Finite Group Databasebeta

← Group #313121

Character table — Group #313121

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444888888888888888888888888881616161616161616161616163232
order12222222444444444488882244444444448888888888888844444488888824
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-11111-1-111-1-11111-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-111
χ3111111111111111111111111-1-11111-1-11111111111111111-1-1-1-1-1-111-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-111-111-1-11111-1-1
χ51111111111111111111111-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ61111111111111111111111-1-111-1-1-1-111-1-11111-1-1-1-11111111-1-11-1-1-1-11111-1-1
χ71111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-111-111-1-1-1-1-1-111
χ9111111111111111111-1-1-1-111111111-1-111-1-111-1-1-1-111-1-1-1-11-1-1-111-1-1-1-1111-1
χ10111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-11111-1-11-1
χ11111111111111111111-1-1-1-111-1-111111111-1-111-1-1-1-111-1-1-1-1-1111-1-1-1-111-1-1-11
χ12111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111111-1-111-11
χ13111111111111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-111111-1-1-111-1-111-1-1-11
χ14111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111-1-1-111-1-111-11
χ15111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-11111-1111-1-1-1-1-1-1111-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-11111111-1-11-1
χ17222222222-22-22-22-2-2-20000220022-2-200-2-200220000-2-2000000000000000000
χ18222222222-22-22-22-2-2-200002200-2-2-2-2002200-2-2000022000000000000000000
χ19222222222-22-22-22-2-2-20000-2-200222200-2-200-2-2000022000000000000000000
χ20222222222-22-22-22-2-2-20000-2-200-2-222002200220000-2-2000000000000000000
χ2122222222-22-22-22-22-2-22222002200002200-2-2000000000000-200-20000000000
χ2222222222-22-22-22-22-2-2222200-2-20000-2-200-2-200000000000020020000000000
χ2322222222-22-22-22-22-2-2-2-2-2-200220000-2-20022000000000000-20020000000000
χ2422222222-22-22-22-22-2-2-2-2-2-200-2-20000220022000000000000200-20000000000
χ2522-2-2-22-2222-2-222-2-2-222i2i−2i−2i00002i−2i00002i−2i2i−2i0000000000000000002-2000000
χ2622-2-2-22-2222-2-222-2-2-222i2i−2i−2i0000−2i2i0000−2i2i2i−2i000000000000000000-22000000
χ2722-2-2-22-2222-2-222-2-2-22−2i−2i2i2i00002i−2i00002i−2i−2i2i000000000000000000-22000000
χ2822-2-2-22-2222-2-222-2-2-22−2i−2i2i2i0000−2i2i0000−2i2i−2i2i0000000000000000002-2000000
χ2922-2-2-22-222-2-222-2-222-2000000002i−2i0000−2i2i000022-2-2002i2i−2i−2i00000000000000
χ3022-2-2-22-222-2-222-2-222-2000000002i−2i0000−2i2i0000-2-22200−2i−2i2i2i00000000000000
χ3122-2-2-22-222-2-222-2-222-200000000−2i2i00002i−2i000022-2-200−2i−2i2i2i00000000000000
χ3222-2-2-22-222-2-222-2-222-200000000−2i2i00002i−2i0000-2-222002i2i−2i−2i00000000000000
χ3322-2-2-22-22-222-2-222-22-22i2i−2i−2i000000000000−2i2i00000000000002i−2i02-200000000
χ3422-2-2-22-22-222-2-222-22-22i2i−2i−2i000000000000−2i2i0000000000000−2i2i0-2200000000
χ3522-2-2-22-22-222-2-222-22-2−2i−2i2i2i0000000000002i−2i00000000000002i−2i0-2200000000
χ3622-2-2-22-22-222-2-222-22-2−2i−2i2i2i0000000000002i−2i0000000000000−2i2i02-200000000
χ372-222-22-2-2020-20-202002-22-2002-200002-20000i2−i20000i2−i2i2−i2i2−i200000000i2−i2i2−i200
χ382-222-22-2-2020-20-202002-22-2002-200002-20000−i2i20000−i2i2−i2i2−i2i200000000−i2i2−i2i200
χ392-222-22-2-2020-20-202002-22-200-220000-220000i2−i20000i2−i2i2−i2i2−i200000000−i2i2−i2i200
χ402-222-22-2-2020-20-202002-22-200-220000-220000−i2i20000−i2i2−i2i2−i2i200000000i2−i2i2−i200
χ412-222-22-2-2020-20-20200-22-22002-20000-220000i2−i20000i2−i2−i2i2−i2i200000000−i2i2i2−i200
χ422-222-22-2-2020-20-20200-22-22002-20000-220000−i2i20000−i2i2i2−i2i2−i200000000i2−i2−i2i200
χ432-222-22-2-2020-20-20200-22-2200-2200002-20000i2−i20000i2−i2−i2i2−i2i200000000i2−i2−i2i200
χ442-222-22-2-2020-20-20200-22-2200-2200002-20000−i2i20000−i2i2i2−i2i2−i200000000−i2i2i2−i200
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000
χ46444-44-4-4-44040-40-400000004-400000000000000000000000000000000000000
χ47444-44-4-4-44040-40-40000000-4400000000000000000000000000000000000000
χ48444-44-4-4-4-40-40404000000000000000000000002i2−2i22i2−2i200000000000000000000
χ49444-44-4-4-4-40-4040400000000000000000000000−2i22i2−2i22i200000000000000000000
χ5044-44-4-44-440-40-40400000000000004i−4i00000000000000000000000000000000
χ5144-44-4-44-440-40-4040000000000000−4i4i00000000000000000000000000000000
χ5244-44-4-44-4-404040-4000000000000000000000002i2−2i2−2i22i200000000000000000000
χ5344-44-4-44-4-404040-400000000000000000000000−2i22i22i2−2i200000000000000000000
χ5444-4-4-44-44-4-444-4-444-4400000000000000000000000000000000000000000000
χ554-444-44-4-40-404040-4000000000000000000002i2−2i20000−2i22i2000000000000000000
χ564-444-44-4-40-404040-400000000000000000000−2i22i200002i2−2i2000000000000000000
χ574-4-4-4444-404040-40-4004i−4i−4i4i0000000000000000000000000000000000000000
χ584-4-4-4444-404040-40-400−4i4i4i−4i0000000000000000000000000000000000000000
χ594-4-4-4444-40-40-40404000000000000000000000000000022−22−222200000000000000
χ604-4-4-4444-40-40-404040000000000000000000000000000−222222−2200000000000000
χ618-88-8-8-888000000000000000000000000000000000000000000000000000000
χ628-8-888-8-88000000000000000000000000000000000000000000000000000000

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