Finite Group Databasebeta

← Group #309255

Character table — Group #309255

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444888888888888888888888888881616161616161616161616163232
order12222222444444444488884444444444448888888888888844444488888844
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-11111-1-111111111111111-1-1-1-1-1-1-1-1-1-111-1-1
χ3111111111111111111111111-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-111
χ4111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1
χ51111111111111111111111-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1
χ61111111111111111111111-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-111
χ9111111111111111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1111-1-1-1-11-1
χ10111111111111111111-1-1-1-11111-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1111-1-1-111-1-1-11
χ11111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-11-1-111111-1
χ12111111111111111111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-11-111-1-111-11
χ13111111111111111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111111111-1-1-11-1-111-1-1-11
χ14111111111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-111111111-1-1111-111-1-1-1-11-1
χ15111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1111-1-111-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-111-1-11-1-1-111111-1
χ172222222222-2-2-222-2-2-20000222200-2-2-2-2000022-2-20000000000000000000000
χ182222222222-2-2-222-2-2-2000022-2-200-2-2220000-2-2220000000000000000000000
χ192222222222-2-2-222-2-2-20000-2-2220022-2-20000-2-2220000000000000000000000
χ202222222222-2-2-222-2-2-20000-2-2-2-2002222000022-2-20000000000000000000000
χ2122222222-2-2222-2-22-2-22222000022000022-2-20000000000000000-2-200000000
χ2222222222-2-2222-2-22-2-222220000-2-20000-2-2-2-200000000000000002200000000
χ2322222222-2-2222-2-22-2-2-2-2-2-20000220000-2-22200000000000000002-200000000
χ2422222222-2-2222-2-22-2-2-2-2-2-20000-2-2000022220000000000000000-2200000000
χ252-22-222-2-222-222-2-2-22-222-2-20000000000002-20000000000002-22-20000000000
χ262-22-222-2-222-222-2-2-22-222-2-20000000000002-2000000000000-22-220000000000
χ272-22-222-2-222-222-2-2-22-2-2-222000000000000-220000000000002-2-220000000000
χ282-22-222-2-222-222-2-2-22-2-2-222000000000000-22000000000000-222-20000000000
χ292-22-222-2-2-2-22-2-22222-20000002i−2i00002i−2i0000000022-2-22i2i−2i−2i00000000000000
χ302-22-222-2-2-2-22-2-22222-20000002i−2i00002i−2i00000000-2-222−2i−2i2i2i00000000000000
χ312-22-222-2-2-2-22-2-22222-2000000−2i2i0000−2i2i0000000022-2-2−2i−2i2i2i00000000000000
χ322-22-222-2-2-2-22-2-22222-2000000−2i2i0000−2i2i00000000-2-2222i2i−2i−2i00000000000000
χ332-22-222-2-2-2-2-22222-2-2222-2-2002i−2i0000−2i2i00-2200000000000000000000002i−2i00
χ342-22-222-2-2-2-2-22222-2-2222-2-200−2i2i00002i−2i00-220000000000000000000000−2i2i00
χ352-22-222-2-2-2-2-22222-2-22-2-222002i−2i0000−2i2i002-20000000000000000000000−2i2i00
χ362-22-222-2-2-2-2-22222-2-22-2-22200−2i2i00002i−2i002-200000000000000000000002i−2i00
χ372-2-222-2-220022-200-2002i−2i2i−2i00002i−2i00002-2002−22−20000i2−i2i2−i2000000i2−i22−20000
χ382-2-222-2-220022-200-2002i−2i2i−2i00002i−2i00002-200−22−220000−i2i2−i2i2000000−i2i2−220000
χ392-2-222-2-220022-200-2002i−2i2i−2i0000−2i2i0000-22002−22−20000i2−i2i2−i2000000−i2i2−220000
χ402-2-222-2-220022-200-2002i−2i2i−2i0000−2i2i0000-2200−22−220000−i2i2−i2i2000000i2−i22−20000
χ412-2-222-2-220022-200-200−2i2i−2i2i00002i−2i0000-22002−22−20000−i2i2−i2i2000000i2−i2−220000
χ422-2-222-2-220022-200-200−2i2i−2i2i00002i−2i0000-2200−22−220000i2−i2i2−i2000000−i2i22−20000
χ432-2-222-2-220022-200-200−2i2i−2i2i0000−2i2i00002-2002−22−20000−i2i2−i2i2000000−i2i22−20000
χ442-2-222-2-220022-200-200−2i2i−2i2i0000−2i2i00002-200−22−220000i2−i2i2−i2000000i2−i2−220000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000
χ4644-44-44-4-44-40004-4000000000000000000000000022−2222−22000000000000000000
χ4744-44-44-4-44-40004-40000000000000000000000000−2222−2222000000000000000000
χ4844-44-44-4-4-44000-4400000004-400000000000000000000000000000000000000
χ4944-44-44-4-4-44000-440000000-4400000000000000000000000000000000000000
χ5044-4-44-44-4004-4400-4000000000000000000000000000022−22−222200000000000000
χ5144-4-44-44-4004-4400-40000000000000000000000000000−222222−2200000000000000
χ5244-4-44-44-400-44-4004004i−4i−4i4i0000000000000000000000000000000000000000
χ5344-4-44-44-400-44-400400−4i4i4i−4i0000000000000000000000000000000000000000
χ544-44-444-4-4444-4-4-4-44-4400000000000000000000000000000000000000000000
χ554-4-444-4-4400-4-440040000000000000000000022−22−22220000000000000000000000
χ564-4-444-4-4400-4-4400400000000000000000000−222222−220000000000000000000000
χ574-4-4-4-44444-4000-4400000000000004-400000000000000000000000000000000
χ584-4-4-4-44444-4000-440000000000000-4400000000000000000000000000000000
χ594-4-4-4-4444-440004-4000000000000000000000000022−22−2222000000000000000000
χ604-4-4-4-4444-440004-40000000000000000000000000−222222−22000000000000000000
χ61888-8-8-8-88000000000000000000000000000000000000000000000000000000
χ628-888-8-88-8000000000000000000000000000000000000000000000000000000

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