Finite Group Databasebeta

← Group #313111

Character table — Group #313111

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444888888888888888888888888881616161616161616161616163232
order12222222444444444488884444444444448888888888888844444488888824
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-11111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111
χ3111111111111111111111111-1-11111-1-11111111111111111-1-1-1-1-1-111-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ51111111111111111111111-1-11111-1-11111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ61111111111111111111111-1-111-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ71111111111111111111111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-1-1-111
χ9111111111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-111-1-1-1-11-111-1-1-1-1-1-1111-1
χ10111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1111111-1-11-1
χ11111111111111111111-1-1-1-111-1-11111111111-1-1-1-1-1-111-1-1-1-1-11-1-111-1-111-1-1-11
χ12111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1111-1-111-1-111-11
χ13111111111111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-111111-111-1-1-1-111-1-1-11
χ14111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11-1-1-11111-1-111-11
χ15111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-11111-11-1-111-1-1-1-1111-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1111111-1-1-1-1-1111-1-11111-1-11-1
χ17222222222-22-22-22-2-2-20000220022-2-200-2-222000000-2-2000000000000000000
χ18222222222-22-22-22-2-2-200002200-2-2-2-20022-2-200000022000000000000000000
χ19222222222-22-22-22-2-2-20000-2-200222200-2-2-2-200000022000000000000000000
χ20222222222-22-22-22-2-2-20000-2-200-2-222002222000000-2-2000000000000000000
χ2122222222-22-22-22-22-2-2222200220000220000-2-20000000000-2-2000000000000
χ2222222222-22-22-22-22-2-2222200-2-20000-2-20000-2-2000000000022000000000000
χ2322222222-22-22-22-22-2-2-2-2-2-200220000-2-20000220000000000-22000000000000
χ2422222222-22-22-22-22-2-2-2-2-2-200-2-200002200002200000000002-2000000000000
χ25222-2-2-22-20-20-20202002i2i−2i−2i002i−2i00002-2002−20000002−2i2i2−i2−i2000000002−2i2−i200
χ26222-2-2-22-20-20-20202002i2i−2i−2i002i−2i00002-200−22000000−22−i2−i2i2i200000000−22−i2i200
χ27222-2-2-22-20-20-20202002i2i−2i−2i00−2i2i0000-22002−20000002−2i2i2−i2−i200000000−22−i2i200
χ28222-2-2-22-20-20-20202002i2i−2i−2i00−2i2i0000-2200−22000000−22−i2−i2i2i2000000002−2i2−i200
χ29222-2-2-22-20-20-2020200−2i−2i2i2i002i−2i0000-22002−20000002−2−i2−i2i2i200000000−22i2−i200
χ30222-2-2-22-20-20-2020200−2i−2i2i2i002i−2i0000-2200−22000000−22i2i2−i2−i2000000002−2−i2i200
χ31222-2-2-22-20-20-2020200−2i−2i2i2i00−2i2i00002-2002−20000002−2−i2−i2i2i2000000002−2−i2i200
χ32222-2-2-22-20-20-2020200−2i−2i2i2i00−2i2i00002-200−22000000−22i2i2−i2−i200000000−22i2−i200
χ332-2-22-222-222-2-222-2-2-222i−2i2i−2i00002i−2i00002i−2i002i−2i00000000000000002-2000000
χ342-2-22-222-222-2-222-2-2-222i−2i2i−2i0000−2i2i0000−2i2i002i−2i0000000000000000-22000000
χ352-2-22-222-222-2-222-2-2-22−2i2i−2i2i00002i−2i00002i−2i00−2i2i0000000000000000-22000000
χ362-2-22-222-222-2-222-2-2-22−2i2i−2i2i0000−2i2i0000−2i2i00−2i2i00000000000000002-2000000
χ372-2-22-222-22-2-222-2-222-2000000002i−2i0000−2i2i000022-2-2002i−2i2i−2i00000000000000
χ382-2-22-222-22-2-222-2-222-2000000002i−2i0000−2i2i0000-2-22200−2i2i−2i2i00000000000000
χ392-2-22-222-22-2-222-2-222-200000000−2i2i00002i−2i000022-2-200−2i2i−2i2i00000000000000
χ402-2-22-222-22-2-222-2-222-200000000−2i2i00002i−2i0000-2-222002i−2i2i−2i00000000000000
χ412-2-22-222-2-222-2-222-22-22i−2i2i−2i00000000000000−2i2i0000000000002-22i−2i00000000
χ422-2-22-222-2-222-2-222-22-22i−2i2i−2i00000000000000−2i2i000000000000-22−2i2i00000000
χ432-2-22-222-2-222-2-222-22-2−2i2i−2i2i000000000000002i−2i0000000000002-2−2i2i00000000
χ442-2-22-222-2-222-2-222-22-2−2i2i−2i2i000000000000002i−2i000000000000-222i−2i00000000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000
χ46444-4-4-44-404040-40-400000000000000000022−22000000−2222000000000000000000
χ47444-4-4-44-404040-40-4000000000000000000−222200000022−22000000000000000000
χ4844-44-4-4-4440-40-40400000000000004i−4i00000000000000000000000000000000
χ4944-44-4-4-4440-40-4040000000000000−4i4i00000000000000000000000000000000
χ5044-44-4-4-44-404040-4000000000000000000000002i2−2i22i2−2i200000000000000000000
χ5144-44-4-4-44-404040-400000000000000000000000−2i22i2−2i22i200000000000000000000
χ524-4444-4-4-44040-40-400000004-400000000000000000000000000000000000000
χ534-4444-4-4-44040-40-40000000-4400000000000000000000000000000000000000
χ544-4444-4-4-4-40-40404000000000000000000000002i2−2i2−2i22i200000000000000000000
χ554-4444-4-4-4-40-4040400000000000000000000000−2i22i22i2−2i200000000000000000000
χ564-4-44-444-4-4-444-4-444-4400000000000000000000000000000000000000000000
χ574-4-4-44-444040-40-404000000000000000000000000000022−22−222200000000000000
χ584-4-4-44-444040-40-4040000000000000000000000000000−222222−2200000000000000
χ594-4-4-44-4440-404040-4004-4-440000000000000000000000000000000000000000
χ604-4-4-44-4440-404040-400-444-40000000000000000000000000000000000000000
χ6188-8-888-8-8000000000000000000000000000000000000000000000000000000
χ628-88-8-88-88000000000000000000000000000000000000000000000000000000

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