Finite Group Databasebeta

← Group #313129

Character table — Group #313129

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444888888888888888888888888881616161616161616161616163232
order12222222444444444488882244444444448888888888888824444488888844
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-111-1-111111111111111-1-1-1-1-1-111-1-1-1-1-1-1
χ3111111111111111111111111-1-11111-1-11111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111
χ4111111111111111111111111-1-111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ51111111111111111111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ61111111111111111111111-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111-1-1-1-1-1-111-1-1111111-1-1-1-111111111-1-1-1-1-1-11111-1-1
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
χ9111111111111111111-1-1-1-11111111111-1-1-1-111-1-1-1-111-1-1-1-11-111-1-1-1-111-1-11-1
χ10111111111111111111-1-1-1-1111111-1-11111-1-111-1-1-1-111-1-1-1-1-11-1-111-1-1-1-111-11
χ11111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-11111-1-1111-1
χ12111111111111111111-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1111-1-11111-1-1-11
χ13111111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-111111-111-1-1-1-1-1-111-11
χ14111111111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-11111-11-1-111-1-111-1-11-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-11-1-1-1111111-1-1-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1111-1-111-1-1111-1
χ17222222222-22-22-22-2-2-200002222-2-200-2-20000220000-2-2000000000000000000
χ18222222222-22-22-22-2-2-2000022-2-2-2-200220000-2-2000022000000000000000000
χ19222222222-22-22-22-2-2-20000-2-2222200-2-20000-2-2000022000000000000000000
χ20222222222-22-22-22-2-2-20000-2-2-2-22200220000220000-2-2000000000000000000
χ2122222222-22-22-22-22-2-22222000000220022-2-2000000000000-2-2000000000000
χ2222222222-22-22-22-22-2-22222000000-2-200-2-2-2-200000000000022000000000000
χ2322222222-22-22-22-22-2-2-2-2-2-20000002200-2-222000000000000-22000000000000
χ2422222222-22-22-22-22-2-2-2-2-2-2000000-2-20022220000000000002-2000000000000
χ25222-22-2-2-20-20-202020022-2-20000002i−2i002i−2i002−200002−222−2−200000000i2−i2i2−i200
χ26222-22-2-2-20-20-202020022-2-20000002i−2i002i−2i00−220000−22−2−22200000000−i2i2−i2i200
χ27222-22-2-2-20-20-202020022-2-2000000−2i2i00−2i2i002−200002−222−2−200000000−i2i2−i2i200
χ28222-22-2-2-20-20-202020022-2-2000000−2i2i00−2i2i00−220000−22−2−22200000000i2−i2i2−i200
χ29222-22-2-2-20-20-2020200-2-2220000002i−2i00−2i2i002−200002−2−2−22200000000i2−i2−i2i200
χ30222-22-2-2-20-20-2020200-2-2220000002i−2i00−2i2i00−220000−2222−2−200000000−i2i2i2−i200
χ31222-22-2-2-20-20-2020200-2-222000000−2i2i002i−2i002−200002−2−2−22200000000−i2i2i2−i200
χ32222-22-2-2-20-20-2020200-2-222000000−2i2i002i−2i00−220000−2222−2−200000000i2−i2−i2i200
χ332-222-2-2-2222-2-222-2-2-222i−2i2i−2i002i−2i00002i−2i002i−2i0000000000000000002-2000000
χ342-222-2-2-2222-2-222-2-2-222i−2i2i−2i00−2i2i0000−2i2i002i−2i000000000000000000-22000000
χ352-222-2-2-2222-2-222-2-2-22−2i2i−2i2i002i−2i00002i−2i00−2i2i000000000000000000-22000000
χ362-222-2-2-2222-2-222-2-2-22−2i2i−2i2i00−2i2i0000−2i2i00−2i2i0000000000000000002-2000000
χ372-222-2-2-222-2-222-2-222-20000002i−2i0000−2i2i00000022-2-2002i−2i2i−2i00000000000000
χ382-222-2-2-222-2-222-2-222-20000002i−2i0000−2i2i000000-2-22200−2i2i−2i2i00000000000000
χ392-222-2-2-222-2-222-2-222-2000000−2i2i00002i−2i00000022-2-200−2i2i−2i2i00000000000000
χ402-222-2-2-222-2-222-2-222-2000000−2i2i00002i−2i000000-2-222002i−2i2i−2i00000000000000
χ412-222-2-2-22-222-2-222-22-22i−2i2i−2i000000000000−2i2i000000000000002i−2i2-200000000
χ422-222-2-2-22-222-2-222-22-22i−2i2i−2i000000000000−2i2i00000000000000−2i2i-2200000000
χ432-222-2-2-22-222-2-222-22-2−2i2i−2i2i0000000000002i−2i000000000000002i−2i-2200000000
χ442-222-2-2-22-222-2-222-22-2−2i2i−2i2i0000000000002i−2i00000000000000−2i2i2-200000000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000
χ46444-44-4-4-404040-40-40000000000000000000022−220000−2222000000000000000000
χ47444-44-4-4-404040-40-400000000000000000000−2222000022−22000000000000000000
χ4844-44-44-4-44040-40-400000004-400000000000000000000000000000000000000
χ4944-44-44-4-44040-40-40000000-4400000000000000000000000000000000000000
χ5044-44-44-4-4-40-40404000000000000000000000002i2−2i22i2−2i200000000000000000000
χ5144-44-44-4-4-40-4040400000000000000000000000−2i22i2−2i22i200000000000000000000
χ524-444-4-4-44-4-444-4-444-4400000000000000000000000000000000000000000000
χ534-44-4-444-4040-40-40400000000000000000000000000002i2−2i2−2i22i200000000000000
χ544-44-4-444-4040-40-4040000000000000000000000000000−2i22i22i2−2i200000000000000
χ554-44-4-444-40-404040-4004i−4i−4i4i0000000000000000000000000000000000000000
χ564-44-4-444-40-404040-400−4i4i4i−4i0000000000000000000000000000000000000000
χ574-4-444-44-440-40-404000000000004i−4i0000000000000000000000000000000000
χ584-4-444-44-440-40-40400000000000−4i4i0000000000000000000000000000000000
χ594-4-444-44-4-404040-4000000000000000000000002i2−2i2−2i22i200000000000000000000
χ604-4-444-44-4-404040-400000000000000000000000−2i22i22i2−2i200000000000000000000
χ6188-8-8-8-888000000000000000000000000000000000000000000000000000000
χ628-8-8-888-88000000000000000000000000000000000000000000000000000000

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