i2−i22-2−2−22200000000i2−i200000
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000
χ46444-4-4-4-4440-40-404004i−4i−4i4i00000000000000000000000000000000000000000000
χ47444-4-4-4-4440-40-40400−4i4i4i−4i00000000000000000000000000000000000000000000
χ48444-4-4-4-44-404040-400000000000000000000000002i2−2i2−2i22i2000000000000000000000
χ49444-4-4-4-44-404040-40000000000000000000000000−2i22i22i2−2i2000000000000000000000
χ5044-444-4-4-40000000000000022−2222−22000000000022−22000000002-22-2000000000000000
χ5144-444-4-4-40000000000000022−2222−220000000000−222200000000-22-22000000000000000
χ5244-444-4-4-400000000000000−2222−2222000000000022−2200000000-22-22000000000000000
χ5344-444-4-4-400000000000000−2222−22220000000000−2222000000002-22-2000000000000000
χ5444-4-4-444-404040-40-400000000000000004-40000000000000000000000000000000
χ5544-4-4-444-404040-40-40000000000000000-440000000000000000000000000000000
χ5644-4-4-444-40-40-4040400000000000000000000000000000000000000000000002i2−2i20
χ5744-4-4-444-40-40-404040000000000000000000000000000000000000000000000−2i22i20
χ584-444-4-44-444-4-444-4-440000-40000000000000000000000000000000000000000000
χ594-44-444-4-44040-40-400000002222−22−22000000000000−22220000000000000000000000000
χ604-44-444-4-44040-40-40000000−22−22222200000000000022−220000000000000000000000000
χ614-4-4-44-444040-40-40400000000000000000000000000000022−22−2222000000000000000
χ624-4-4-44-444040-40-404000000000000000000000000000000−222222−22000000000000000
χ634-4-4-44-4440-404040-40000004-4-44000000000000000000000000000000000000000
χ644-4-4-44-4440-404040-4000000-444-4000000000000000000000000000000000000000
χ658-8-88-88-88000000000000000000000000000000000000000000000000000000000

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